Relationship between Retinal Vascular Caliber and Coronary Artery Disease in Patients with Non-Alcoholic Fatty Liver Disease (NAFLD)
2013

Pikkel Josef
Department of Ophtalmology
Ziv Medical Centre
13100SafedIsrael

Faculty of Medicine at Galilee
Bar Ilan University
13100SafedIsrael

Ibrahim Ali email@example.com
Department of Ophtalmology
Ziv Medical Centre
13100SafedIsrael

Liver Unit
Ziv Medical Centre
13100SafedIsrael

Prober Ariel email@example.com
Department of Radiology
13100SafedIsrael

Marmor Alon firstname.lastname@example.com
Faculty of Medicine at Galilee
Bar Ilan University
13100SafedIsrael

Assy Nimer
Faculty of Medicine at Galilee
Bar Ilan University
13100SafedIsrael

Liver Unit
Ziv Medical Centre
13100SafedIsrael

I A

International Journal of Environmental Research and Public Health

Relationship between Retinal Vascular Caliber and Coronary Artery Disease in Patients with Non-Alcoholic Fatty Liver Disease (NAFLD)

Int. J. Environ. Res. Public Health
10201310.3390/ijerph10083409Received: 22 May 2013; in revised form: 11 July 2013 / Accepted: 31 July 2013/* Author to whom correspondence should be addressed; E-Mail: firstname.lastname@example.com;cardiovascular diseasefatty liverretinal vascular calibreretinal arteryretinal veincardiac CTintimae media thickening
Objective: To evaluate the relationship between retinal vascular caliber and cardiovascular disease in non-alcoholic fatty liver disease (NAFLD) patients without diabetes and hypertension. Methods: Intention to treat study of individuals who underwent cardiac computed tomography (CT) during a two year period. Coronary artery disease (CAD) was defined as stenosis of >50% in at least one major coronary artery. Liver and spleen density were measured by abdominal (CT); intima-media thickness (IMT) by Doppler ultrasound; retinal artery and vein diameter by colored-retinal angiography; and metabolic syndrome by ATP III guidelines. Serum biomarkers of insulin resistance, inflammation, and oxidant-antioxidant status were assessed. Results: Compared with 22 gender and age matched controls, the 29 NAFLD patients showed higher prevalence of coronary plaques (70% vs. 30%, p < 0.001), higher prevalence of coronary stenosis (30% vs. 15%, p < 0.001), lower retinal arteriole-to-venule ratio (AVR) (0.66 ± 0.06 vs. 0.71 ± 0.02, p < 0.01), higher IMT (0.98 ± 0.3 vs. 0.83 ± 0.1, p < 0.04), higher carotid plaques (60% vs. 40%, p < 0.001), higher homeostasis model assessment of insulin resistance (HOMA) (4.0 ± 3.4 vs. 2.0 ± 1.0, p < 0.005), and higher triglyceride levels (200 ± 80 vs. 150 ± 60, p < 0.005) than controls. Multivariate analysis showed fatty liver OPEN ACCESS Int. J. Environ. Res. Public Health 2013, 10    3410 (OR 2.5; p < 0.01), IMT (OR 2.3 p < 0.001), and retinal AVR ratio (OR 1.5, p < 0.01) to be strongly associated with CAD independent of metabolic syndrome (OR 1.2, p < 0.05). Conclusions: Patients with smaller retinal AVR (<0.7) are likely to be at increased risk for CAD and carotid atherosclerosis in patients with NAFLD even without hypertension or diabetes.

Introduction

Nonalcoholic fatty liver disease (NAFLD) is increasingly recognized as the most common liver disorder in Western countries. It is the most common cause of liver enzyme abnormalities in clinical practice, with a prevalence of 46% in the general population, increasing steadily to 70%-90% in obese and type 2 diabetic patients [1,2]. The pathogenesis of NAFLD includes four major mechanisms: lipotoxicity of fatty acids, insulin resistance, systemic inflammation, and increased oxidative stress and lipid peroxidation [3,4]. Recently, elevated prothrombotic factors that aggravate atherosclerosis have been implicated in nonalcoholic steatohepatitis (NASH) [5,6], the evolutive counterpart of NAFLD. Liver biopsy, the gold standard for diagnosing NASH, is performed sparingly in clinical practice. CT scanning has no role in clinical practice, and ultrasound (US) represents the first line imaging technique and may be particularly useful when semi-quantitative indices are determined [7].

Atherosclerosis risk factors such as hypertension, obesity, diabetes, dyslipidemia, and insulin resistance frequently accompany NAFLD [8]. Moreover, NAFLD has been recently included among the early precursors to metabolic syndrome, a clinical condition associated with a high risk of coronary heart disease [9][10][11]. However, few clinical studies have examined the association between NAFLD and coronary atherosclerosis in patients with low cardiovascular risk factors. Theoretically, the increased cardiovascular risk in patients with NAFLD might reflect the coexistence of underlying metabolic syndrome risk factors. Alternatively, NAFLD itself might confer a cardiovascular risk above and beyond that associated with the individual components of the metabolic syndrome [12].

Coronary artery disease (CAD) has been found to associate with plaque rupture, independent of the degree of coronary luminal narrowing [13][14][15]. Plaque that is vulnerable to rupture shows positive remodelling of the vessel, i.e., a lipid core (soft plaque), spot calcification (calcified plaque), and a thin fibrous cap. Recent observations by intravascular US suggest that the majority of patients with ischemic heart disease have previously ruptured coronary artery plaque in non-culprit coronary arteries, in addition to infarcted-related culprit arteries [16][17][18]. Multislice coronary computed tomography angiography (cardiac CT) has been proposed as a non-invasive modality to detect coronary plaques and classify CAD [19].

Carotid atherosclerosis has been detected in patients with non-alcoholic fatty liver disease in cross-sectional studies; and more recently, carotid intima-media thickness (IMT) has been related to the severity of liver damage [20]. Retinal arteriolar abnormalities have been recognized as associating with hypertension and diabetes mellitus. Although many studies have demonstrated associations between hypertension and retinal arteriolar changes in people without diabetes [21], few have examined the associations of these arteriolar changes with other risk factors like fatty liver. The relationship of these arteriolar changes with atherosclerotic, inflammatory, and other pathogenic processes is largely unknown. More recently, Miller et al. showed that smaller arterial caliber may indicate an increased risk of CAD in patients with diabetes [22].

Accordingly, the purpose of the present study was to explore an association between retinal arteriolar changes and atherosclerosis (coronary plaques, carotid plaques, and IMT) in individuals with fatty liver but without hypertension and without diabetes.

Materials and Methods

This is an observational study. During the period April 2006 to June 2008, 150 individuals were referred to the cardiology unit at our medical center for cardiac CT for various clinical reasons consistent with routine care.

Inclusion criteria for participation in the study were low risk for coronary artery disease (CAD), the presence of fatty liver (liver minus spleen density ≥ −10 HU by CT), and the absence of diabetes and hypertension. Of 150 patients referred, 99 were excluded due to high risk for CAD, presence of diabetes, and/or hypertension. Of the remaining 51 patients, 29 had fatty liver disease and 22 did not. Exclusion criteria comprised severe obesity (BMI > 35; recent history of acute illness; clinical history of ischemic heart disease and cerebrovascular disease, typical chest pain, previous CAD, conventional coronary angiography, percutaneous intervention, coronary bypass grafting, renal failure, cancer; and use of drugs that may induce hepatic steatosis (such as corticosteroids, estrogens, methotrexate, amiodarone). Specific exclusion criteria for cardiac CT were high risk for CAD, the presence of multiple ectopic beats, atrial fibrillation, heart rate more than 75/min despite therapy, severe lung disease, and a history of allergic reaction to iodine-containing contrast agents.

The study was approved by the local ethics committee at Ziv Medical Center, Israel. Informed consent was obtained from each individual who met inclusion/exclusion criteria. All subjects underwent a complete family history, physical examination, and non-contrast CT of the liver with measurement of liver and spleen density. All were evaluated for markers of insulin resistance (fasting glucose and homeostasis model assessment of insulin resistance-HOMA-IR). HOMA-IR was derived from the following equation: IR = (fasting plasma glucose level mg% × 0.055) × (fasting plasma insulin level mU/L/22.5). Body mass index (BMI) was calculated as weight in kilograms divided by the square of height in meters. Obesity was determined as BMI exceeding 30 kg/m² and overweight as BMI 25-28 kg/m 2 ; new diabetes onset was determined by fasting plasma glucose levels >126 mg/dL. Markers of lipotoxicity including triglyceride and cholesterol levels were obtained, as well as markers of inflammation including C-reactive protein (CRP) and fibrinogen. CRP was determined by the nephlometric method, and fibrinogen by the coagulative method of von Clauss [23,24]. Markers of oxidant-anti-oxidant status that were assessed included paraoxonase, alpha-tocopherol, and malondialdehyde (MDA). Paraoxonase activity was measured as previously described, using phenyl acetate as substrate [25]; α-tocopherol was estimated spectrophotometrically [26]. Lipid peroxidation (MDA concentration) was estimated spectrophotometrically using thiobarbituric acid assay [27].

Hepatic steatosis was defined as liver minus spleen density > −10 Hounsfield units by CT [7,28] ( Figure 1). All CT examinations were performed by the same experienced radiologist (LA, 20 years experience in radiology) blinded to the clinical status of the patients. The retinal photography procedure followed standardized methods. Briefly, after 5 min of dark adaptation, a 45°, retinal photograph was taken of one randomly selected eye using an auto focus camera. The photograph was centered on the region of the optic disc and the macula. The photographs were digitized by a high-resolution scanner and the diameters of individual arterioles and venules coursing through a zone located one half to 1 disc diameter from the optic disc margin were measured on the computer by trained graders who were masked to subject identity. These measurements were summarized as a retinal arteriole-to-venule ratio (AVR). The AVR accounts for magnification differences between photographs; it is characterized by normal distribution in the general population. A smaller AVR indicates narrower arterioles, since venular diameters vary little with blood pressure [20]. Intragraded and intergraded reliability coefficients for repeated AVR measurements were 0.84 and 0.79, respectively. Examples of low and high AVR are shown in Figure 2.  Assessment of coronary atherosclerosis was performed according to cardiac CT protocols. The patients were studied in the supine position. A bolus of 70-90 mL iomeprol contrast medium (400 mg/mL, Iomeron 400, Bracco, Milan, Italy) was injected intravenously (4 mL/s) followed by 50 mL bolus of saline via an 18 gauge catheter placed in the antecubital vein. Scan delay was determined employing an automatic bolus test in which the region of interest was located on the ascending aorta. Patients were instructed to maintain an inspiratory breath hold while CT data and electrocardiograph (ECG) trace were acquired. A 64-row scanner with a slice thickness of 0.625 mm (Brilliance Philips Medical Systems, Andover, MA, USA) was employed. For multidetector CT angiography, retrospective ECG gating was used, with heart rate adjusted gantry rotation of 350-500 ms to enable multi-segmented reconstruction. Temporal resolution was as low as 53 ms using 0.4 rotation and adaptive multicycle reconstruction. Pitch and tube currents of 200-500 mA were determined by patients' weight. Beta blockers (propranolol 20 mg tab) were administered orally if resting heart rate was above 70 beats per minute. If heart rate was more than 80 beats per minute the patient was excluded from the study. Raw image data sets from all acquisitions were analysed by two independent specialists (AM > 20 years experience in cardiology and LA > 20 years experience in radiology) unaware of the hepatic and lipid profile of the patients. Intra-observer and inter-observer variability was measured by two readings of each observer. The two independent observers visually graded the degree of coronary stenosis ( Figure 3). The degree of stenosis was considered significant if >50% occlusion of the arterial lumen was present [29]. Plaques were classified as soft (none calcified) and calcified on a segmental basis according to plaque features, including volume, attenuation, and calcification pattern. In case of discrepancy between readers, a consensus reading was performed. Multi-segment reconstruction was performed with 0.6 slice thickness; 0.3 mm overlap; multiple phases of 70, 75, and 80%; and ECG editing (curved multiplanar reformat).

For bilateral assessment of carotid atherosclerosis, all subjects underwent carotid ultrasound for evaluation of intima-media thickness (IMT) and plaques. Carotid scans were acquired using high-resolution ultrasound (Sonos 5500, Agilent Technologies, Palo Alto, CA, USA) and a 10-MHz linear array transducer. Longitudinal views of the left and right common carotid, carotid bifurcations, and internal and external carotid arteries were obtained and recorded on super VHS tapes. All ultrasound studies (carotid and brachial flow-mediated dilation (FMD)) were analyzed off-line by specially trained technicians blinded to other study variables using the prosound system; IMT was measured over 10 mm in the far wall of the common carotid within 2 cm proximal to the bulb. The region with the thickest IMT without focal lesions was measured. Left and right carotid IMTs were averaged. Intima media area in mm 2 was defined as: (IMT mm) × (length over which IMT was measured (20 mm)). Plaques were quantified in all carotid segments (common, internal, and external carotid arteries, Figure 4). Plaque was defined as any focal protrusion above the intima [30].

Statistical Analysis

Continuous variables are displayed as mean and standard deviation, and categorical variables as percentage. Differences in demographic and clinical variables between groups were compared using Χ 2 analysis for categorical variables and student T-test for continuous variables. We used multiple logistic regression analysis after adjustment for possible confounding factors to assess the association among liver steatosis, markers of insulin resistance, lipotoxicity, inflammation, oxidant and antioxidant status, and coronary atherosclerosis (plaque and stenosis). Variables included as covariate were age, gender, LDL-cholesterol, metabolic syndrome ( (ATP III Guidelines) [11], and biomarkers. Results were expressed as odds ratios. Intra-observer and inter-observer agreement between readers and kappa statistics were calculated. Winstat statistic for window, version 3.0, Kalmia Co. Inc. (Cambridge, MA, USA) was used for statistical analysis.

Results

Twenty-nine subjects were diagnosed with NAFLD (without hypertension and without diabetes ) defined by CT (liver minus spleen density ≥ −10 HU), absence of alcohol use (<20 g/day), negative serology for hepatitis B or C diagnosis, negative auto-antibodies, and absence of history of another known liver disease. The control group consisted of 22 gender and age-matched individuals without NAFLD. Intra-observer and inter-observer variability for coronary artery disease (CAD) (stenosis > 50%) was 1% and 5% respectively. Baseline clinical and biochemical characteristics of NAFLD subjects and controls are shown in Table 1. Liver-spleen density was significantly lower in patients with NAFLD than in controls (−15.3 ± 8.9 vs. +6.8 ± 6.7, p < 0.001). The prevalence of smoking was similar among NAFLD patients and controls. Subjects diagnosed with NAFLD had higher triglyceride levels, HOMA values, and waist circumference measurements than controls. All 51 subjects, NAFLD patients and controls, were overweight (BMI 25-30 kg/m 2 ) without statistically significant differences in BMI between the groups (Table 1). Compared with controls, NAFLD patients had a higher percentage of atherosclerotic plaques (70% vs. 30%, p < 0.001), as well as soft plaques (50% vs. 30%, p = 0.001), and greater prevalence of coronary artery disease (30% vs. 15%, p < 0.008), higher right mean IMT, lower retinal artery diameter, and lower AVR ( Table 2). After adjustment for possible confounding factors that were identified in univariate analysis, multiple logistic regression analysis demonstrated that NAFLD, IMT, and retinal AVR were strongly associated with CAD, whereas CRP, a biomarker of inflammation was not ( Table 3). The association of NAFLD with more severe coronary atherosclerosis remained significant also after adjustment for metabolic syndrome, age, and LDL cholesterol.

Discussion

This study demonstrated that subjects with NAFLD had significant retinal vascular changes (lower AVR), and a higher prevalence of cardiovascular diseases than controls. Moreover, intima media thickness and retinal AVR were found to be strongly associated with CAD in patients with NAFLD, independent of metabolic syndrome. Retinal arterial caliber has previously been shown to be associated with blood pressure; retinal venular caliber has been associated with smoking, atherosclerosis, lipid levels, obesity, and inflammation [31]. Importantly, our patients were non-diabetic and non-hypertensive.

The independent association between AVR and coronary plaques reflects microvascular rather than macrovascular processes. Our findings are supported by cross-sectional data from the United States National Health Examination Survey. An explanation for lower AVR as an indicator of more severe coronary artery disease remains to be determined. One possibility is that patients with NAFLD have increased endothelial dysfunction (IMT > 0.7 mm, retinal AVR < 0.7), which results in increased incidence of atherosclerosis, and ultimately in significant coronary artery disease [32].

Retinal vascular caliber changes reflect cumulative responses to aging, cardiovascular risk factors, inflammation, nitric oxide-dependent endothelial dysfunction, and other processes [32]. Recent epidemiological studies have shown that changes in retinal arteriolar and venular caliber size may reflect the differential effects of a range of systemic, environmental, and genetic risk factors [33]. Narrower retinal arteriolar caliber and smaller arteriovenous ratio are associated with older age and higher levels of blood pressure and obesity; and predict the incidence of diabetes and coronary heart disease. In contrast, wider retinal venular caliber is associated with younger age; impaired fasting glucose and diabetes; dyslipidemia; obesity; and systemic markers of inflammation, endothelial dysfunction, and cigarette smoking; and predicts the risk of stroke and coronary heart disease [32]. Whether fatty liver per se increases the risk of cardiovascular disease or reflects liver systemic insulin resistance is unknown. Studies suggest that both mechanisms are involved [34,35]. NAFLD is a strong risk factor for endothelial dysfunction [36]. While oxidative stress may influence the risk of cardiovascular disease, we did not observe significant differences in oxidation biomarkers between patients with NAFLD and controls.

Systemic inflammation may account for increased coronary plaques. Our study showed a significant difference in CRP levels between patients with severe fatty liver and controls. Recently, it has been shown that patients with elevated CRP and receiving rosovastatin had 48% reduction in stroke prevalence, 46% reduction in the need for intervention to reopen blocked blood vessels, and a 20% reduction in all-cause mortality (JUPITER Trial) [37]. Increases in CRP or TNF-alpha are key to the control of metabolism and inflammation, and an independent determinant of NAFLD [37]. Other potential mechanisms by which fatty liver may increase cardiovascular risk beyond that imposed by the metabolic syndrome are lipotoxicity and increased circulating IGF-1 and IGFBP-3 [38]. Lipotoxicity may account for the increased risk of coronary plaque by a rise in serum oxidized fatty acid, which has been associated with increased IMT [39]. Unfortunately, we did not measure the levels of free fatty acids and oxidized LDL in our study population.

This case controlled study suggests that fatty liver, IMT, and retinal AVR are the strongest predictors of coronary plaques independent of the metabolic syndrome. The clinical implication of this finding is that patients with NAFLD should be screened regularly for other cardiovascular risk factors and that the presence of fatty liver may improve stratification of these patients. This notion is reinforced by the fact that NAFLD may occur in children, preceding the onset of cardiovascular risk factors [40]. Importantly, our findings were independent of BMI, even though obesity and metabolic syndrome have been shown to be the main risk factors for fatty liver [41]. The majority of patients in the current study had vulnerable soft plaques. Recently, Pundziute et al. reported the prognostic value of cardiac CT in known and suspected coronary artery diseases [42]. They demonstrated that non obstructive lesions were an independent predictor of future cardiac events. Considering the fact that coronary occlusion and myocardial ischemia may frequently arise from mild to moderate coronary stenosis [43,44], identification of coronary artery plaques in NAFLD patients seems valuable for risk stratification and for guiding therapy. The detection of coronary plaques in patients with NAFLD may suggest the need for pharmacological therapy with insulin sensitizing agents, statins, or RAS inhibitors [45,46]. The significant association we observed between IMT and HOMA-IR (r = 0.8; p < 0.001) in the overall series and in controls is consistent with the association that has been demonstrated between increased fasting glucose and impaired glucose tolerance) and increased carotid IMT [47]. Interestingly, a moderately increased risk for cardiovascular events in patients with type 2 diabetes and associated non-alcoholic fatty liver disease compared with those without non-alcoholic fatty liver disease was reported in a large prospective study [47]. The same authors found IMT and alanine-aminotransferase to be higher in patients with non-alcoholic fatty liver disease than in controls, with the highest values in non-alcoholic steatohepatitis [35,48]. The pathogenesis of retinal arteriolar changes (focal narrowing, AVR, and arteriovenous nicking) in patients with NAFLD is unknown. These three changes could be related to hypertension, but none of our patients had hypertension. Inflammatory factors may contribute to narrowing, and vascular endothelial dysfunction may contribute to nicking [49]. Atherosclerosis, a disease of large arteries, is a major cause of CAD and stroke. Arterial narrowing, which is now shown to occur independent of atherosclerosis, might predict ischemic heart and cerebral vascular diseases [49]. Retinal arterial narrowing has been considered an early sign of hypertension [50]. In our study, lower AVR was strongly associated with coronary artery disease in patients with NAFLD. This suggests a diffuse effect of disease in the coronary and in the carotid artery rather than a local process. Retinal artery narrowing shares many risk factors with atherosclerosis. These include hypertension, smoking, and acute inflammation [51,52]. Inflammation may explain the association between low AVR and fatty liver, since cytokines causing the innate inflammatory response may originate in adipose tissues. Understanding the pathogenesis of a low AVR is important because it may explain in part, the pathogenesis of coronary or carotid plaques. The impaired microvascular function is thought to be a key factor in the development of atherosclerosis. From practical point of view, smaller retinal AVR have an added value compared to others methods for the determination of cardiovascular risk; it is simple, cost effective, accurate, and help in the decision making about risk of atherosclerosis that other methods do not cover [53].

Limitations of our study include the small sample size which prevent detailed analysis of the role of age, gender and gallstones in mediating the link between NAFLD and vascular disease [54], the absence of liver biopsies as the gold standard for the diagnosis of fatty liver and NASH and whether its it is pure steatosis rather than NASH that increase cardiovascular risk [55], and limited imaging quality which does not appear useful in understanding the mechanism involved in the pathogenesis of vascular damage in all thosde individuals with NAFLD and coronary atherosclerosis [56]. An additional limitation was that participants who underwent laser photocoagulation (diabetic and hypertensive) had to be excluded from the analysis, as the procedure is known to decrease vessel diameter. These persons were likely the patients with the most advanced micro vascular disease, so their exclusion may have introduced a selection bias in which the patients at highest risk for CAD were not addressed. However, it is likely that excluding these patients actually attenuated the relationship between retinal arteriolar and venular caliber and CAD, rather than artificially leading to the results observed here. Further studies incorporating noninvasive stress test are needed. We do not know whether the data in individuals with fatty liver with hypertension and diabetes are different from the present data

In conclusion, narrow retinal artery caliber and small retinal AVR may indicate increased risk for CAD and carotid atherosclerosis in patients with NAFLD even without hypertension or type 2 diabetes. Additional studies are needed to examine the role of retinal microvascular changes in the pathogenesis of CAD in patients with NAFLD.

Conclusions

The conclusions of this work may be summarized as follows:

Advances in Knowledge 1. Carotid atherosclerosis has been documented in patients with non-alcoholic fatty liver disease;

and more recently, carotid intima-media thickness has been related to the severity of liver damage. 2. Retinal arteriolar abnormalities have been recognized as associating with hypertension and diabetes mellitus.

Implications

1. Smaller retinal arterial caliber may indicate an increased risk of cardiovascular disease in patients with NAFLD and may allow intervention at earlier stage. 2. More individuals from the general population with sub clinical coronary artery diseases will be detected at earlier stage when fatty liver and retinal vascular changes are identified.

Summary

Narrower retinal artery caliber and smaller retinal AVR may indicate increased risk for cardiovascular disease in patients with NAFLD, even without hypertension or diabetes.

Conflicts of Interest

The authors declare no conflicts of interest.

Figure 1 .
1Example of fatty liver diagnosed by CT: liver minus spleen density > −10 Hounsfield units (HU).

Figure 2 .
2Digitized retinal photographs showing examples of low and high arteriole-to-venule ratio (AVR). (A), AVR = 0.789; (B), AVR = 0.973. Arterioles are lighter in intensity compared with venules. (Two different patients). Digitized Retinal Photographs Showing Examples of Low vs High Arteriole-to-Venule Ratio (AVR). A, AVR = 0.789; B, AVR = 0.973. Arterioles are lighter in intensity compared with venules.

Figure 3 .
3Cardiac CT: Example of soft (non calcified) coronary plaques at the proximal area of the right coronary artery (arrow).

Figure 2 :
2Figure 2:

Figure 4 .
4Example of abnormal intima media thickening (IMT). Normal values of IMT: (age > 50 years; women < 0.7 mm, men < 0.8 mm).

*
Odds ratios (OR) are adjusted for gender, age, smoking habits, metabolic syndrome, diabetes, BMI, and levels of ALT, HDL and LDL-cholesterol, triglycerides, and fasting glucose.

Table 1 .
1Clinical and laboratory characteristic of patients with NAFLD (without hypertension and without diabetes) and controls.With NAFLD
N = 29

Controls
N = 22

p value
NAFLD vs. Controls
Age (years)
53 ± 7
51 ± 10
0.3
Sex (male), n, %
86
85
0.08
BMI
30 ± 3
30 ± 4
0.08
Waist circumference (cm)
107 ± 8
103 ± 11
0.03
AST (IU/L)
27 ± 8
24 ± 6
0.05
ALT (IU/L)
36 ± 18
25 ± 10
0.005
Alk-Phos (IU/L)
74 ± 20
76 ± 18
0.3
GGT (IU/L)
37 ± 16
32 ± 18
0.05
Triglycerides (mg/dL)
209 ± 88
148 ± 70
0.005
LDL cholesterol mg/dL)
117 ± 36
113 ± 33
0.3
HDL cholesterol (mg/dL)
43 ± 12
46 ± 12
0.2
Metabolic syndrome (%)
62
31
0.008
Liver-Spleen Density (HU)
−15.3 ± 8.9
+6.8 ± 6.7
0.001

Table 2 .
2Cardiac CT, carotis Doppler ultrasound, and retinal angiography findings and biomarkers in patients with NAFLD and controls.with NAFLD
N = 29

Controls
N = 22

p value NAFLD
vs. Controls

Table 3 .
3Multivariate model for prediction of coronary artery disease in patients with fatty liver.
© 2013 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

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BMC Genomics Assessment of differential gene expression in human peripheral nerve injury
2002

Yuanyuan Xiao email@example.com
Department of Biopharmaceutical Sciences
University of California
San Francisco94143San FranciscoCAUSA

Mark R Segal firstname.lastname@example.com
Department of Epidemiology and Biostatistics
University of California
San Francisco94143San FranciscoCAUSA

Douglas Rabert firstname.lastname@example.com
Neurobiology Unit
Roche Bioscience94304Palo AltoCAUSA

Andrew H Ahn email@example.com
Department of Anatomy and Neurology
University of California
San Francisco94143San FranciscoCAUSA

Praveen Anand email@example.com
Division of Neuroscience and Psychological Medicine
Peripheral Neuropathy Unit
Imperial College of Science, Technology and Medicine
Hammersmith Hospital
W12 ONNLondonUK

Lakshmi Sangameswaran email@example.com
Pherin Pharmaceuticals
94043Mountain ViewCA

Donglei Hu
Department of Biopharmaceutical Sciences
University of California
San Francisco94143San FranciscoCAUSA

C Anthony Hunt
Department of Biopharmaceutical Sciences
University of California
San Francisco94143San FranciscoCAUSA

BMC Genomics Assessment of differential gene expression in human peripheral nerve injury

BMC Genomics
2002BioMed Central Page 1 of 11 (page number not for citation purposes) Research article Donglei Hu -firstname.lastname@example.com; C Anthony Hunt* -email@example.com *Corresponding author †Equal contributors
Background: Microarray technology is a powerful methodology for identifying differentially expressed genes. However, when thousands of genes in a microarray data set are evaluated simultaneously by fold changes and significance tests, the probability of detecting false positives rises sharply. In this first microarray study of brachial plexus injury, we applied and compared the performance of two recently proposed algorithms for tackling this multiple testing problem, Significance Analysis of Microarrays (SAM) and Westfall and Young step down adjusted p values, as well as t-statistics and Welch statistics, in specifying differential gene expression under different biological states.Results: Using SAM based on t statistics, we identified 73 significant genes, which fall into different functional categories, such as cytokines / neurotrophin, myelin function and signal transduction. Interestingly, all but one gene were down-regulated in the patients. Using Welch statistics in conjunction with SAM, we identified an additional set of up-regulated genes, several of which are engaged in transcription and translation regulation. In contrast, the Westfall and Young algorithm identified only one gene using a conventional significance level of 0.05.Conclusion:In coping with multiple testing problems, Family-wise type I error rate (FWER) and false discovery rate (FDR) are different expressions of Type I error rates. The Westfall and Young algorithm controls FWER. In the context of this microarray study, it is, seemingly, too conservative. In contrast, SAM, by controlling FDR, provides a promising alternative. In this instance, genes selected by SAM were shown to be biologically meaningful.

Background

Injuries to nerve or tissue cause an immediate sensation of pain, or acute pain, which resolves with the resolution of the injury. Less commonly, these injuries produce a heterogeneous group of pathological states that produce chronic pain that is unresponsive to the analgesics used to treat acute pain. It would be therefore of great interest to map the characteristic features of gene expression following nerve injuries, as they may reveal mechanisms of chronic pain and genetic targets for the design of novel therapies. In this study we apply the powerful microarray technology to study the injuries of the brachial plexus, a typical form of nerve injury from motorcycle or workplace incidences [1]. Since this is largely a paper focusing on methodology, we refer the readers to our website [2] for details of the brachial plexus injuries.

The goal of this study, detection of condition or state-dependent differentially expressed genes, is an important problem in the context of microarrays. Fold changes and t tests have been applied to microarray datasets to yield lists of genes that have undergone altered expression under a certain significance threshold. Although these methods are useful in identifying potential gene targets, they are best applied to small sets of hypothesis tests. In the context of microarray experiments where thousands of genes are commonly evaluated simultaneously, the probability of detecting false positives rises sharply. Two recently proposed algorithms seeking to address this multiple testing problem, Significance Analysis of Microarray (SAM) and Westfall and Young step-down adjusted p values, will be investigated in our study. We note at the outset that our investigation of methods for detection of such differentially expressed genes has several limitations. Firstly, it is based solely on the brachial plexus injury data which, in turn, is limited by small sample sizes (10 injured patients and 3 controls). However, such small sample sizes are characteristic of many current microarray studies, in view of technologic expense, so that exploration in this setting is purposeful. Secondly, our investigation is largely empiric, there being no overarching theory by which to arbitrate competing approaches. Nonetheless, it is the frequently observed heteroskedasticity of gene expression measurements that motivates our extension of the SAM methodology (see below) to Welch statistics.

SAM was designed to evaluate the significance of changes in gene expression between different biological states [3]. SAM assigns a score to each gene (here and below what we refer to as genes are actually probe sets on the chip that target full length cDNAs or ESTs) as an index of the relative difference between groups. A gene is labeled as significant if its score surpasses a threshold. SAM terms the percentage of genes identified by chance the false discovery rate (FDR) and estimates this quantity by recourse to permutation. The threshold can be adjusted to identify different sizes of sets of putatively significant genes, and FDRs are modified accordingly. We note here that this differs from the formulation and sequential control of FDRs as originally proposed by Benjamini and Hochberg [4]; see Storey [5] and Storey and Tibshirani [6] for discussion of the distinctions and considerations pertinent to microarray data analysis. Throughout, we will use FDR in the sense of SAM. Tusher, et al. used SAM to study the transcriptional response of lymphoblastoid cells to ionizing radiation, and they were successful in identifying 34 biologically meaningful genes. A different algorithm, proposed by Westfall and Young and adapted by Dudoit et al. [7] for microarrays, tackles the multiple testing problem from a different angle. It controls the family-wise Type I error rate (FWER), which is the probability of having at least one false positive among all hypotheses tested. It provides less conservative control than the traditional Bonferroni, Šidák, and Holm corrections and is able to handle the dependence (e.g. co-regulation) among gene expression profiles. In a study that tested whether alterations in the expression of genes related to high-density lipoprotein metabolism affects the expression of other genes, multiple-testing methods identified 5 genes that showed significant altered expression levels in scavenger receptor BI transgenic mice and 4 genes in apolipoprotein AI-knockout mice [8]. Further discussions, additional approaches and comparisons can be found at [9].

In the comparison of expression levels of more than 5000 probe sets between normal subjects and brachial plexus injury patients, we adopt both SAM and Westfall & Young algorithms using regular t statistics assuming equal variances and t statistics assuming unequal variances (hereafter called Welch statistics). The application of Welch statistics is motivated by the work of Thomas, et al. [10]. In their paper, they applied Welch tests on a leukemia dataset [11] and demonstrated the importance of allowing for unequal variances. Following a similar approach, we have identified a set of known and novel genes that largely fall into six categories: cytokines / neurotrophine, myelin function, signal transduction, cytoskeleton, transcription / translation and others. Some genes are confirmed by literature; others still require explanation and future research. We also compared the performance of SAM and Westfall & Young algorithms, as well as t statistics and Welch statistics. In this study, we hope to provide a framework for future experimental research in avulsion injuries and pain. In addition, we illustrated the use of appropriate multiple testing methods for microarrays in monitoring differential gene expression between different biological states. Figure 1 is a scatter plot of the intensity readings for a patient (P15) and the corresponding readings of a control (C1). The considerable deviation from the identity line indicates that gene expression is substantially disturbed as a consequence of the avulsion injury. For comparison, the scatter plots for a pair of control and a pair of patient data sets clearly show less deviation.

Results

Data displays for test statistics

The frequency distribution of t statistics and the normal Q-Q plot for t-statistics are provided in Figure 2. Both the histogram and the Q-Q plot show that the distribution of t-statistics is not normal. However, in our study we are more interested in identifying genes with substantial t-statistics than in testing the distribution of t-statistics. The genes having t-statistics that deviate markedly from the bulk of the observations were labeled as potentially having biological significance and may deserve further investigation [8]. Plots of t-statistics against average intensities and different components of t-statistics against each other ( Figure 3) are especially useful in identifying genes with substantial statistics and in studying the features of these genes [7]. The average intensity for each gene is the average of the mean expression level for the patient and the control groups. In Figure 3, large t-statistics were easily visualized and labeled in red. They correspond to the same genes identified as outliers in the Q-Q plot ( Figure 2). The six genes that have the largest t-statistics do so by virtue of having denominators close to zero, implying near constant expression levels. Further, their expression levels are observed to be very low. Consequently, these genes might be of little biological interest. In order to more systematically evaluate differential expression and complement these graphical approaches, we next apply SAM.

Application of SAM: t-SAM and Welch-SAM t-SAM Experimental outline

We used the SAM methodology to identify genes with statistically significant changes in expression. For the i th gene a modified t-statistic, d(i), was used to quantitate differential expression.

All quantities here and below are defined in the Methods section. The s 0 factor was added to help ensure that the variance of d(i) is independent of gene expression level and to mitigate problems caused by small denominators. A similar strategy derived from a Bayesian approach is detailed in [12]. In order to select an appropriate s 0 value for this dataset, we plotted ∆ against FDR using different values of s 0 . Figure

Expression Levels of C2

minimum of the pooled standard deviations over all the genes, which fails to reduce FDRs. We therefore elected to set s 0 at the 5 th percentile of the pooled standard deviations (s 0 = 2.8); this choice does reduce FDR.

As ∆ increases, the number of significant genes decreases, but at the same time the percentage of falsely called genes also decreases. The curve of FDR vs. ∆ in Figure 4 shows that FDR generally decreases monotonically as ∆ increases, but from some ∆ on the decrease flattens markedly (see also Table 1). The choice of ∆ is somewhat arbitrary, but is driven by choosing an acceptable FDR and an appropriate number of significant genes. We choose ∆ = 12, corresponding to an FDR at 18%. This yields a set of 73 significant genes that are described next. Not surprisingly, the concordance between genes identified via graphical methods and those selected by SAM is high.

Genes identified by t-SAM

The 73 genes that are most highly ranked by t-SAM may represent more than one interacting molecular network and could be divided into different functional categories. Interestingly, only one gene (Autoantigen pericentriol material) has increased expression while the expression of the other 72 genes is decreased in the patient group. Unfortunately, in the present instance samples are no longer available and experimental verification of identified genes awaits future studies.

Cytokines / Neurotrophines

Mild tissue damage, nerve damage and infection produce inflammation and associated pain. This results in the migration of immune cells to the site of injury, which is fol-lowed by release of cytokines [13]. Five genes identified as significant by t-SAM have been reported in the literature as relevant to the inflammation and pain pathways. Interleukine 13 inhibits inflammatory cytokine production. Midkine is associated with neurite growth and was recently discovered to have potent neuroprotective activity in vivo [14]. IGFBP6 plays a significant role in the differentiation, maintenance and regeneration of the central cholinergic neurons [15]. Cysteine-rich fibroblast growth factor receptor is also implicated in neuronal growth and differentiation. TrkA plays a crucial role in the development and function of the nociceptive reception system.

Myelin function

Three genes were identified that are involved in myelin structure and myelination: MPZ (myelin protein zero), PLP1 (myelin proteolipid protein 1) and MBP (myelin basic protein). Defects in these genes are the cause of demyelinating neuropathies.

Figure 2

Histogram and QQ plot of t-statistics calculated from the normalized gene expression levels. Large t-statistics are labeled in red.  Signal transduction PKC and Frizzled play roles in apoptosis. The down regulation of both might represent a cellular response to prevent neurons from death.

Cytoskeleton

Three genes: Myosin light chain, Myosin heavy chain and MLCK (Myosin light-chain kinase) are notable in this category. The altered expression of them together suggests a probable link between calcium signaling and rearrangement of the cytoskeleton, possibly leading to long-term changes in neuronal morphology.

Others

MT-III has been recently implicated as being involved in sensory and nociceptive transmission [16]. Its down regu-lation might also lead to promotion of neurite extension to promote recovery in the patients.

Welch-SAM

Thomas, et al. [10] showed that in the two-group microarray study setting the t-statistic assumption of equal variances between the two groups could result in poor performance. We therefore extended the SAM framework to include Welch statistics. Under the assumption of unequal variances, the associated degrees of freedom are variable, and the strict monotonic decreasing relationship between p values and test statistic values no longer holds. Accordingly, it is misplaced to use the values of the statistics under permutation. Rather, for each data permutation, we standardized the Welch statistic using an appropriate t referent distribution and used the resultant "p values" as described in the Method section; see also

denominators vs. t numerators

Westfall and Young [17]. By so taking into account between-group heterogeneity, Welch-SAM identified a set of up regulated genes that were not detected by t-SAM. Several of these up regulated genes are engaged in transcription and translation regulation: transcription factor AP-4, transcriptional coactivator Pc4, Nrf2, EIF5 (Eukaryotic translation initiation factor 5), and PABPL1 (polyadenylate-binding protein 1). In addition, two genes are involved in cell cycle regulation: Autoantigen pericentriol material and CDC-like kinase. Their identification suggests a secondary mechanism to repair the damaged cells. The entire list of genes identified by t-SAM and Welch-SAM can be found at [2].

t-SAM vs. Welch-SAM

The relationship between FDR and ∆ for Welch is also included in Figure 4. The un-pooled variance in the denominator of Welch statistic is highly unstable under permutation in this small sample setting. Consequently, FDR for Welch-SAM is not a smooth function of ∆, as is the case of t-SAM. FDR values for selected ∆s for both t-SAM and Welch-SAM when s 0 was chosen at the 5 th percentile of standard deviations, are listed in Table 1 along with corresponding numbers of significant genes and false positives.

Application of Westfall and Young step-down adjusted p values

Westfall and Young's step-down adjusted p values were calculated using both t-statistics and Welch statistics. As before, the Welch statistics and p values are not monotonely related because of the variation in degrees of freedom. So, we again calibrated the Welch statistic against the appropriate t referent distribution and determined (unadjusted) "p values" for each permutation. The smallest Westfall and Young adjusted p values for t and Welch statistics were 0.053, 0.042 respectively. Figure 5 illustrates the relationship between adjusted p values and the number of genes being tested. A small simulation shows that this relationship is governed by the number of true null hypotheses in the tests (unpublished data). Profiles for nine selected genes are displayed; t-statistics are presented in Figure 5A and Welch-statistics in Figure 5B. For each gene, the adjusted p value increased with the increase of the number of null genes being tested. Genes with smaller statistics had greater adjusted p values and their adjusted p values increased at a greater rate when the number of null genes being tested was larger.

Discussion

FWER vs. FDR

In a single hypothesis test, a Type I error occurs when a true hypothesis is rejected. In multiple testing, FWER refers to the probability of rejection of any true hypothesis. When many hypotheses are tested, such as expression data of thousands of genes being compared between different groups, FWER increases dramatically, and is typically much larger than the significance level at which the individual hypotheses are tested.

As defined by Shaffer, given any test procedure, an adjusted p value corresponding to the test of a single hypothesis H j is the level of the entire test procedure at which H j would just be rejected, given the values of all test statistics involved [18]. Several approaches have been proposed to calculate adjusted p values for the purpose of providing control of FWER. Among these, the method developed by Westfall and Young is best suited for microarray data analysis. It is superior to the single-step methods proposed by Bonferroni and Šidák by allowing different p values to be adjusted differently; therefore the power of the procedure is improved. It is also able to take into account the dependence structure between variables. In a biological system, expression levels of groups of genes may correlate with each other for various reasons such as co-regulation.   number of permutations we can do is only 285. A more balanced experimental design will increase the number to 1715 (13 choose 6, then minus 1). Second, the vast majority of genes are expressed at low levels, as depicted in Figure 3, where biological signals may become indistinguishable from noise. For those cases where the difference in mean expression levels is small, a pooled standard deviation that is also small can give rise to a significant statistic, where in fact no difference exists. Third, Figure 5 shows that adjusted p values are sensitive to the number of null genes being tested. Given that many genes are likely to be irrelevant to the biological processes underlying the brachial plexus injuries and hence are expected to show little difference in their expression levels between injured patients and control subjects, it is not surprising that no significant result was obtained for t-SAM when applying the complete data set. In Figure 5 we also try to illustrate the potential abuse of using filtered gene subsets (based on statistics measuring differential expression) to achieve significant results, given that such filtering is commonplace in microarray literature. Last, although Westfall and Young's algorithm is more powerful than Bonferroni, Šidák, and Holm adjustments by taking into account the joint distribution of the test statistics, it may still be too stringent. The same result also occurred for Tusher, et al. [3] when applying this algorithm to study the transcriptional response of lymphoblastoid cells to ionizing radiation. A less stringent method may therefore be needed to analyze microaray data.

The FDR provides a different point of view on how the errors in multiple testing should be controlled. Having many hypotheses rejected signals clearly that many hypotheses are not true. It is therefore more crucial to control the rate of false positives among all rejected hypotheses than the probability of one single erroneous rejection. It might thus be argued that the control of FDR is a more appropriate approach to dealing with the multiplicity concern. That argument is especially true in the setting of microarray data analysis, where one is more interested in studying as many relevant genes as possible, and less interested in sacrificing possible targets for the concern of making one mistake [6]. The algorithm of SAM proposed by Tusher, et al. [3] provides an estimate of the FDR for each value of the parameter ∆ in the application of microarray settings. The estimated FDR is computed from permutation of the data and allows for the possibility of dependent tests [3]. We derived a set of 73 significant genes using SAM, out of which 13 were false positives, giving rise to a FDR of 18%. Although SAM is not able to disclose the identities of these false positives, it does provide biologists a reasonable set of potential target genes and a sense of the trustworthiness of the outcome. By estimating FDR by permutations of the data, SAM assumes that all null hypotheses are true; hence the estimated FDR is biased upward. Storey and Tibshirani tackled this problem by multiplying FDR by an estimate of the proportion of true null hypotheses, π 0 . A detailed description of the algorithm can be found in Storey and Tibshirani [6]. Following their approach, the 18% false discovery rate is lowered to about 13% by assuming that not all hypotheses are null. Further recent comparisons of multiple testing procedures are provided by Holland and Cheung [19].

t-statistics vs. Welch statistics

We applied both t-statistics and Welch statistics. The Welch statistics identified a set of genes having increased expression in the patient group that were not detected by t-statistics under the same stringency. One can argue that the active genes have greater variability in gene expression than inactive ones have [20]. Such a difference will be reflected in larger variances in the patient group relative to the control group, a scenario more appropriate for Welch statistics than t-statistics. In addition, subjects (patients) in our analysis might be in different conditions. Some patients might have more tissue damage and/or more severe pain than others. Further, the patient group is likely to be inherently more heterogeneous with respect to the extent of tissue damage and other relevant yet unmeasured attributes. These considerations also argue for the appropriateness of Welch statistics. Thomas, et al. also found that Welch statistics conformed better than t-statistics to their regression modeling approach used to discover differentially expressed genes in a microarray setting where between-group heterogeneity was evident [10]. There are drawbacks, however, to using the Welch statistics. Firstly, they need to be calibrated, introducing distributional assumptions. Secondly, and more importantly, there are stability and power concerns that pertain in small sample settings [17].

Conclusion

The use of high-density microarray technology to identify specific genes that are expressed differently under one or more biological conditions is particularly relevant to drug discovery and development. However, in the context of microarray data analysis, multiple testing concerns are forefront. In this study, we attacked the very important problem of application of appropriate multiple testing methods in identifying differential gene expression, and in addition, we have provided a framework for future experimental research in brachial plexus injuries and pain pathways. Simple statistical summaries, such as fold change, t-statistics and Welch statistics, have been applied.

To further investigate some recently proposed multiple testing schemes, we compared the performance of two approaches, SAM and Westfall and Young step down adjusted p values, as applied to a microarray study of gene expression in a brachial plexus injury. Our results show that using SAM and controlling FDR leads to identification of a set of potentially interesting genes consistent with prior knowledge of their function. In addition, SAM readily quantitates the trade-offs between false discovery rates and numbers of selected genes. On the other hand, the Westfall and Young algorithm, by controlling FWER, is highly conservative in this small sample setting. To the extent that FWER provides appreciably more stringent selection, attendant findings of significant differential gene expression are more likely to be validated (by follow-up experiment) than those deriving from FDR-controlling methods. However, there has been recent recognition [5,6,21] and our study also shows that FWER-control can be unnecessarily stringent since falsely selecting a few genes will not be a serious problem if the majority of differentially expressed genes are chosen correctly. In addition to comparing multiple testing algorithms, we also compared the performance of t-statistics and Welch statistics. By taking into account the heterogeneous nature of the patient group, Welch statistics identified a set of genes having increased expression in the patient group, whereas these genes were not selected by the t-statistics under the same criteria.

Methods

Materials

Briefly, cervical avulsed human DRG tissues (n = 10) were removed in the setting of a dorsal rhizotomy of lower cervical (and upper thoracic in one case) nerve roots in patients with persistent pain syndromes after accidental avulsion injuries. Details on obtaining, processing and measuring the expression of total RNA in the human DRG and control tissue samples are located elsewhere [http:// itsa.ucsf.edu/~yxiao/Avulsion]. The control human DRG sample was pooled from total RNA (n = 8; prepared by Clontech) obtained from post-mortem tissues. The pool of n=8 was then run in triplicate (n=3). Total RNA was extracted from the tissue by Trizol (LifeTechnologies) extraction and polyA + RNA was recovered by Oligotex mRNA Spin Columns (Qiagen). Biotinylated cRNA targets were prepared and hybridized to Affymetrix HU6800 oligonucleotide arrays according to the manufacturer's protocol (Affymetrix, Santa Clara, California).

Data analysis methods Normalization

All data from patient and control samples were preprocessed (background subtraction, differential intensities) using Affymetrix GeneChip software, and average differential intensity (ADI) was used for analysis. The average of all ADI values of each chip was calculated and the mean of average values of all chips was used as the target intensity. The ADI value of each chip was normalized to be equal to the target intensity. Since negative, zero, and very small positive values (<20) of ADI most likely represent noise instead of actual gene expression, all such values were truncated at 20 resulting in 5,638 probe sets for analysis.

Graphical display A Quantile-Quantile plot (Q-Q plot) was generated by plotting the quantiles of t statistics of all genes against the quantiles of a standard normal distribution. In addition to examining the distribution of t statistics, we used this plot to observe points that deviate markedly from the bulk of the observations since they may represent difference in means of the patient and control groups. Four scatter plots were generated to study the features of large t statistics: t statistics vs. average intensities, t statistics vs. t denominators, t statistics vs. t numerators, and t numerators vs. t denominators.

Significance Analysis of Microarrays (SAM)

The SAM procedure described by Tusher et al. [3] based on the t-statistic (under the assumption of equal variances between the two groups) and the Welch statistic (under the assumption of unequal variances between the two groups) was modified as follows:

1. The relative difference in the expression d(i) for the i th of k = 5638 probe sets was defined as,

Figure 1
14 shows that calculating s 0 according to the Tusher, et al. prescription yields a value equal to the Global comparison of the differences in gene expression levels between a) a patient (P15) and a normal subject (C1); b) a pair of patients (P15 and P12); c) a pair of normal subjects (C1 and C2).

3
3Plots of t-statistics, t-numerators, t-denominators and average intensities against each other. Large t-statistics are labeled in red.

However, when the Westfall and Young's permutation algorithm was applied to calculate step-down adjusted p values in our dataset, only one of the adjusted p values from Welch statistics reached a conventional significance level of 0.05. A few factors might contribute to the absence of adjusted p values at that significance level. First and foremost, the small sample sizes are limiting. Furthermore, the unbalanced allocation of (10) patients and(3)controls limits the precision of the adjusted p values. The

Figure 4
4The relationship between FDR and in SAM. t-SAM is represented with three different lines with different s 0 values: s 0 = 0, S 0 = 0.034 (the minimum of the pooled standard deviations) and S 0 = 2.761 (5 th percentile of the pooled standard deviations). Welch-SAM is graphed with S 0 = 2.000 (5 th percentile of the pooled standard deviations).

Figure 5
5The relationship between adjusted p values and number of genes tested. a) t-statistics; b) Welch statistics. Colored lines are genes ordered by their unadjusted p values, e.g. gene1 has the smallest unadjusted p value and gene600 has the 600 th smallest unadjusted p value. c) A comparison of panel a) and b). Red lines represent the results of Welch statistics and black lines represent the results of t-statistics.

; i = 1
1, 2, ..., k where and are means of expression levels of probe set i in the patient and control groups, respectively. the variances of expression levels for probe set i in the patient and control groups. The determination of s 0 is discussed in the Results section. For all d(i) values, corresponding p values were calculated with d(i) referenced to an appropriate t distribution.2. All p values were ordered: p 1 ≤ p 2 ≤ ... ≤ p k .

Table 1 :
1Comparison of t-statistics and Welch statistics in identifying significant genes under different values of ∆s∆
Significant genes False positives
FDR

t-statistics

2
622
312
50%
4
223
77.3
35%
6
131
35.1
27%
8
88
21.2
24%
12
73
13.3
18%
16
62
9.8
16%
20
57
7.7
14%
25
46
5.8
13%
40
30
3.4
11%
60
27
2.4
9%
90
19
1.5
8%

Welch statistics

2
1348
648.3
48%
4
525
155.9
30%
6
264
64.5
24%
8
97
24.0
25%
12
50
10.4
21%
16
20
4.0
20%
20
12
2.5
21%
25
7
1.0
14%
40
7
1.0
14%
60
6
0.4
7%
90
6
0.4
7%

Figure
(page number not for citation purposes)
t / S0=0 t / S0=0.034 t / S0=2.761 w / S0=2.000FDR
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AcknowledgementsWe thank Dr. Dirk Kreder for invaluable technical assistance during the preliminary analyses of the data. We thank Dr. Allan Basbaum for insightful discussions regarding the biology of avulsion injuries. We thank four anonymous reviewers from Roche Biosciences and BioMed Central for their detailed and helpful comments. This work was funded jointly by Roche Biosciences and the University of California through grant L-0098-17 (to CAH) from the Life Sciences: Information Technology sector [http://uc-in-3. An exhaustive set of 285 (286 minus the original configuration, 286 being 13 choose 3) permutations were conducted. For each permutation b, p values were calculated and ordered in the way of 4. Expected p values for all probe sets were calculated as , where i = 1, 2, ..., k.5. For a fixed threshold ∆, a probe set was called "significant" if its p value satisfied the criterion . The total number of "significant" probe sets was counted. The p i largest among the "significant" probe set was defined as the cutoff value.6. For each permutation, all probe sets whose p values were smaller than the cutoff value were found and were called "falsely significant". The total number of these probe sets was counted. The estimated number of "falsely significant" probe sets was defined as the average of the number of "falsely significant" probe sets from all permutations. The false discovery rate (FDR) was computed as the ratio of the estimated number of "falsely significant" probe sets to the total number of "significant" probe sets.FDR was computed with different values of threshold ∆.Westfall and Young step-down adjusted p valuesBoth t-statistics and Welch statistics were used to compare gene expression between the patient and control groups. Our data were organized in a matrix in which each row represents the expression of one gene for all subjects and each column represents the expression of all genes for one subject. The permutation algorithm developed by Westfall and Young to obtain step-down adjusted p values was then applied as follows. Note that the procedures were modified when using Welch statistics. Instead of using the Welch statistic to compute adjusted p values, we used unadjusted p values derived from Welch statistics and the appropriate degrees of freedom. An exhaustive set of 285 permutations were conducted.1. Compute the t statistic for each gene in the original dataset.2. Order them: |t r1 | ≥ |t r2 | ≥ |t r3 | ≥ ... ≥ |t rk |.3. Permute the 13 columns of the data matrix. The first 10 columns now represent the pseudo-patient group and the other 3 columns represent the pseudo-control group. where I(•) is the indicator function setting to 1 if the condition in parentheses is true and 0 if false. The monotonicity was enforced as , for 2 ≤ j ≤ k.Supplementary materialSupplementary material is located at [2]. This web page includes our data analysis results and also further tissue and patient information.Authors' contributionsYX performed the statistical studies, participated in its coordination, and drafted the manuscript. MRS initiated and designed the statistical analyses and drafted the manuscript. DR carried out the tissue preparation and microarray hybridization. AHA participated in the drafting of the manuscript regarding the biology of avulsion injuries. PA initiated and organized the study, and participated in the collection and tissue dissection of the DRG. LS initiated the study and participated in its design and coordination. DH participated in the statistical analyses and the initial manuscript drafting. CAH initiated the different methods of statistical analysis and participated in its design, coordination and manuscript drafting. YX and MRS contributed equally to this work.NoteRevisions to the text were added in proof
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