In genome-wide association (GWA) studies, test statistics that are efficient and robust across various genetic models are preferable, particularly for studying multiple diseases in the Wellcome Trust Case-Control Consortium (WTCCC, 2007, Nature 447, 661-678). A new test statistic, the minimum of the p-values of the trend test and Pearson's test, was considered by the WTCCC. It is referred to here as MIN2. Because the minimum of two p-values is no longer a valid p-value itself, the WTCCC only used it to rank single nucleotide polymorphisms (SNPs) but did not report the p-values of the associated SNPs when MIN2 was used for ranking. Given its importance in practice, we derive the asymptotic null distribution of MIN2, study some of its analytical properties related to GWA studies, and compare it with existing methods (the trend test, Pearson's test, MAX3, and the constrained likelihood ratio test [CLRT]) by simulations across a wide range of possible genetic models: the recessive (REC), additive (ADD), multiplicative (MUL), dominant (DOM), and overdominant models. The results show that MAX3 and CLRT have greater efficiency robustness than other tests when the REC, ADD/MUL, and DOM models are possible, whereas Pearson's test and MIN2 have greater efficiency robustness if the possible genetic models also include the overdominant model. We conclude that robust tests (MAX3, MIN2, CLRT, and Pearson's test) are preferable to a single trend test for initial GWA studies. The four robust tests are applied to more than 100 SNPs associated with 11 common diseases identified by the two WTCCC GWA studies.
Summary Phase II clinical trials are often conducted to determine whether a new treatment is sufficiently promising to warrant a major controlled clinical evaluation against a standard therapy. We consider single-arm phase II clinical trials with right censored survival time responses where the ordinary one-sample logrank test is commonly used for testing the treatment efficacy. For planning such clinical trials this paper presents two-stage designs that are optimal in the sense that the expected sample size is minimized if the new regimen has low efficacy subject to constraints of the type I and type II errors. Two-stage designs which minimize the maximal sample size are also determined. Optimal and minimax designs for a range of design parameters are tabulated along with examples.
When testing genetic linkage and association, test statistics that follow a normal or Chi-square distributions are often used. These statistics are usually derived under a specific mode of inheritance (genetic model). Common genetic models include, but not limited to, the recessive, additive, multiplicative, and dominant models. For many diseases, their underlying genetic models are often unknown. Instead, a family of scientifically plausible genetic models may be available, which includes the four commonly used models. Hence, the optimal test is not available. Employing a single test statistic which is optimal for one model may suffer from substantial loss of power when the model is misspecified. In this situation efficient robust tests are useful. In this tutorial, we first review several commonly used robust statistics, including maximum efficiency robust tests, maximal tests, and constrained likelihood ratio tests for three common designs in genetic studies: (i) linkage analysis using affected sib-pairs, (ii) association studies using parents-offspring trios, and (iii) case-control association studies (unmatched and matched). Codes in the R statistical language for applying these robust statistics to test for linkage and association are presented with examples. We also provide some comparisons of the performance of the various robust tests via simulation studies. Guidelines for applications are also given for each study design. Finally, applications of robust tests to genome-wide association studies and meta-analysis are discussed.
To detect association between a genetic marker and a disease in case-control studies, the Cochran-Armitage trend test is typically used. The trend test is locally optimal when the genetic model is correctly specified. However, in practice, the underlying genetic model, and hence the optimal trend test, are usually unknown. In this case, Pearson's chi-squared test, the maximum of three trend test statistics (optimal for the recessive, additive, and dominant models), and the test based on genetic model selection (GMS) are useful. In this article, we first modify the existing GMS method so that it can be used when the risk allele is unknown. Then we propose a new approach by excluding a genetic model that is not supported by the data. Using either the model selection or exclusion, the alternative space is reduced conditional on the observed data, and hence the power to detect a true association can be increased. Simulation results are reported and the proposed methods are applied to the genetic markers identified from the genome-wide association studies conducted by the Wellcome Trust Case-Control Consortium. The results demonstrate that the genetic model exclusion approach usually performs better than existing methods under its worst situation across scientifically plausible genetic models we considered.
Our goal was to examine the effect of area-level deprivation on patient survival time for seven major cancers — stomach, colon, liver, lung, breast, cervix, and thyroid cancer. Data on 10,902 subjects who were diagnosed with major cancers from 2010 and 2011 in Busan were collected regarding the survival time along with several important prognostic factors and an area-level deprivation index was constructed from education, income, unemployment, and welfare assistance, to assess the comprehensive area-level socioeconomic status. A multilevel Cox proportional hazard model was used to investigate the effects of multiple risk factors such as gender, age, tumor stage, diagnosis path, and the area-level deprivation. After adjusting for risk factors the area-level deprivation index was found to be significant in associating with higher hazard rate for several cancers. Estimated hazard ratios (95% CI) were 1.08 (0.99–1.18), 1.23 (1.12–1.36), 1.36 (1.21–1.53) for the second, the third, and the fourth quartile of deprivation index groups, respectively, when compared to the least deprived group. When compared with the least deprived group, the more deprived group showed significant decrease in survival time for major cancers. This novel finding may contribute to the literature regarding the association of area-level socioeconomic status and highlight the importance of careful monitoring of socioeconomic characteristics for cancer prevention and care services.
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