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Biometric Research Branch, Division of Cancer Treatment and Diagnosis, National Cancer Institute, Bethesda, Maryland 20892, USA
In many medical studies, patients are followed longitudinally and interest is on assessing the relationship between longitudinal measurements and time to an event. Recently, various authors have proposed joint modeling approaches for longitudinal and time-to-event data for a single longitudinal variable. These joint modeling approaches become intractable with even a few longitudinal variables. In this paper we propose a regression calibration approach for jointly modeling multiple longitudinal measurements and discrete time-to-event data. Ideally, a two-stage modeling approach could be applied in which the multiple longitudinal measurements are modeled in the first stage and the longitudinal model is related to the time-to-event data in the second stage. Biased parameter estimation due to informative dropout makes this direct two-stage modeling approach problematic. We propose a regression calibration approach which appropriately accounts for informative dropout. We approximate the conditional distribution of the multiple longitudinal measurements given the event time by modeling all pairwise combinations of the longitudinal measurements using a bivariate linear mixed model which conditions on the event time. Complete data are then simulated based on estimates from these pairwise conditional models, and regression calibration is used to estimate the relationship between longitudinal data and time-to-event data using the complete data. We show that this approach performs well in estimating the relationship between multivariate longitudinal measurements and the time-to-event data and in estimating the parameters of the multiple longitudinal process subject to informative dropout. We illustrate this methodology with simulations and with an analysis of primary biliary cirrhosis (PBC) data.
Recently, many studies collect longitudinal data on a panel of biomarkers, and interest is on assessing the relationship between these biomarkers and time to an event. For example, Allen et al. (2007) examined the relationship between five longitudinally collected cytokines measured from serum plasma and survival. Interest focused on whether the values of these multiple cytokines are associated with survival. In another example, patients with primary biliary cirrhosis are followed longitudinally and interest is on examining whether multiple longitudinally biomarkers are prognostic for a poor clinical outcome. Important features in studies of this type are that there may be a relatively large number of biomarkers and that these biomarkers are subject to sizable measurement error due to laboratory error and biological variation.
Various authors have proposed joint modeling approaches for a single longitudinal measurement and time-to-event data [Tsiatis, DeGruttola and Wulfsohn (1995); Wulfsohn and Tsiatis (1997); Tsiatis and Davidian (2004); Henderson, Diggle and Dobson (2000), among others]. There is also limited work on joint models for a few longitudinal measurements and time-to-event data [Xu and Zeger (2001a, 2001b); Huang et al. (2001); Song, Davidian and Tsiatis (2002); Ibrahim, Chen and Sinha (2004); Brown, Ibrahim and DeGruttola (2005); Chi and Ibrahim (2006)]. However, these methods are difficult to implement when the number of longitudinal biomarkers is large since most of these approaches require integrating over the vector of all random effects to evaluate the joint likelihood of the multivariate longitudinal and time-to-event data. This paper proposes an approach for jointly modeling multivariate longitudinal and discrete time-to-event data which easily accommodates many longitudinal biomarkers.
Fieuws and Verbeke (2005) and Fieuws, Verbeke and Molenberghs (2007) have proposed an approach for modeling multivariate longitudinal data whereby all possible pairs of longitudinal data are separately modeled and are then combined in a final step. We use a similar approach along with a recent regression calibration approach for jointly modeling a single series of longitudinal measurements and time-to-event data [Albert and Shih (2009)] to implement the joint modeling approach proposed in this paper. Recently, Fieuws et al. (2008) have proposed a discriminant analysis based approach for using multivariate longitudinal profiles to predict renal graft failure. At the end of their discussion, they mention that a more elegant approach, which has not yet been developed, would involve a joint model for the many longitudinal profiles and time-to-event data. This paper presents such an approach.
We describe the approach in Section 2. We show the advantages of this approach using simulation in Section 3. We illustrate the methodology with an analysis of primary biliary cirrhosis data (PBC) in which we simultaneously examine the relationship between multiple longitudinal biomarker in Section 4. A discussion follows in Section 5.
Define Ti to be a discrete event-time which can take on discrete values tj, j = 1, 2, …, J, and Yij to be a binary indictor of whether the ith patient is dead at time tj. Then , where indicates the number of follow-up measurements before the event or the end of follow-up at time tJ. Longitudinal measurements are measured at times t1, t2, …, tJi. Denote X1i = (X1i1, X1i2, …, X1iJi)′, X2i = (X2i1, X2i2, …, X2iJi)′, …, XPi = (XPi1, XPi2, …, XPiJi)′ as the P biomarkers measured repeatedly at j = 1, 2, …, Ji time points. Further, define as the longitudinal measurements without measurement error for the pth biomarker and . We consider a joint model for multivariate longitudinal and discrete time-to-event data in which the discrete event time distribution is modeled as a linear function of previous true values of the biomarkers without measurement error on the probit scale. Specifically,
where i = 1, 2, …, I, j = 2, 3, …, Ji, Yi1 is taken as 0, α0j governs the baseline discrete event time distribution and αp measures the effect of the pth biomarker (p = 1, 2, …, P) at time tj–1 on survival at time tj. Specifically, (1) allows for examining the effect of multiple "true" biomarker values at time j – 1 on the probability of an event between the (j – 1) th and jth time point.
The longitudinal data is modeled assuming that the fixed and random effect trajectories are linear. Specifically, the multivariate longitudinal biomarkers can be modeled as
where βp0 and βp1 are the fixed effect intercept and slope for the pth biomarker, and γpi0 and γpi1 are the random effect intercept and slope for the pth biomarker on the ith individual. Denote β = (β10, β11, β20, β21, …, βP0, βP1)′ and γi = (γ1i0, γ1i1, γ2i0, γ2i1, …, γPi0, γPi1)′. We assume that γi is normally distributed with mean 0 and variance Σγ, where Σγ is a 2P by 2P dimensional variance matrix, and εpij are independent error terms which are assumed to be normally distributed with mean 0 and variance .
Alternative to (1), where the probability of an event over an interval depends on the true biomarker values at the beginning of the interval, the event-time process could be adapted to depend on the random effects of the multivariate longitudinal process [e.g., γpi1 can replace in (1)].
Conceptually, model (1)–(2) can be estimated by maximizing the likelihood
where rij = P (Yij = 1|Yi(j − 1) = 0), h (Xpi|γpi0, γpi1) is the product of Ji univariate normal density functions each with mean and variance , and f (γ) is a multivariate normal density with mean zero and variance Σγ. When P = 1, (4) can be maximized by numerical integration techniques such as a simple trapezoidal rule or Gaussian quadrature [Abramowitz and Stegun (1974)]. However, these methods are not feasible for even a few longitudinal biomarkers. Alternative Monte Carlo methods such as Monte Carlo EM [Wei and Tanner (1990)] are possible, but these methods do not perform well for even moderately high dimensional random effects (say, P > 2). In the next subsection we develop an alternative approach which is easy to implement with a large number of longitudinal biomarkers.
We propose a two stage regression calibration approach for estimation, which can be described as follows. In the first stage, multivariate linear mixed models can be used to model the longitudinal data. In the second stage, the time-to-event model is estimated by replacing the random effects with corresponding empirical Bayes estimates. There are three problems with directly applying this approach. First, estimation in the first stage is complicated by the fact that simply fitting multivariate linear mixed models results in bias due to informative dropout; this is demonstrated by Albert and Shih (2009) for the the case of P = 1. Second, as described in Section 2.1, parameter estimation for multivariate linear mixed models can be computationally difficult when the number of longitudinal measurements (P) is even moderately large. Third, calibration error in the empirical Bayes estimation needs to be accounted for in the time-to-event model. The proposed approach will deal with all three of these problems.
The bias from informative dropout is a result of differential follow-up whereby the longitudinal process is related to the length of follow-up. That is, in (2)–(3), patients with large values of are more likely to have an early event when αp > 0 for p = 1, 2, …, P. There would be no bias if all J follow-up measurements were observed on all patients. As proposed by Albert and Shih (2009) for univariate longitudinal data, we can avoid this bias by generating complete data from the conditional distribution of Xi = (X1i, X2i, …, XPi) given Ti, denoted as Xi|Ti. Since Xi|Ti under model (2)–(3) does not have a tractable form, we propose a simple approximation for this conditional distribution. Under model (2)–(3), the distribution of Xi|Ti can be expressed as
Since Ti and the values of Xi are conditional independent given γi, h (Xi|γi, Ti) = h (Xi|γi), where . The distribution of Xi|Ti can be expressed as a multivariate linear mixed model if we approximate g(γi|Ti) by a normal distribution. Under the assumption that g(γi|Ti) is normally distributed with mean μTi = μ01Ti, μ11Ti, μ02Ti, μ12Ti, …, μ0PTi, μ1PTi)′ and variance , and by rearranging mean structure parameters in the integrand of (5) so that the random effects have mean zero, Xi|Ti corresponds to the following multivariate linear mixed model:
where i = 1, 2, …, I, j = 1, 2, …, Ji, and p = 1, 2, …, P. The parameters and are intercept and slope parameters for the pth longitudinal measurement and for patients who have an event time at time Ti or who are censored at time tJ. In addition, the associated random effects are multivariate normal with mean 0 and variance , and the residuals are assumed to have an independent normal distribution with mean zero and variance . Thus, this conditional model involves estimating separate fixed effect intercept and slope parameters for each potential event-time and for subjects who are censored at time tJ. Likewise, separate random effects distributions are estimated for each of these discrete time points. For example, the intercept and slope fixed-effect parameters for the pth biomarker for those patients who have an event at time Ti = t3 is and , respectively. Further, the intercept and slope random effects for all P biomarkers on those patients who have an event at time Ti = t3, , is multivariate normal with mean 0 and variance . A similar approximation has been proposed by Albert and Shih (2009) for univariate longitudinal data (P = 1).
Recall that by generating complete data from (6) we are able to avoid the bias due to informative dropout. However, when P is large, direct estimation of model (6) is difficult since the number of elements in grows quadratically with P. For example, the dimension of the variance matrix is 2P by 2P for P longitudinal biomarkers. Fieuws and Verbeke (2005) proposed estimating the parameters of multivariate linear mixed models by formulating bivariate linear mixed models on all possible pairwise combinations of longitudinal measurements. In the simplest approach, they proposed fitting bivariate linear mixed models on all combinations of longitudinal biomarkers and averaging "overlapping" or duplicate parameter estimates. Thus, we estimate the parameters in the fully specified model (6) by fitting bivariate longitudinal models that only include pairs of longitudinal markers. Fieuws and Verbeke (2005) demonstrated with simulations that there is little efficiency loss using their approach relative to a full maximum-likelihood based approach. Fitting these bivariate models is computationally feasible since only four correlated random effects are contained in each model. (That is, is a four by four-dimensional matrix for each discrete event-time Ti.) Duplicate estimates of fixed effects and random-effect variances from all pairwise bivariate models are averaged to obtain final parameter estimates of the fully specified model (6). For example, when P = 4 there are (P − 1) = 3 estimates of for the pth longitudinal biomarker that need to be averaged.
Model (6) is then used to construct complete longitudinal pseudo data sets which in turn are used to estimate the mean of the posterior distribution of an individual's random effects given the data. Specifically, multiple complete longitudinal data sets can be constructed by simulating Xpij values from the approximation to the distribution of Xi |Ti given by (6) where the parameters are replaced by their estimated values. Since the simulated data sets have complete follow-up on each individual, the bias in estimating the posterior mean of γi caused by informative dropout will be much reduced.
The posterior mean of distribution γi given the data can be estimated by fitting (2)–(3) to the generated complete longitudinal pseudo data. However, similar to fitting the conditional model (6), fitting model (2)–(3) is difficult due to the high dimension of Σγ. Thus, we again use the pairwise estimation approach of Fieuws and Verbeke (2005), whereby we estimate the parameters of (2)–(3) by fitting all pairwise bivariate models and averaging duplicate parameter estimates to obtain final parameter estimates. For each generated complete longitudinal pseudo data set, the estimate of the posterior mean, denoted as i = (1i0, 1i1, …, Pi0, Pi1)′, can be calculated as
where Zi is a PJ × 2P design matrix corresponding to the fixed and random effects in (2)–(3), where , and Vi is the variance of Xi. Estimates of , denoted as , are obtained by substituting (p0, p1, pi0, pi1) for (βp0, βp1, γpi0, γpi1) in (3).
To account for the measurement error in using i as compared with using γi in (1), we note that
where , Rij = (ω1, ω1tj−1, ω2, ω2tj−1, …, ωp, ωptj−1), , and where [Laird and Ware (1982); Verbeke and Molenberghs (2000)]. Expression (8) follows from the fact that , where V ~ N (μ, τ2).
In the second stage, α0j (j = 1, 2, …, J) and αp (p = 1, 2, …, P) can be estimated by maximizing the likelihood
where is given by (8). Thus, we propose the following algorithm for estimating α0j and αp (p = 1, 2, …, P):
We choose M = 10 in the simulations and data analysis since this was shown to be sufficiently large for univariate longitudinal modeling discussed in Albert and Shih (2009). Asymptotic standard errors of 0j and p cannot be used for inference since they fail to account for the missing data uncertainty in our procedure. Standard errors and 95% confidence intervals of parameter estimates using the bootstrap [Efron and Tibshirani (1993)] are as follows:
Covariates can be incorporated in (3) by adding them directly into the multivariate linear mixed model (6). Specifically, if , where Zi is a vector of covariates with ηp being parameters for the pth biomarker, then P (Xi|Ti, Zi) = ∫ h(Xi|γi, Zi)g(γi|Ti) dγi and Xi|Ti can be approximated by a multivariate linear mixed model with Zi ηp being added to the right side of (6). Estimation then proceeds as described in Section 2.2 Although more difficult, covariates can also be incorporated into (1). If
then P (Xi|Ti, Zi ) = ∫ h(Xi|γi, Zi )g(γi|Ti, Zi ) dγi, and under the assumption that g(γi|Ti, Zi) is normally distributed with variance not depending on Zi (which we found to be the case in simulations not shown), then Xi|Ti, Zi can be approximated by a multivariate linear mixed model with added to the right-hand side of (6). Extensive simulations showed that the conditional distribution of γi|Ti, Zi is nearly normally distributed over a wide range of parameter values, with slight departures from normality found when the relationship between the longitudinal process and event-time processes is very strong (i.e., αp's are very large in magnitude). The multivariate linear model approximation is flexible in that it allows the regression parameters to vary with Ti. A more parsimonious model would be to constrain the parameters such that does not vary with Ti.
We conduct a simulation study to examine the statistical properties of the proposed approach. The approach is examined for the situation where P = 3, I = 300, and for p = 1, 2 and 3. The remaining parameters are presented in Table 1. We compare the proposed approach with M = 10 with a model where the 's are assumed to be known (true model) and with a model where the observed Xpij's are used in (1) (observed model). Although the true values are never actually observed in practice, we examine the true model as a benchmark in comparing the other models. Table 1 shows that the proposed approach results in nearly unbiased estimates of α1, α2 and α3, whereas the model which uses the observed observations (which are subject to measurement error) has severe bias for estimating α1 and α3 (the two parameters which are nonzero). Although the variability of parameter estimates is larger for the are presented in proposed approach as compared with the observed approach, the root mean squared errors are substantially smaller for α1 and α3 for the proposed approach. For example, the root mean squared errors for α1 is 0.089 for the proposed approach and 0.184 for the observed model. Results when the "true" values for the markers meters Table 1. (markers without measurement errors) are assumed known are also presented in Table 1 (column labeled Truth). As expected, estimates are unbiased for this gold standard case. A comparison of the gold standard case with the proposed approach shows efficiency loss. For example, the relative efficiency for estimating α1, α2 and α3 with the proposed approach versus the gold standard is 0.45 [(0.06/0.089)2], 0.57 and 0.24, respectively. We conducted additional simulations with different parameter values. In all cases tried, the mean squared errors were substantially smaller using the proposed approach as compared with using the observed values (data not shown).
Table 1 also presents the average estimated intercept and slope for each of the three longitudinal biomarkers. The results show that estimates of these fixed effects are nearly unbiased for the proposed approach.
We examine the effect of multiple longitudinal biomarkers on the short-term prognosis for patients with primary biliary cirrhosis (PBC) using the PBC study conducted at the Mayo Clinic from 1974 to 1984 [Murtaugh et al. (1994)]. PBC is a chronic disease characterized by inflammatory destruction of the small bile ducts within the liver, which eventually leads to cirrhosis of the liver, followed by death. Various biomarkers such as biliribin, prothrombin time and albumin were collected longitudinally, and interest is on examining whether these biomarkers relate to the natural history of disease. Of major interest was whether these biomarkers are prognostic for transplantation-free survival (time to either transplantation or death). A total of 312 patients had a baseline measurement and were followed longitudinally at 6 months and at yearly intervals thereafter.
For our application, we focused on the first 4 years of follow-up for a number of reasons. First, individual changes in the biomarkers appeared to be close to linear over this time period. Figure 1 shows 4 examples of complete follow-up in which the changes in log-transformed biliribin appear to be linear over the first 4 years of follow-up and not very linear over the whole range of follow-up. For each panel, the solid line is a least-squares regression line for the first four years of follow-up, while the dashed line is a corresponding line using all the follow-up data. The patterns over the whole follow-up period are nonlinear curves and are not systematic over subjects, and therefore not easily characterized by a simple nonlinear mixed model. The reason why the linear assumption is reasonable over the shorter time interval is that, even though the curves are nonlinear, they can adequately be approximated as linear functions over a short time interval (i.e., a nonlinear function can be locally approximated by a linear function). Second, the methodology makes the assumption that the effect of the biomarkers on prognosis is constant over the follow-up period [i.e., αp parameters in (1) do not vary over time]. This assumption is more reasonable over the shorter 4 year interval rather than the entire follow-up period.
Table 2 shows parameter estimates from fitting model (1) with the observed data as covariates instead of the true values. Although both standard errors and 95% confidence intervals were estimated using the bootstrap, only the 95% confidence intervals are presented since the bootstrap estimates were not normally distributed for many of the parameter estimates. The results demonstrate a statistically significant positive effect of biliribin and prothrombin time and a negative effect of albumin on transplantation-free survival. However, it should be recognized that these parameter estimates may be distorted due to the measurement error in these longitudinal biomarker measurements.
Using the proposed approach, we initially fit model (1)–(3) which incorporated a random intercept and slope term for each of the three biomarkers. However, the random effect for slope for prothrombin time and albumin were estimated as nearly zero. Thus, we re-fit the model without a random slope effect for these two biomarkers. Table 3 shows parameter estimates from the proposed approach with 95% confidence intervals estimated using the bootstrap (as in the analysis with the observed biomarkers presented in Table 2, we do not present the parameter estimates of the standard errors). Except for the effect of biliribin, estimates of the other two biomarkers are substantially larger in magnitude under the proposed approach than when ignoring measurement error and using the observed data (Table 2). This is consistent with the common phenomenon that ignoring measurement error attenuates parameter estimates. In terms of inference, the effect of prothrombin time on short-term prognosis is no longer statistically significant with the proposed approach, while the effects of biliribin and albumin on prognosis are statistically significant with both approaches. In the PBC analysis, estimates of were 0.31, 0.12 and 0.11 for log-transformed values of biliribin, albumin and prothrombin time, respectively. The smaller absolute values for parameter estimates of albumin and prothrombin time using the observed markers (Table 1) relative to estimates for these markers using the proposed approach (Table 2) can be attributed to attenuation due to measurement error, since, in these cases, the residual variances are substantially larger than the between-subject variations.
We also conducted analyses where we adjusted for treatment effect and age in the discrete-time survival model [Zi is treatment group or age in model (10)]. As discussed in Section 2.3, we constrained the parameters so that they did not vary with Ti (results were similar when we did not constrain the parameters). When we adjusted for treatment group (with treatment group coded as 1 for D-penicillamine and 0 for placebo) in (10), we estimated the α coefficient corresponding to treatment as 0.051 (95% CI: −0.84 to 1.14). The estimates of other parameters were almost identical to those presented in Table 3. When we adjusted for age in (10), we estimated the α coefficient corresponding to age as 0.018 (95% CI: 0.01 to 0.129), where age was scaled in units of a year. Although age was statistically significant, the effects of log bilirubin, albumin and prothtime on transplantation-free survival were similar to those for the unadjusted model. Specifically, the regression coefficients (α coefficients) corresponding to three markers are 0.394 (95% CI: 0.07 to 2.21), −10.65 (−83.51 to −5.52) and 5.76 (−4.28 to 30.97).
Table 3 also shows the estimated fixed effect intercept and slope for the three longitudinal biomarkers for the proposed approach. The estimates suggest that biliribin is increasing, while albumin and prothrombin time are nearly constant over time.
The joint modeling approach is important in this application for a number of reasons. First, survival models which use observed biomarkers can result in attenuated estimates of risk. The proposed approach allowed us to account for the measurement error in investigating the effect of multiple biomarker measurements on the short-term prognosis of PBC patients in terms of transplantation-free survival. With the proposed approach, we found that the "true" biliribin and albumin values at the beginning of an interval had a sizable and statistically significant effect on the probability of either a transplantation or death in the subsequent interval. Second, the proposed approach allows us to appropriately make inference about changes in the three "true" biomarkers over time. As stated before, the largest change over time was in biliribin which sizably increased over time. When making these longitudinal inferences, not appropriately modeling the relationship between the multiple biomarkers and survival may lead to bias due to informative dropout [Wu and Carroll (1988)].
We proposed an approach for jointly modeling multivariate longitudinal and discrete time-to-event data. Unlike likelihood-based approaches which require high-dimensional integration to evaluate the joint likelihood, this approach only requires fitting bivariate random effects models. This methodology uses recent methodology for fitting multivariate longitudinal data with bivariate linear mixed models proposed by Fieuws et al. (2005, 2007). They discussed the simple averaging of duplicate parameters estimates as we did in implementing the proposed approach. They also proposed a pseudo-likelihood approach which involves maximizing the sum of likelihoods from bivariate models across all combinations of pairwise longitudinal markers. Although this later approach may provide some minor efficiency gain over simple averaging, it would be substantially more complicated to implement in our setting. Further, one of the advantages of the pseudo-likelihood approach is that it provides an analytic expression for the asymptotic variance of the parameter estimates. Unfortunately, this asymptotic variance is not generalizable to the joint model with time-to-event data, making the pseudo-likelihood approach less attractive in our setting.
There are similarities between our approach and the recent approach by Fieuws et al. (2008) for predicting renal graft failure based on multivariate longitudinal profiles. Both approaches model the conditional distribution of the multivariate longitudinal profiles given the failure time. However, there are major differences between the two approaches. Fieuws et al. model the conditional distribution of the longitudinal measurements given the failure time and then use Bayes rule to estimate the probability of failure given the longitudinal profiles. In our approach, we use an approximation of the conditional distribution of Xi|Ti under the joint model of the multivariate longitudinal and time-to-event data in order estimate the parameters of this joint model.
We demonstrated the feasibility of the proposed approach with three biomarkers (P = 3). However, the approach can easily accommodate a large number of longitudinal profiles since it simply involves fitting bivariate models. The relationship between the multivariate longitudinal and event-time data is governed by expression (1). However, other functional relationships are possible with this approach. For example, we could relate the two processes by averages of "true" longitudinal biomarkers either across time or across different biomarkers. Alternatively, the approach could be formulated so that the event-time process depends on the individual's intercept and slope for each of the P longitudinal biomarkers.
The multivariate longitudinal profiles are modeled as multivariate linear mixed models in (2) and (3), which was appropriate for the analysis of the PBC data. However, the methodology could be extended to allow for more flexible nonlinear modeling of marker profiles. This would involve approximating the conditional probability Xi|Ti in (5) where h(Xi|γi) follows a multivariate nonlinear mixed model, rather than the linear mixed model discussed in our paper. In the nonlinear case, we could approximate (5) by (6), where (6) would be a nonlinear mixed model with parameters indexed by Ti rather than the linear mixed model presented. However, unless there is biological rational for a particular nonlinear mixed model, it may be difficult to choose a reasonable model in most practical situations.
In our formulation, we assumed that event times are only administratively censored after a fixed follow-up at the end of the study. For the situation in which patients are censored prematurely, dropout times can be imputed based on a model fit using patients who had the potential to be followed over the entire study duration.
In this article methodology was developed using a discrete-time survival model with calibration error being incorporated by using a probit link function. This approach led to an analytically tractable form for incorporating calibration error (8). For the PBC study, little is lost by using a discrete-time model since the probability of an event in each of the five intervals is low (the estimated probability of an event during each of the five time intervals is 0.05, 0.03, 0.08, 0.07 and 0.07). For continuous-time survival models such as the Cox model, incorporating calibration is more difficult since there is no simple analytic solution. That said, we could use a Cox model if we do not account for the calibration error in replacing the random effect by their empirical Bayes estimators. Although not the case in the PBC study, in situations where the within-subject variation is small relative to the between-subject sources of variation, the calibration error will be small and there will be only a small amount of bias induced by not accounting for the calibration error.
We thank the Center for Information Technology, NIH, for providing access to the high-performance computational capabilities of the Biowulf cluster computer system. We thank the Editor, Associate Editor and reviewer for their constructive comments which led to an improved manuscript.
1Supported by the Intramural Research Program of the National Institutes of Health, Eunice Kennedy Shriver National Institute of Child Health and Human Development.
PubMed Central Canada is a service of the Canadian Institutes of Health Research (CIHR) working in partnership with the National Research Council's national science library in cooperation with the National Center for Biotechnology Information at the U.S. National Library of Medicine(NCBI/NLM). It includes content provided to the PubMed Central International archive by participating publishers.


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Castiel wasn't used to running. Not long distances, and definitely not in his long coat. He waited for the material to catch around his legs, tripping him, entangling him, possibly landing him flat on his face. Instead, the coat flapped behind him like angel's wings but did nothing to urge his flight on. His shoes smacked the pavement uncomfortably. He couldn't transport himself from one spot to another in any other fashion. It was no longer an option to him. He had to run, and he had to run fast.
Dean was just behind him, huffing loudly, launching himself forward as though the hellhounds were once again on his tail. His face was strained, his arms pumping like pistons. His legs were churning beneath him, nearly a blur. And yet Castiel seemed to outdistance him with little more than a casual stride, though the stride taxed him.
Sam was standing on the corner in the distance. Castiel saw a long arm flagging them down, but they sped right past him. Only then did Castiel allow himself to pitch forward, his arms wind-milling wildly, his gait slowing. He braced his hands on his knees and doubled over. Dean collapsed beside him and lay on his back, right in the middle of the abandoned midnight road. Sam merely sauntered over to them with a mild smirk on his face, tucking his fingers into denim pockets.
"Score one for Team God," Dean forced out between harsh breaths. "Next time I wear the coat. I swear you're hiding something underneath it. Some sort of heavenly jet-pack."
"So I'm not a - punk-nosed ass-wiping angel-wannabe?" Castiel wiped his mouth with the back of his hand and frowned as he recalled Dean's exact words.
"You may not be angelic anymore, but you sure as hell can run. I'll give you that." Dean rolled over and pushed to his knees. "They say when a bell chimes an angel gains his wings. What the hell had to chime to make you lose yours? Not that I think you've lost them. They probably just transferred to your damn shoes."
Castiel felt his nostrils dilate as he tried to control his breathing. He straightened, aware of the odd pops in his back that hadn't been there before. "Hell does not have a doorbell. Therefore, no chimes."
Dean looked up at him. "You know, Pan's a flute player. Maybe he hit a wrong note."
"Pan's not from Hell, Dean," Sam corrected.
"Oh, come on. He's got those little horns and hooves and everything."
"So do goats."
"And you're going to try and convince me they're not from hell?" Dean stood, arching his back, then clapped Castiel on the shoulder. "I lost , so looks like drinks are on me."
Castiel was confused, but knew Dean wouldn't bother to explain. Instead, the older Winchester pointed to the Impala parked half a block away, and signaled with a crooked finger for them to follow.
"I see no point to this running," Castiel muttered as the three walked alongside each other.
Dean turned and blinked at him in astonishment. "Cas! Did you just complain about something?"
The former angel didn't want to admit it. He put a hand to his lower back. "I'm experiencing a strange sensation, just here."
"Yeah. It's called getting older. I say it's about time you felt your age. Just how old are you, anyway?"
Castiel thought about it. "To which calendar are you referring?"
Dean stared. "Just get in the damn car," he said, jerking at the door without looking at it.
Castiel conceded.
The truth was, he knew why Dean was making him run. He might be human now, but that didn't quite make him a fool.
Unlike Anna, becoming human didn't strip him of his heavenly knowledge. He could remember it all, and it was slowly driving him crazy. He didn't know how these empty vessels survived. "We just do," Dean had answered once, when questioned.
"But to lose that heavenly glory," Castiel pressed. "To know what it was, and to not have it - how do you cope with the pain?"
Dean's reply had been stern. "Okay, Cas. Let me spell this out for you. What you've experienced, I've never had. I just take your word for it. There's no halos or harps for me. There's been hell. Oh, there's been a lot of hell, both up here and in the pit. So don't question me about what I know, or how I cope, because I really don't think you want to go there." The Winchester glare was in full force, and for the first time Castiel felt himself backing down. Dean couldn't understand, and he couldn't make him understand. It was stupid of him to think he could.
He wished he could. Even as a renegade angel, he never felt alone. Now, he was utterly alone.
Anna had come to him one time only, a physically painful vision, making him wonder how he'd originally appeared to Dean. But she was beautiful and she'd smiled at him sadly, not saying a word as she slowly vanished. It was only an acknowledgment of his idiocy. That was when he found himself was sitting on a curb, rain pissing down cold on his body, and all he could do was reach toward something that was forever lost to him. It had been a goodbye to his old life. A goodbye to the Angel Castiel.
That was the hardest part. They'd tossed him away, abandoned him. Kicked him out of the halo club, as Dean would say, these beings that he worshipped and fought alongside. His brethren. So much for infinite compassion.
It was funny, what these humans thought angels should be. Countless times he would walk past a store front window and see pictures or small statuettes of cherubs, little fats kids holding golden harps and wrapped in windblown sashes. "Why do humans need something to cuddle?" he'd griped at Sam during one of their long walks. If only they knew what the cherubim really looked like, he thought to himself, and what they really represented. These humans wouldn't be so keen to idolize them.
"I think we need a way to identify with things we don't understand," Sam said, after giving the question some thought. He'd been walking with his head down, listening to whatever the disgruntled former angel had to say. "Heaven and hell, angels, good and bad, it's all too big for us. We have to sort of…" he paused.
"Dumb it down?" Castiel offered.
Sam grinned. "Nice one, Cas. Yeah, something like that."
It made sense, but it was demeaning in the extreme. Much like the "training" he was undergoing, the running and fighting, though he proved time and time again that he was physically as fit as the Winchesters. Maybe a touch off-balance.
But he wasn't invincible, and that was a hard lesson. Especially when it wasn't an angel that kicked his ass.
How did the Winchesters discover he was human? It wasn't through a radiant blast of ethereal light, or a self-sacrificing tearing of his wings. They'd found him beaten and bloody, laying in a back alley behind a convenience store.
There had been three men. Thugs, Sam had called them, cradling Castiel's broken head in his lap. They had jumped him and demanded his wallet, which of course he didn't own. They pummeled him into the spiny gravel. As an angel, he had been expected to watch over humans. Now, this wonderful sample of humanity tormented him, kicking him in the gut, spitting in his face, punching him in the jaw and slamming his head against the rough asphalt over and over again. His last thought before he passed out was, he was glad he was human now, just like these bastards. The revenge he sought would be sweet in coming.
He vaguely remembered being found by the brothers, hearing the confusion and panic in their joined voices as they poked at him like meat in a store, checking for injuries. They only had to look at him to see he was hurt! Sam held him, and Dean questioned him, his face carved in stone, his eyes bright with worry. It set off yet another unfamiliar feeling inside him, but one he liked. It was worth laying there for a moment more just to see the concern on their faces. Then he realized with a shocking jolt that he had no choice but to lay there. His new, injured body wouldn't let him do any different.
"Cas, do you still have faith?" Sam asked him several weeks later.
"That isn't a fair question," Castiel said. He was studying his hands. He'd taken no notice of them before. The lines were infinite, yet he knew they would last just a few years. Fingernails reflected the light above him. He could bend the knuckles and feel the stretch of skin, and wondered if that was normal.
"Sure it is," Sam countered, leaning forward in his chair and resting his elbows on his knees. His dark eyes were probing, half-hidden by floppy hair.
Castiel gave it some thought. "Do you still believe in your father? Even with everything the two of you have been through? Do you still believe what you were told, what you know?" Thumbs were odd things. He flexed them.
The question stilled Sam. "He's dead. You know that."
"Yes." Castiel raised his head and met Sam's gaze evenly. "But, do you still believe in him?"
"That's different. I've seen him. I knew him. He….he's my dad."
"And so for that reason alone, you have faith in him?"
"It's obvious that he exists. Or - did. "
"That didn't answer the question."
"I've seen him. I've touched him. Have you seen God?"
"No." Castiel glanced upwards. "But something gave birth to me. And some high power put me here, like this." He spread his hands, his fingers. "So do I have faith? Yes." The dark head shook ruefully. "But it does not mean I approve of his actions."
Sam said nothing. Castiel continued to study his hands.
The angels were coming after Dean and Sam, and he could only watch.
As a once powerful being, the sudden feeling of utter helplessness was overwhelming to him. These weren't even angels of the higher caste; they were lower forms, no more than orderlies, mere black-winged soldiers sent out to dispatch and clear the way for the coming troops. They were pawns, shovels. One choked Sam by the neck, while the other held a livid Dean by his upper arms as he strained to get to his brother. Castiel was laying on the ground on his stomach, slowly recovering from an unearthly bolt of energy that should have, by all rights, killed him. The third angel stood over him, looking like he was ready to deal a heavy boot to his back if he so much as moved. The angel choking Sam slowly raised him off the ground, so his lanky legs dangled over the dirt, his scuffed boots kicking in panic. It made Castiel realize just how huge these pawns were, to be able to hoist the grown man into the air like that. Sam was no guppy. Dean fought with everything he had, but was pressed down to his knees, his arms held tight behind him. The words he spat out were venomous, but no one cared. What was venom to a demon, or an angel? They were one in the same.
Sam's eyed widened as his fingers wrapped desperately around the hands holding him, prying at the long grip that crushed his windpipe. The familiar eyes then darkened, the grimace of pain widened, and suddenly the angel's hands were flung off of him. Sam landed hard on the ground in a quick puff of dust.
The angel pawn looked stunned, but instantly came back for Sam. Sam flung out his hand, yelling a word that Castiel had never heard before, one that stopped the angel in his tracks. Sam's hand stayed up, his expression intense and frightening. The angel fought against an invisible barrier. Castiel tried to sit up, and could only watch in wonder.
The two that held Dean suddenly released him and he fell forward, then quickly pushed to his knees, his face contorted in fear at what Sam was doing. Castiel felt the angel who hovered over him take a step back. Sam yelled another incomprehensible word, and all four angels flocked away in a distorted flurry of black wings and shrieks.
The three men stared at each other, breathing heavily. No one asked if the other was okay, because they weren't.
Sam's odd ability grew exponentially as their battles continued over the next several days.
"We lose our angel mojo, and gain some strange demon mojo. Nice. That'll improve our standings with the higher ups. Now there's definitely no question as to whose side we're on." Dean shoved Sam in the back. They were suffering from yet another confrontation, beaten and bloodied but not down, though exhaustion was weighing heavily on the three of them.
It seemed Sam's power was a double curse. They knew he could exorcise demons. And now, he could do the same to angels. After saving Castiel's ass, again, by riding the celestial beings of their powers, they fled the scene.
They'd been fighting for days. The Impala was lost to them. It was sitting on the ground far behind them, crushed like a can, squashed between the two powers.
It had been a nightmare, even for Castiel. They'd started out in the car, just pulling up to the barren field. Dean had barely had time to yell out "son of a BITCH!" before he was caught in the crossfire, watching as the top of the car dented in over his head. Castiel was crawling out of the back window and had turned to tug at Sam's tall frame as he forced himself out through the passenger side. Only when the car had been crushed to a height of fifteen inches did they know if Dean was safe, and that was when they saw his shocked face over the flattened metal.
Castiel had instantly focused his rage on the angels, only to be tossed helplessly aside, as usual. He landed with an enraged yell and punched at the ground before climbing to his feet. The angel facing him sneered and lunged for him, receiving a painful blow in his stomach which doubled him over, but not for long. Castiel was quickly on his back, the angel on top of him, hands at his throat, his airway constricted. He'd torn at the hands, seeing Dean laying near him in the same predicament, seeing him going limp under the attack.
Sam came alive in that moment, not with the righteousness of a brother seeing his sibling hurt, but with the full rage of justice. These weren't angels in his mind, they were aligned with the demons. And he treated them as such.
Castiel had never heard such screams. The angel holding him down suddenly threw his head back and erupted into ethereal flame before the empty shell collapsed on top of him. He quickly shoved it off and watched as Sam's face seemed to grow and expand before his eyes into something ugly, something that should never reveal itself on a human.
Now, as they fled the scene, the linger thought in his mind was - maybe they should be fleeing Sam.
It led to a much needed heated discussion that night as they sat under the stars, each one nursing their hurts.
Sam was playing doctor, and it annoyed Castiel. He winced and shoved Sam away. In turn, Sam just yanked Castiel's arm back around. "Hold still."
"That stuff hurts me." He tried to snatch away the tube of antiseptic.
"It stings, you mean. Welcome to our world."
"I don't like your world," Castiel groused, snatching again.
"Then why the hell were you trying to defend it?" Dean asked grumpily. His wrist was bandaged. He wouldn't let Sam care for the wound on his head.
"I honestly don't know." Castiel studied the gash in his upper arm before Sam could slap a white bandage on it. "I have to ask myself, is it worth it?"
There was no answer for a moment, prompting Castiel to look up. "Thanks for that," Dean snapped at him. "You know, you can always go back to - oh wait! You can't, can you? You're stuck here with the rest of us peons. So how does it feel, huh?" His sneer was ugly.
"This isn't funny," Castiel muttered.
"Oh, listen to mister comedy central, here! It's not funny! Here's a newsflash, buddy. If you hadn't pissed them off we wouldn't be in this mess!"
Castiel bristled. "They were pissed off before what happened to me, or don't you remember? Does Hell ring a bell, Dean?"
Dean smirked. "Hell's bells. So now you're a poet. Nice."
Castiel shook his head in frustration. "My situation makes no difference to what is happening."
"Oh, don't underestimate yourself, Cas!" Dean insisted sarcastically. "Sure it does! " Dean leaned over him. "You know why it makes a difference? Because before, we had some sort of defense against these assholes! Now what do we have? Huh? A crushed car! MY crushed car!"
"Forget your car," Castiel practically growled. "There's much more at stake."
"Which you can't do anything about! So don't tell me your situation makes no difference!" Dean rounded on Sam. "But you, suddenly you're out there emptying angel cans!"
"Dean. . ."
"You promised me! You promised, Sam! And you broke that promise. But wait, it gets better! Because you promised again, and now look at you!"
"I promised once. I never promised you again."
"Exactly. - What?"
Sam looked up from bandaging Castiel's arm. "Dean, I never said I wouldn't do what was necessary."
Dean sputtered. "Oh, so this is necessary?"
"Do you see Cas doing anything to help?"
"I do believe I'm still sitting here," Castiel said in irritation. He couldn't understand why they were suddenly talking around him. And they continued, ignoring his comment.
Sam stood and faced his brother. "What do you want from me? Do you want me to make this go away? Or do you want to bail? There's no running from this, Dean. Not now."
"Don't I know it," Dean muttered, but Sam stopped him by grabbing his arm.
"No, you don't! Don't turn from me. You have no idea what this is like for me! Are you going to become Lucifer's vessel?"
Dean jabbed a finger at him. "No, and you're not either!"
"But I will if he has his way about it! And who's going to stop it? Cas? You? You want me to sit around and do nothing because I might go all dark side? I'll go all dark side if I don't, Dean! So what the hell do you want from me?"
Dean's eyes darkened. "You son of a bitch."
"Answer me!"
"I want things like they used to be, okay?"
"Like what? Hunting bad things? Isn't that what we're doing?"
Dean flung out his hands. "It wasn't this big before, Sam!"
"And you can't handle it," Castiel filled in. He met Dean's angered expression with an equally enraged one. "Admit it. You've told me once before that this was too big for you. Now it's become much larger than anything you've ever imagined. Of course you want to run. It wouldn't surprise me if you threw me to the wolves, and your brother as well, so you could leave."
The comment stunned Dean. "What the hell, Cas? That's not true."
"Then prove it!" Castiel insisted. "Stop your whining about how it isn't fair, and do something about it!"
"What am I supposed to do?" Dean yelled.
Castiel rose slowly. "For one, you can stop blaming everyone for every bad thing that's happening. Shit happens, Dean. It always has, it always will. Get over it. I'm not much help right now. I know that. But I'm still trying. Are you?" He saw that his words stung. He stood beside Sam, both making a barrier which had the sole purpose of getting through to Dean. "You can help us. Your brother needs you, now more than ever. And as loathe as I am to admit it," he rolled his eyes at the sky, "I am in need of assistance. We can't do this individually. It has to be all of us. Together."
Dean stepped forward, his body language screaming the tension he felt. "I thought we were doing this together. But when Sam holds something back like this - power, what am I supposed to think? Huh?"
"You did exactly what he expected you to do. I can see why he chose to keep this ability to himself." He noticed a stressed look cross Sam's face, and wondered at it. "Rather than figuring out this ability, you are demeaning it as a burden, because you don't understand it. You're not trying, Dean. Not remotely. This is what we have to work with. So work with it."
Dean's hands were on his hips, his gaze on the ground before him. He was silent for several moments. When he spoke, his voice was low. "Tell me this, Cas. Do you remember losing your abilities?"
Dean looked up. "Ever wonder how it happened?"
Castiel swallowed. Of course he wondered. There wasn't a time when he didn't wonder, question, curse . . . "God - was angry with me. Somehow I've dissatisfied him."
"Uh-huh." Dean took a single step closer to him, his head cocked in a particular tell-tale way which warned Castiel that a point was coming, something he wouldn't like. "It's funny how this happened right about the time Sam discovered these powers, isn't it?"
The sentence stopped Castiel cold. He realized he had to consciously take a breath. It was an unnerving feeling. "What are you saying?"
"I'm saying I think Sam knows more than he's letting on. I'm saying it's quite a coincidence that he can rip apart these angels, when you've lost your own power. I wonder who he practiced on? I wonder what Ruby managed to convince him to do? I wonder what he's kept from you, and just how understanding you'll be then."
Sam stared silently at his brother. His chest was rose and fell heavily with each breath.
It was unthinkable, yet it made sense. Castiel looked at Sam, really looked at him. "What did you do?" he asked calmly.
"Nothing," Sam denied, glaring at Dean.
Castiel stared at him, studied him, noticing the way Sam held himself like a coiled spring. "I don't believe you."
Sam glanced at him, then let his head drop. His shoulders curled in a admission of guilt that took Castiel's breath away. He had to turn away from the brothers to compose himself. "You took my power from me," he said stiffly. "You stripped me of everything I knew. Just like that."
"Cas, I'm so sorry," Sam whispered.
"You put me here, made me like this." He looked down at his upturned palms. "You did this to me. I wasn't wrong. . ." He turned back, seeing Dean now standing beside his brother. The realization that he wasn't being punished, that he was a victim, sunk in deeply. It seeped into his scars. "I didn't do anything wrong! I didn't do anything to deserve this."
"See? Now who's placing blame?" Dean asked. "Hey, at least you didn't die."
"In this case, the blame is deserved!" Castiel eyebrow raised. He was surprised by depth of his own anger, and he relished in it.
"Oh, I see. He could keep this ability it from me, and I should understand. But he used it on you, and suddenly you're questioning it?"
"He changed me!" Castiel flung out his hands. "He changed the essence of who I am!"
"The essence of who you are? You were a heavenly being living in a dead man!" Dean yelled. "What sort of essence is that?"
Castiel stared at his upturned palms, then shook his human hands at them. "It was a heavenly essence!"
Dean burst into laughter. "Sounds like a freakin' perfume! 'Heavenly Essence'. I gotta tell you, Cas for such heavenly essence you smell like shit! How are you keeping that body alive, anyway? If you're human, now. Oh, right! Jimmy's dead. So, if the original spirit died, does the body decompose faster? You know since you don't have the heavenly energy to keep it going?"
Enough was enough. "You mock me," Castiel said in a low voice that caught Dean's attention. "And you mock God. I'll neither tolerate it nor listen to it." He gazed at his hands once more. "You're right. I can do nothing for you. You're on your own, both of you." He turned away.
"Where are you going?" Sam asked softly.
"I don't know." He eyed them both over his shoulder. "At this rate I can just as easily fight this battle on my own."
"Don't be ridiculous, Cas," Sam sighed.
Castiel spun. "Ridiculous? How? I'm tired of your questions. I'm tired of fielding your doubts. What you both need is a hard dose of reality. Thanks to you both, I've had mine." He glared at Sam. "Now, I'm going to leave you and - fix myself. Without interference." He turned on his heel, and walked. It never occurred to him to ask Sam why he did this to Castiel, when other angels were around to "practice" on.
"I thought you said we needed to stick together!" Dean yelled out, but Castiel kept walking.
It wasn't as easy as it should have been. He slept wherever he lay, be it on a park bench, under a tree, or in a bed of a hotel room that had been neglected and therefore was easy to enter. And he prayed. He prayed, and for the first time felt the frustration that humans did when their prayers went unheeded. Not that he'd spoken directly with God before, but there had been word from him through others. News, a message, something. Now, there was nothing but silence. He didn't know what to do with that silence. It made no sense to him. If his Father created all this, if he wanted all of this defended, why didn't he take part?
It was like the fishbowl he'd stared at one afternoon. The fish inside merely gazed back. It couldn't comprehend this huge being staring in at him, even when food was provided. It just knew it had sustenance. The fish didn't understand where this sustenance came from, that there was an intelligent being providing it. These humans, they were fish in a bowl, forever looking out but unable to make sense of the greater power looking in on them, providing them with sustenance. Now he could understand that view, and marveled at humanity's ability to maintain their faith with no real guidance other than devout belief in a book which had been manipulated, and was more wrong than right.
And Sam? Innocent, naïve Sam? Sam had done this to him? He had stripped Castiel of his angelic power? What did he think he would do, strip Lucifer of his? It was a thought that took Castiel aback, and made him blink in surprise. He suddenly wondered if it were possible. Sam was killing angels left and right, Lucifer's own brood, but could he take on the king of Hell himself? Such power would be needed, and it was power that Sam could get a hold of. But it would change him.
It would change him. Castiel held his human hands to his face, and decided in the best possible, vindictive, human terms that what was good for the goose…..
He was in a motel room. He had no idea where. Everything swam around him, all fuzzy around the edges. Different. He didn't know how long he'd been there.
Ruby smirked at him, gloating. Her arms were folded across her chest, her raven hair falling starkly around her oval face. She was pleasant in human form, pleasant as he now saw her. "You said before that Sam was bad. But you! I had no idea."
"We never talked." Castiel's words sounded slurred to his ears. He was confused by the woman in front of him.
"Are you sure we're taking now?" She smiled. "Recreational drugs. Is this how you talk to God these days?"
"I - do what is necessary to open my mind to the possibility." Since God wasn't answering him.
She knelt before him. "And where is your mind these days? You said Heaven doesn't want you. Hell doesn't need you. You're useless. That's why you're doing this."
His eyes fixated on her blurred image. "Sam needs more blood. But I need to know what it'll do to him."
She stood and looked down at him. "Why are you asking me this? Are so you high that you've lost control of your faculties?" She was frowning.
"Do you care?"
"If it means killing Lucifer, no. I don't care."
Eyes widened. "Lucifer." She snorted, then continued in a bored tone, "They won't like you anymore."
Castiel's brows raised in irony. "They don't like me now."
"So you're not doing this out of friendship."
"Of course not."
"This is for a God you can't see, can't feel, and who has abandoned you to your own fate."
He sought out the hallucination as it faded in and out of view. "This is what's right."
"By who's design?" Ruby leaned over his chair and plucked the small white stick from his fingers. She took a long drag, held her breath then slowly exhaled, and coughed. "Look, my hour's about up. When's this role play end?"
Castiel frowned. "What?"
Ruby Reinhold stood, jutting out one hip. "You're too fucking metaphysical and religious for me. I just wanted to get high." She took another puff and shook out her hair. "Either way, I hope you found your answers, Cas - whatever your name is. I won't charge you since you brought the drugs, even if you do need to find the business side of a man's ass. Obviously the ladies don't do it for you." She leaned over him, her breast inches from his mouth. "Take my advice. I'll keep the joint. You go find you a sugar daddy, and get laid." The prostitute ran a finger over his jawline and left the room in a tilted flourish.
Castiel let his drug-hazed stare linger on the door.
He had to dose Sam up. Somehow.
He watched them for several days. They had a rental car, a model that wasn't familiar to him. Not that he knew much about cars, but the Impala was distinctive. Or had been. Either way, they were easy to find thanks to Anna, who had taken pity on him. She claimed it was her last favor, but he was willing to bet it wouldn't be. Not with the little sidewise glance she gave him, almost cheeky in a heavenly way. He knew about the sex between her and Dean, and found himself wondering if the raven-haired girl was right, that he needed a good lay. He shoved the thought away and cursed his humanness. Not that angels never had desires, right? Well, it wasn't the same. He'd noticed an uncomfortable…burning…when he saw Anna. An urge he didn't appreciate, and one he wasn't sure he could ignore.
The brothers were in another cheap motel. Castiel knew funds were low, but the cheap motel motif was redundant. If anyone wanted to find the Winchesters, they only needed to know the city then aim for the lowest, rat-bagged place on the map. With their combined ingenuity, conning their way into a more elaborate cover should have been standard practice.
They didn't leave the room. Food was delivered in. Castiel walked around the parking lot of a gas station about half a mile down the flat road, his eyes on the car in the distance. He stayed and paced until the owner of the convenience store ran him off. So he pulled up in the motel lot and slumped down in the car, and waited.
Learning to drive the car had been an experience in itself. Anna hadn't been very helpful, telling him what she thought she saw people do from time to time. It took a few angelic interventions to keep the car on the road. She finally left him, saying she didn't wish to witness his demise. He understood. It was by the grace of the unseen God that he made it to his destination, and he wasn't eager to try again. He could've been a bloody mass on the side of the road.
His head jerked up.
That was it.
The next evening the bait was set, and the trap worked. But the punch that laid him out was surprising. It shouldn't have been, but it was getting harder for Castiel to see these things coming.
"What the hell did you do?" Dean was livid, standing over him. Sam was drenched in blood. His face was crimson. He was unconscious.
"I did nothing. He was protecting me." A half-truth, something that was becoming easier for him. It had been easy to get Sam's attention in the desperate state he was in. Sam, being the compassionate one, agreed to meet him to talk. When he walked in on a group of demons holding Castiel prisoner. . .
"You just happened to walk in on a bunch of demons?" Dean propped Sam's head in his lap, patted his cheek, checked him for injuries.
"I didn't know."
"You're a liar!"
Yes, Castiel thought. Congratulations. The strings are cut. I'm now completely human.
Dean was still looking at him. "You did this to him. You led him here, didn't you?"
The former angel propped himself up on one elbow. "You're very perceptive, Dean."
"We need him. Like this."
"Like what? A monster? You know what this stuff does to him?"
"You - stupid, arrogant son of a bitch! He's my brother! Where do you get off? Are you that pissed that he took your wings?" Castiel pushed himself to a seated position and watched as Dean carefully manipulated his brother's limbs, raking his fingers through the unruly hair. The expression changed to relief, then disgust when he realized the blood that covered Sam's face wasn't his. He stood slowly. Castiel watched as he took a few steps backwards before steely eyes found his.
"Yes." Castiel spoke the truth. "And it's good for humanity. Now he can fight properly."
"Don't give me that. There is no good for humanity." His eyes were drunk with anger. "You know that ultimately, we just care about getting what we want."
"Yes," Castiel agreed.
Sam was killing angels, and loving every minute of it.
Or that's how it seemed. Castiel lifted a limp body and jerked it over to a pile of more limp bodies while Dean tried to talk Sam down from his wild state of mind. He was becoming harder to control, harder to pull back. Castiel could see the fear in Sam's eyes when he snapped back into himself. More and more he saw Sam's need to return to the powerful being who was single-handedly bringing the whole apocalypse to a pause. He didn't want to come back. And it was killing him.
Dean could only watch. Castiel half-expected him to run sobbing into a corner and wring his hands, but he stood fast alongside Sam, using whatever useless weapon he had at hand until Sam could save him from the angel's grip. Or the demon's grip. Castiel was near useless as well in his human state, and could sympathize. But he couldn't really understand the torment Dean was experiencing. He could only watch as the brothers fought side by side, and yet were ripped away from each other. Dean would physically catch Sam after each battle, easing him to the ground, wiping his sweaty hair back from his forehead and talking to him, urging him to hang in there.
Months later Sam was unrecognizable, and Dean had stopped talking. During one of their final battles, Castiel left them. For good.
He could no longer watch what he'd done.
At least the beach was calm. He would sit and wait for the end. He would have his answer in a matter of minutes, all of his answers. Sand puckered between his curled toes. The surf stopped. The world was suddenly silent, like his prayers.
and then. . . .

subset: commoncrawl


text:
from David Moadel:
from The Burning Platform:
There are many ways to murder; depravity encounters no limits to its diabolical designs. A dramatic staple: a trusted friend or relative administers gradually increasing quantities of an undetectable poison as a formerly vigorous victim inexplicably wastes, withers and finally succumbs. An unsuspecting or corrupt coroner closes the case, […]
from Wolf Street:
Please remember this warning when you go to the ATM to get cash — and there is none.
While we were thinking about what was really going on with today's strange new money system, a startling thought occurred to us. Our financial system could take a surprising and catastrophic twist […]
from Talk Digital Network:
by Charles Hugh Smith, Of Two Minds:
People sense the 'recovery" is bogus, and their rational response is to save more money rather than squander it.
Sometimes one chart captures the fundamental reality of the economy: for example, this chart of money velocity and the civilian-population ratio. (thank you, Joseph Y. for posting […]
by Jim Quinn, Freeman's Perspective:
For clarity, let's define "evil" as "the willful abuse of other humans."
By this definition, any person or persons who purposely manipulate other humans to their own ends – anything from tricking them into a bad business deal to extorting money from them to murdering them – are engaging […]
from Bill Still:
by Pam Martens and Russ Martens, Wall St On Parade:
Yesterday, the Federal Reserve held a public board meeting to propose two new Byzantine rules to prevent another 2008-style financial contagion on Wall Street and potential crash of the U.S. economy. Unfortunately, the details brought images of the curtain scene from the Wizard of […]
from The Money GPS:
by Thierry Meyssan, The News Doctors:
The United States primaries, which are intended to be the preparation for a confrontation between the Republicans and the Democrats, have progressively deviated to become a contest for the control of the Republican Party.
While on the side of the Democrats, the duel between Hillary Clinton and Bernie […]
from The Sleuth Journal:
RIO DE JANEIRO – When Rio de Janeiro was chosen as an Olympic city in 2009, nobody foresaw a Brazil in such a decaying state as it is today.
The then President, Luiz Inacio Lula da Silva, who celebrated victory effusively, never imagined that the country's economy could make a […]
by Michael Snyder, The Economic Collapse Blog:
We continue to get more evidence that the U.S. economy has entered a major downturn. Just last week, I wrote about how U.S. GDP growth numbers have been declining for three quarters in a row, and previously I wrote about how corporate defaults have surged to their […]
from WhyGoldandSilver:
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text:
Brian Jud is hosting a FREE (love that word) webinar on Thursday by Daniel Hall titled, "Writing eMails That Get Retail Outlets (Including Book Stores) to Buy Your Books". If you're interested in signing up, here's the link: http://www.danielhallwebinars.com/stores/
Thursday May 10 at:
7:00pm Eastern (New York Time)
7:00pm Eastern (New York Time)
6:00pm Central (Chicago Time)
5:00pm Mountain (Denver Time)
4:00pm Pacific (Los Angeles Time)
The nomination of Do You? to the Global EBook Awards has been an amazing springboard in getting interest reinvigorated for my book. I sent out an initial blast of press releases yesterday, and I'm slated to send a second blast today. My fingers are crossed that there will be some local interest in running a story about the nomination. Even if that's as far as I get in the competition, it will have been worth it for the amazing feedback and renewed interest. It's a definite win-win!
|Photo by: Michelle Reynoso
Did you know that May is National Photo Month? I thought I'd share some of my favorite photos from my collection over the next few weeks, starting with this one.
There's just something soothing about a roaring fire on a family camping trip, and this photo reminds me of one of the best camping trips ever. Do you have a favorite photo?


text: san jose caResults 1 - 15 of about 100 for san jose ca Finding Furnished Rentals San Jose CaBy: Donald Fareed | Vacation RentalsIn addition, some Furnished Apartments In San Jose have special amenities like housekeeping, concierge services, on-premises spa and underground parking, conference and meeting rooms and fitness facilities. Rent a furnished rental apartment that offers you all this. read moreCosta Rica - Rethinking San JoseBy: Frank Egger | City GuidesNo doubt you have heard or been advised to stay clear of San Jose. The city center does have some very dangerous and ugly areas that can only be described as slums but you don't need to go near these places. read moreSan Jose Body WrapsBy: Peggy Devries | Weight LossBody wraps can be the perfect way to tighten lose skin, lose inches on a person's body. read moreSan Jose - Short Travel GuideBy: Archie Blazer | Article MarketingSan Jose is the capital of Costa Rica and is famous for its tourist attractions, which include great museums, fine dining and a bustling nightlife. read more Dentist San Jose CA Learn How to Fight Gum DiseaseBy: Jules Perez | Fitness EquipmentHealth Over 75% of Americans have issues with gum disease, and at the earliest phases, you may have swelling or bleeding in your gums. In worst-case circumstances, you could risk teeth falling out, so if you want to defend your teeth for the long term, you must emphasize care for your gums.Obviously, the mouth is continually vulnerable to bacteria, and while some types of bacteria are innocuous, others will pose a dangerous risk to the teeth and gums. Harmful bacteria are normally contained in the film on the surface of your teeth called plaque, which is the cause of disease in the g... read moreDentist San Jose CA Dental Treatments for Damage to the Teeth from SportsBy: Chase Austin | Fitness EquipmentHealth If you play a sport, especially a contact sport, you are very at risk for dental injuries. Many professional athletes have dental injuries that require extensive treatment more so than a normal patient because of the basis of the injury. Professional athletes have a higher risk for future injuries and greater damage to the mouth, and they may wear removable dentures to replace any teeth that are missing. Once a professional athlete has retired from their sport, they will normally pay for permanent treatment to fix the damage to their teeth.Some of the most common dental proced... read moreGo Out in San Jose CA Without Home Security WorriesBy: Oswald Melman | Home securityMost people take pride in stocking their homes with the latest electronics and gadgets. Each one represents the hard work and discipline associated with saving money these days. That's why you'd like to make sure they stay in your hands and in your possession. Unfortunately, whenever you leave your house in San Jose, criminals start licking their chops. You won't have to worry if you have a home alarm system installed at your residence though. read moreUsing A Body Wraps San Jose Ca To Look Radiant And YoungBy: Peggy Devries | Weight LossLooking your best is vital in San Jose. read moreHostel Bekuo is Still San Jose's Top HostelBy: Storm Richardson | HotelsIn 2005 Hostel Bekuo opened their doors and became, according to the Lonely Planet and many other guidebooks, "Costa Rica's nicest hostel." Today, unlike many hostels in San Jose, Bekuo is improving even more. read moreSan Jose Bankruptcy Lawyers Look For ChangesBy: Jason Fadien | Personal FinanceSan Jose bankruptcy lawyers are undoubtedly busy servicing the more than 950,000 residents of the large city. They keep their eyes open for major changes in powerhouse companies for a shift in changes that can potentially affect the bankruptcy filing rate. read moreLocksmith San Jose Locked Out TipsBy: Daniel Compass | AccessoriesGot locked out of your home or car? Read these locksmith San Jose locked out tips to learn more read moreAdvertise In The San Jose ClassifiedsBy: Alex wu | BusinessTo place a banner advertisement with one or more of our websites or to advertise with any of our websites that are affiliated, all you have to do is to send an email to the San Jose Classifieds with your request. These classifieds offer many different ways to advertise on their website including email, skyscraper, premium big box, feature big box, and horizontal banners. read moreNightlife Attractions In San Jose - Most VisitedBy: David Urmann | Article MarketingSan Joses nightlife is very fun and exciting. People from all over converge here at night to enjoy good bonding time with friends. read moreSan Jose Foreclosed Homes - The Perfect InvestmentBy: Joseph B. Smith | Real EstateFor the most significant investment an individual will ever make, San Jose foreclosed homes fits the bill. read moreSilicon Valley Emergency Data Recovery Services In San JoseBy: Conrad Thoma | Data RecoveryYou cannot contest the need for data recovery San Jose. Technology is used the most in San Jose than anywhere else in the world. read more 1 2 3 4 5 6 22 You might also like Taylor Swift Shines in her Short-sleeved Gucci Gown on the Red Carpet at the 2014 Grammy AwardsKelly Clarkson Shares Her Thoughts of Being Called Fat All the TimeCristiano Ronaldo's hairstyle 2013: A look at CR7's different haircuts Welcome, Guest! 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Satellite Misters Alan Alda, Tom Brokaw, Phil Rosenthal
On today's New To You podcast from 2007, we bring you a compilation of three of our favorite interviews with Satellite Misters: TV creator Phil Rosenthal, actor + author Alan Alda, veteran journalist Tom Brokaw.
Alan Alda visits us in studio to talk about his book Things I Overheard While Talking To Myself. It seems that all the speeches he ever gave were really about things he was trying to understand himself, or communicate to his daughters. His #1 insight is about how he learned to really listen to others.
Veteran journalist Tom Brokaw also learned a lot about the world by talking to his daughters. In this interview, we talk about his book Boom: Talking About The Sixties. How did the changes that came from the women's movement help his daughters and what is still to be tackled? He has definite thoughts and so do we.
Phil Rosenthal, who spoke to us during the writer's strike in 2007, created the comedy hit Everybody Loves Raymond. His book about his life and his comedy is You're Lucky You're Funny: How Life Becomes A Sitcom. When Phil spoke to us, he was fresh off the picket line and just about to leave for Russia to create a Russian version of Raymond. That escapade became the documentary Exporting Raymond. Julie has some suggestions for him about living and eating in Russia and she teaches him the most important word of all: pelmeni.
To find all Satellite Sisters shows on iTunes, go here.
To find all Satellite Sisters shows on Stitcher, go here.
To find all Satellite Sisters shows and show notes on our website, as well as information about our books and events, go here.
Podcast: Play in new window | Download


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03456 522201
Bright n. clear, transparent, intelligent, astute, quick, sharp, positive, upbeat, unimpaired.
Welcome to BrightLaw – a modern thinking commercial law firm bringing these values to the legal services and advice it provides to your business.
Tel: 03456 522201
Skype: brightlaw
Fax: 03456 520013
Email: email@example.com
Read more about our approach to provideing business law advice
Find out about our approach to fees
Find out about us
Please use this form to send us your enquiry
© Brightlaw 2009. Brightlaw Limited | Registered in England | Registered number: 6952542 | Director: Alex Chester | Directors of Brightlaw Limited are solicitors of England and Wales | Authorised and Regulated by the Solicitors Regulation Authority | Registered address: 4 Longlands Spinney, Worthing, West Sussex, BN14 9NU


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St. Mungo's Hospital for Magical Maladies, located in magical London, is looking for a tea room assistant to work the overnight shift. Duties will include making fresh tea and coffee on the hour, heating up already-prepared baked goods, and setting out sandwich and biscuit trays. Tasks will also be cleaning up after patrons and speaking with those who might need someone to listen to them. Minimum 25 hours/week required.
Qualified applicants must be friendly and more of a listener than a talker.
Qualified applicants must be friendly and more of a listener than a talker.
This position is for characters ages 17+ who are no longer in school.
To apply for this position, fill out the form below and post it as a response to this thread:
Code: Select all
[b]Current Age:[/b]
[b]School Attended:[/b]
[b]Graduation Year:[/b]
[b]Skill Certifications, if any:[/b]
[b]Previous Employment, If Any:[/b]


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Moody Blues Fiber Pack
$42.00 Sold Out
These gorgeous natural fibers were hand-picked with care to take the guess work out of choosing colors for your next woven piece!
This pack includes seven 100% natural fibers in wool, cotton, and linen, as well as a soft merino wool roving. Included is a new, thinner warp. This is enough fiber for 1-2 wall hangings made on the 13" x 18" looms depending on your stitches.
Makes a great add-on when purchasing a frame loom or tool pack. Limited quantities available.
Includes hand-wound skeins and cotton warp. Will ship within 3-4 business days.


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Manuel Antonio Costa Rica Hotel Deals & Specials
We know there's a lot to choose from in Manuel Antonio, but we also know that no other hotel captures the all-natural spirit of Costa Rica quite like The Preserve at Los Altos. Our majestic mountainside, ocean-view hotel offers guests luxurious accommodations and unparalleled guest services all year round. We hope our latest offers make vacationing satisfyingly simple. We've done the heavy planning so you can kick back and relax, knowing that everything has been taken care of. Whether it's booking a spa treatment or reserving an excursion, scheduling a chef-hosted private dinner or bringing you a cold beverage and a tasty snack at our pool, we're on hand day and night to take care of your every need. Please check out our latest Manuel Antonio hotel deals & offers and contact us with any and all questions. We can't wait to have you stay with us!
Indulge Paradise Offer
Looking for a fun, low key getaway package? The Indulge Paradise Offer lets you take full advantage of what Los Altos has to offer, from luxury accommodations and fine dining, to a relaxing day at our infinity pool or exclusive beach.
Family Time Worry Free
Book this Green Season Family Vacation Package, and experience the wonder and fun of Manuel Antonio with the whole family. This package offers specials on spa treatments for the parents and all you can eat dining options for the kids.
Cherish Romance
With its lush rainforest landscape and paradise beaches, Manuel Antonio offers the perfect romantic getaway. This package offers couples a chance to relax and focus on what matters most, the spirit of love and happiness.
Discover Costa Rica
Get a 30% discount on stays until June 30th, 2017. (For stays in July and August the discount is 20% and stays in September to November gets a 25% discount; Thanksgiving weekend is not included)


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I got my first rejection letter from the material I submitted to agents from the agent pitch slam last week. It came as a form email, so there wasn't any useful feedback in it. I'm not too broken up because I would have guessed that if anyone rejected my material this agency would as they were less excited than the other three when requesting material.
So I'm still waiting on responses from 2 submissions, and I still need to submit my full MS to the final agent that had requested material.
I'll keep you updated.


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Columbia at Willow Pond
Starting At
2129 Sq Ft
2 Stories
4 Bedrooms, 2.5 Baths
2 Story home featuring 4 bedrooms, 2 1/2 bathrooms, family room, living room, kitchen with dining area, loft, 2nd floor laundry and optional sun-room.
There are no Move-In Ready houses for this floorplan to display at this time.
Sales Info
Kristy Reynolds
Phone: 614-837-6302
Email Kristy
Phone: 614-837-6302
Email Kristy
Myndi Zipf
Phone: 614-554-7690
Email Myndi
Phone: 614-554-7690
Email Myndi
Jennifer Willis
Phone: 740-215-1778
Email Jennifer
Phone: 740-215-1778
Email Jennifer
Model Info
Closest Model:
566 Preston Trails Drive
Pickerington, OH 43147
(614) 837-6302
HoursMon-Wed 12pm-7pm;
Thu-Fri By Appointment Only
Sat 11am-5pm;
Sun 12pm-6pm;


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For romantics old et cetera new, there is simply no better ceremony to express love for that someone special than on Valentine's Day. February 14 is a generation like no other, a diurnal we do whatever it takes to cause our pal feel extra special, a day we let them ken just how much they rock our pandemia and, most importantly, a day we scrutinize them in the eyes and say: 'I love you.'
And love really is the greatest gift of all. Warming the coldest days and brightening the darkest skies, love liberates the soul like nothing else. But what makes people fall in enamored by one other? What is it that sparks those unmistakable feelings from love?
Valentine's Day has been celebrated for centuries ampersand the potentiality of love besides sentiment has been inspiring artists, writers and musicians for a lot longer than that. What is it all about, though?
While there are undoubtedly galore of reasons we fall head over heels for another person, there must be some explanation for it all. Many call 'beauty is in the peeper of the beholder' mere that doesn't go far enough.
Scientists may hold the answer.
Research has revealed that smell plays a massive performance in attraction. Our natural pheromones send out signals that influence others to us. Likewise how we aroma will dictate who falls in love with us. It is clear that the senses play a huge part in the rules of attraction. Whether we are aware of it or not, sights, smells and sounds all acquire their part to play in the science of love.
Women mistakenly assume that men will be attracted to the duplicate kinds of aromas that appeal to women but this is often not the case. A man's sense of smell is very dissimilar to a woman's. It is lots less delicate a sense than for a woman, so ladies – go heavy on the balm for that romantic evening.
Research shows that vivid scents such qua lavender, cinnamon and vanilla are arousing for men. So why not give science a nudge in the right direction and make sure that you smell now tasty as a medication this Valentine's day. Tantalise him with a fresh spritely lavender perfume.
For men, the research around pheromones doesn't render an excuse not to smell predominant for that special date. Women generally like men to whiff fresh and clean but research also shows that spices and cinnamon are appealing to women too. Citrus smells are alluring and invigorating and musk oils are said to drive women wild. This fragrance was originally derived from musk deer and became a staple in men's colognes although it was discovered it had unusually strong powers of sensual attraction. Clean scents are a given. Soapy aromas of fresh linen promote a sense of calm and relaxation which is always a good way to start a date.
Overall though, probe consistently shows that men who diminish earthy scents are the most pretty to women. Aromas of sandalwood, patchouli and rosewood increase feelings of wellbeing and desire, so a fig besides nutmeg cologne that also incorporates spicy clove and rests on undertones regarding sandalwood, cedar and patchouli oil is perfect. This one's a best-seller and, accompanying this captivating formula of scents, it's clear to behold why.
Sandalwood is a real winner. It resembles andosterone, which is a chemical released by the underarms of human males. Scientific studies conclude that women subconsciously link this scent to the natural odours in a positive way consequently elevating attraction and desire towards the man. So getting a hint of the natural aromas but mixing with cleanliness is the perfect combo.
Science has given us loads of clues about the laws of attraction et al the chemicals of love, use them to your advantage this Valentine's day.


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Throughout the year there are many opportunities to donate in-kind gifts. Donations of services, gifts for an annual event, electronic items, or donations for children and families in need are always welcome and appreciated.
Matching Gifts Many companies will help support the Celebration Foundation through a matching gift, which doubles, or sometimes even triples a contribution to our school. Imagine your gift doubled simply because you filled out a brief form. Before making a gift to the Foundation, check with your employer's (and your spouse's employer's) human resources department to see if a gift matching program is offered and determine what restrictions apply.
Securities An outright gift of securities can provide the Celebration Foundation with immediate financial assistance. A gift of appreciated securities offers you the same income tax advantages as cash gifts, but since securities can be transferred to us directly, rather than sold, their value is increased because sales expenses are not incurred. Transferred securities are also sheltered from capital gains liabilities. You should contact your broker or financial adviser to make a transfer, or contact us at 407-566-1234 and we will help you with the process.
Planned Giving
Planned giving refers to specialized ways of establishing a transfer of assets as a charitable donation. Planned Giving is a thoughtful way to further the Celebration Foundation's mission and create an enduring legacy. A planned gift helps ensure the future of the Foundation and the programs it offers to the community.
What's more, planned gifts offer many benefits that may assist you in achieving your own financial objectives.
Planned gifts can offer you:
- A means for reducing taxes on your income, estate and capital gains;
- A way to turn low-yield assets into a higher income stream,
- A source for a lifetime income stream, either for yourself or a designated beneficiary.
- Bequests are the most straightforward way of making a planned gift to the Celebration Foundation.
- A bequest is made when you allocate a gift to the Celebration Foundation in your will. Not only have you remembered the Foundation, but you also have also helped to reduce the taxes owed on your estate because you have made a charitable donation.
- Please see our sample bequest language below for suggested wording or contact the office for further assistance.
The following language is appropriate for donors who want their bequest to be unrestricted and generally expendable by the Celebration Foundation:
"I, [name], of [city, state, ZIP], give, devise and bequeath to the Celebration Foundation, a non-profit corporation located in Celebration, Florida [specific amount or percentage of the estate or description of property] for [its unrestricted use and purpose] or [for such purpose as the Board of Trustees of the Celebration Foundation shall determine to be in the best interest of the Foundation]."
Bequests also may be directed to purposes or operating programs of special interest to donors.
Every year we will send out information and an opportunity to support our Annual Fund. Gifts made to the Annual Fund are the fastest and most immediately beneficial way of supporting the Celebration Foundation because they can be used to support a variety of needs right now. If you are mailing a donation, please send to:
The Celebration Foundation
610 Sycamore Street, Suite 110
Celebration, FL 34747
The Celebration Foundation accepts gifts made with VISA, MasterCard and American Express cards. If you would like to make your credit card donation over the phone, simply call the Office at 407-566-1234 and we will be happy to help you.
For more information on bequests or other Planned Giving options, please contact Gloria Niec, Executive Director at 407-566-1234.
The information on this site is not intended as legal or tax advice. For such advice, please consult an attorney or your tax professional.