 univariate Cox proportional hazards models to determine which parameters showed individual prognostic value for survival. Multivariate Cox proportional hazards models were then performed to evaluate the independent prognostic significance of all variables that were evaluated in univariate analysis. We adjusted for the following variables in the multivariate analysis: age, ECOG performance status, body mass index (BMI), prostate specific antigen (PSA), season of blood draw, CTCA hospital, serum albumin, corrected serum calcium, bone metastasis and nutritional status as measured using Subjective Global Assessment (SGA). Corrected serum calcium was used instead of total serum calcium to allow for the change in total calcium due to the change in albumin-bound calcium. Season of blood draw was defined as winter: December-February; spring: March-May; summer: June-August, or fall: September-November. The effect of serum 25(OH)D and other variables on patient survival was expressed as hazard ratios (HRs) with 95% confidence intervals (CIs). For serum vitamin D, the "sufficient" category was defined as the reference category.
Cox regression with time-invariant covariates assumes that the ratio of hazards for any two groups remains constant in proportion over time. We checked this proportional hazards (PH) assumption using a combination of graphical and statistical testing procedures. First, we examined log-minus-log plots for categorical predictors. As a second approach, we ran an extended Cox model with time-dependent covariates for continuous predictors. Finally, a goodness-offit testing approach based on Schoenfeld residuals was used to evaluate the PH assumption. Finally, to assess the possible influence of sample bias on the results, as well as to investigate the stability of the model coefficients, we performed a bias-corrected and accelerated (BCa) bootstrap resampling procedure. We generated 1000 samples, each the same size as the original data set, by random selection with replacement. Cox regression was then run separately on these 1000 samples to obtain robust estimates of the standard errors of coefficients, and hence the p values and 95% BCa CIs of the model coefficients [25]. All data were analyzed using IBM SPSS version 20.0 (IBM, Armonk, NY, USA). All analyses were two-tailed, and a difference was considered to be statistically significant if the p value was < = 0.05. Table 1 displays the baseline characteristics of our patients. The median follow-up was 31 months. At the time of this analysis, 49 (39.2%) patients had expired while 76 (60.8%) were considered censored. Only 6 patients were taking vitamin D supplements at the time of diagnosis. Of these 6 patients, 2 each were taking 5000, 2000 and 400 international units (IU) per day. At the time of diagnosis, bone was the most common site of metastasis with 74 (59.2%) people having bone involvement. 107 (85.6%) patients received chemotherapy, 98 (78.4%) received hormonal therapy and 66 (52.8%) received radiation therapy at our institution. A total of 50 (40%) patients received all 3 treatment modalities of chemotherapy, radiation therapy and hormonal therapy. Table 1 also describes the patient characteristics stratified by the 2 categories of serum vitamin D (deficient and not deficient). Season of blood draw and serum albumin were the two variables of statistical significance. Patients diagnosed in the summer months were less likely to be deficient in vitamin D compared to those diagnosed in fall and spring. Interestingly, patients diagnosed in the winter months also had lower prevalence of vitamin D deficiency compared to those diagnosed in fall and spring. Patients with vitamin D deficiency had lower serum albumin levels compared to those with non-deficient serum vitamin D levels (p = 0.05). Well-nourished  Table 2 shows the median survival times as a function of various clinical and demographic variables. There was no statistically significant difference in the median survival times across the 3 categories of serum vitamin D, as displayed in Fig. 1. Well-nourished patients had a significantly greater median survival than malnourished patients. Patients with bone metastasis had a significantly worse median survival than those without. Table 3 summarizes the results of univariate and multivariate Cox regression analyses. In the univariate analysis, each predictor was tested in isolation for its association with survival. Every 1 mg/dl increase in corrected serum calcium was associated with a 56% reduction in mortality hazard (HR = 0.44; p = 0.01) and every 1 g/dl increase in serum albumin was associated with a 42% reduction in mortality hazard (HR = 0.58; p = 0.05). Bone metastasis and nutritional status were also significantly associated with survival such that patients with bone metastasis and those who were malnourished had significantly worse survival compared to those with no bone metastasis and those who were well-nourished respectively. In the full model, all variables tested in the univariate analysis were evaluated simultaneously in the same model. Five variables demonstrated statistically significant associations with survival: CTCA hospital, age, bone metastasis, serum albumin and corrected serum calcium. Patients with bone metastasis had a significantly worse survival than those without it. Every 1 mg/dl increase in corrected serum calcium was associated with a 57% reduction in mortality hazard (HR = 0.43; p = 0.01). Every 1 year increase in age was associated with a 4% reduction in mortality hazard (HR = 0.96; p = 0.03). Finally, every 1 g/dl increase in serum albumin was associated with a 58% reduction in mortality hazard (HR = 0.42; p = 0.02).

Univariate and Multivariate Survival Analysis
In the final model, only those 5 variables that were statistically significant in the full model were evaluated together. All 5 of them were found to be statistically significant.
In order to account for potential sampling bias and further investigate the stability of the classical multivariate Cox model reported in Table 3, we conducted a bootstrap resampling procedure based on 1000 samples. We found no significant differences in regression coefficients and their corresponding p values between the classical Cox regression and bootstrap Cox regression models.

Discussion
The goal of this study was to investigate the association between serum 25(OH)D and survival in newly diagnosed prostate cancer patients. We found that vitamin D deficiency, defined as circulating levels of serum 25(OH)D <20 ng/ml, was not significantly associated with prostate cancer survival. The findings of our study are in contrast with the findings of positive association published in two earlier reports in prostate cancer investigating the same research question [20,21]. However, there are some noteworthy differences between those studies and our study that deserve careful attention.  Tretli et al. investigated 137 newly diagnosed in conjunction with 31 previously treated prostate cancer patients of all stages who previously received hormonal therapy [20]. In the previously treated subgroup, the serum 25(OH)D measurements were made on an average of 2.4 years after diagnosis and it is possible that the serum 25(OH)D levels could have been affected by the treatment received or by the disease itself. In the study by Fang et al., the serum vitamin D and survival association was rendered insignificant after adjustment for cancer stage and Gleason score [21]. Moreover, the serum vitamin D assessments were made up to several years before the diagnosis of prostate cancer. In our study, we focused on a homogeneous population of newly diagnosed stage IV prostate cancer thereby minimizing the possibility of potential confounding by disease stage and prior treatment history. Unlike the studies by Tretli et al. and Fang et al., we measured serum vitamin D within 30 days of patients' first visit to our hospitals.
Our study findings are consistent with those recently published by Holt et al. who found no relationship between post-diagnostic serum levels of 25(OH)D and the risk of recurrence/progression or mortality in a large population-based cohort of prostate cancer patients [22]. The lack of a significant association between serum vitamin D and survival in our study could perhaps be due to the fact that the disease was far too advanced in our patients for vitamin D levels to have any impact on prognosis. However, in the studies by Holt et al. and Fang et al., no significant association was seen in early-stage disease either. Collectively, the results of our study considered against the backdrop of the existing literature in this area suggest that serum vitamin D levels measured either pre-or post-diagnosis might not be independently predictive of survival in prostate cancer after controlling for the most relevant potential confounders.
Although not statistically significant, we found lower serum levels of 25(OH)D to be associated with higher BMI, in accordance with previously published research [11,[26][27][28]. Multiple mechanisms have been proposed to explain the association of obesity with hypovitaminosis D, including lack of sunlight exposure from physical inactivity [29] and sequestration of vitamin D in subcutaneous fat depots [30]. Another hypothesis suggests that alteration of the vitamin D endocrine system in obese subjects is characterized by secondary hyperparathyroidism which is associated with enhanced renal tubular reabsorption of calcium and increased circulating 1,25 (OH)2D which causes a feedback inhibition of 25(OH)D synthesis [31]. As a result, it has been proposed that BMI should be taken into account when assessing a patient's vitamin D status and more aggressive vitamin D supplementation should be considered in obese cancer patients [28].
We found higher corrected serum calcium levels in our population to be significantly associated with better survival. Research has noted these variables to be inversely related, typically in the setting of hypercalcemia associated with bone metastases and more advanced disease [32,33]. Our mean corrected serum calcium was 9.2 mg/dl which is within the normal limits of 8.5 to 10.1 mg/dl. Only 6 patients had serum levels below 8.5 mg/dl and only 5 patients had serum levels above 10.1 mg/dl, with the remaining patients having serum levels within the normal range. As a result, we don't believe this finding to have any major clinical relevance in our study.