The Cochran-Armitage trend test is commonly used as a genotype-based test for candidate gene association. Corresponding to each underlying genetic model there is a particular set of scores assigned to the genotypes that maximizes its power. When the variance of the test statistic is known, the formulas for approximate power and associated sample size are readily obtained. In practice, however, the variance of the test statistic needs to be estimated. We present formulas for the required sample size to achieve a prespecified power that account for the need to estimate the variance of the test statistic. When the underlying genetic model is unknown one can incur a substantial loss of power when a test suitable for one mode of inheritance is used where another mode is the true one. Thus, tests having good power properties relative to the optimal tests for each model are useful. These tests are called efficiency robust and we study two of them: the maximin efficiency robust test is a linear combination of the standardized optimal tests that has high efficiency and the MAX test, the maximum of the standardized optimal tests. Simulation results of the robustness of these two tests indicate that the more computationally involved MAX test is preferable.

Erythrocyte measures are heritable and have important health implications, yet their genetic determinants are largely unknown. We performed genome-wide association analyses in 24,167 European-ancestry individuals for six erythrocyte traits and identified associations at 23 loci (P values 5×10-8 to 1×10-57). Replication testing in an independent set of 9,456 European-ancestry individuals showed strong evidence of association in all 23 loci in meta-analysis of the discovery and replication cohorts. Our findings include previously identified loci (HBS1L/MYB, HFE, TMPRSS6, TFR2, SPTA1) and novel associations (EPO, TFRC, SH2B3, and 15 other loci). This study has identified novel determinants of erythrocyte traits, offering insight into common variants underlying variation in erythrocyte measures.

Test statistics for association between markers on autosomal chromosomes and a disease have been extensively studied. No research has been reported on performance of such test statistics for association on the X chromosome. With 100,000 or more single-nucleotide polymorphisms (SNPs) available for genome-wide association studies, thousands of them come from the X chromosome. The X chromosome contains rich information about population history and linkage disequilibrium. To identify X-linked marker susceptibility to a disease, it is important to study properties of various statistics that can be used to test for association on the X chromosome. In this article, we compare performance of several approaches for testing association on the X chromosome, and examine how departure from Hardy-Weinberg equilibrium would affect type I error and power of these association tests using X-linked SNPs. The results are applied to the X chromosome of Klein et al. [2005], a genome-wide association study with 100K SNPs for age-related macular degeneration. We found that a SNP (rs10521496) covered by DIAPH2, known to cause premature ovarian failure (POF) in females, is associated with age-related macular degeneration.

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The Cochran-Armitage trend test (CATT) is well suited for testing association between a marker and a disease in case-control studies. When the underlying genetic model for the disease is known, the CATT optimal for the genetic model is used. For complex diseases, however, the genetic models of the true disease loci are unknown. In this situation, robust tests are preferable. We propose a two-phase analysis with model selection for the case-control design. In the first phase, we use the difference of Hardy-Weinberg disequilibrium coefficients between the cases and the controls for model selection. Then, an optimal CATT corresponding to the selected model is used for testing association. The correlation of the statistics used for selection and the test for association is derived to adjust the two-phase analysis with control of the Type-I error rate. The simulation studies show that this new approach has greater efficiency robustness than the existing methods.

Functional connectivity in the DMN was impaired in patients with ESRD, with further reduction in the MPFC with the development of MNE, which might explain the reduced performance of these patients on neurocognitive tests. Serum creatinine level might be associated with impairment of the DMN in patients with ESRD.

To investigate the pattern of brain volume changes in patients with end-stage renal disease (ESRD) using voxel-based morphometry (VBM) and correlation with clinical and neuropsychological (NP) tests. Fifty seven ESRD patients with no anatomical abnormalities in conventional magnetic resonance imaging [24 patients with abnormal NP scores, 16 male, 39 ± 12 years; 33 patients with normal NP scores, 23 male, 35 ± 9.7 years] and 22 age- and gender-matched healthy controls (14 male, 36 ± 10.1 years) were recruited in this study. Results from VBM analysis were analyzed with ANOVA test among 3 groups (controls, minimal nephro-encephalopathy group, non-nephro-encephalopathy group). Multiple linear regression analysis was used to investigate the effect of serum urea and creatinine, and dialysis duration on the brain volumes in ESRD patients. Correlation analysis was performed to investigate the association between NP scores with the brain volumes in ESRD patients. Compared with healthy controls, ESRD patients showed diffusely decreased gray matter volume that further decreased in the presence of encephalopathy. Multiple linear regression results showed that serum urea was negatively associated with changes in gray matter volume in many regions, while dialysis duration was negatively associated with some white matter volume changes (All P < 0.05, AlphaSim correction). NP scores correlated with some decreased gray matter volume in ESRD patients (All P < 0.05, AlphaSim correction). No correlation was found between white matter volume and any NP test scores in ESRD patients. This study found predominantly decreased gray matter volume in ESRD patients, which was associated with neurocognitive dysfunction. Serum urea level may be a risk factor for decreased gray matter in ESRD patients.

SummaryGenome-wide association study (GWAS), typically involving 100,000 to 500,000 single-nucleotide polymorphisms (SNPs), is a powerful approach to identify disease susceptibility loci. In a GWAS, single-marker analysis, which tests one SNP at a time, is usually used as the first stage to screen SNPs across the genome in order to identify a small fraction of promising SNPs with relatively low p-values for further and more focused studies. For single-marker analysis, the trend test derived for an additive genetic model is often used. This may not be robust when the additive assumption is not appropriate for the true underlying disease model. A robust test, MAX, based on the maximum of three trend test statistics derived for recessive, additive, and dominant models, has been proposed recently for GWAS. But its p-value has to be evaluated through a resampling-based procedure, which is computationally challenging for the analysis of GWAS. Obtaining the p-value for MAX with adjustment for the covariates can be even more time-consuming. In this article, we provide a simple approximation for the p-value of the MAX test with or without adjusting for the covariates. The new method avoids resampling steps and thus makes the MAX test readily applicable to GWAS. We use simulation studies as well as real datasets on 17 confirmed disease-associated SNPs to assess the accuracy of the proposed method. We also apply the method to the GWAS of coronary artery disease.