It is more and more important to consider the dependence structure among multiple testings, especially for the genome-wide association studies (GWAS). The existing procedures, such as local index of significance (LIS) and pooled local index of significance (PLIS), were proposed to test hidden Markov model (HMM)-dependent hypotheses under the framework of compound decision theory, which was successfully applied to GWAS. However, the etiology of complex diseases is not only with respect to the genetic effects, but also the environmental factors. Failure to account for the covariates in multiple testing can produce misleading bias of the association of interest, or suffer from loss of testing efficiency. In this paper, we develop a covariate-adjusted multiple testing procedure, called covariate-adjusted local index of significance (CALIS), to account for the effects of environmental factors via a factorial hidden Markov model. The theoretical results show that our procedure can control the false discovery rate (FDR) at the nominal level and has the smallest false non-discovery rate (FNR) among all valid FDR procedures. We further demonstrate the advantage of our novel procedure over the existing procedures by simulation studies and a real data analysis.

考虑多个测试之间的依赖性结构越来越重要，尤其是对于全基因组关联研究（GWAS）。提出了现有的程序，例如局部重要性指数（LIS）和合并局部重要性指数（PLIS），以在复合决策理论的框架下测试依赖于隐马尔可夫模型（HMM）的假设，并将其成功应用于GWAS 。但是，复杂疾病的病因不仅与遗传效应有关，而且还与环境因素有关。未能在多次测试中考虑协变量会产生令人误解的兴趣关联偏差，或导致测试效率下降。在本文中，我们开发了一种经协变量调整的多重检验程序，称为经协变量调整的局部显着性指标（CALIS），通过阶乘隐马尔可夫模型解决环境因素的影响。理论结果表明，我们的程序可以在名义水平上控制错误发现率（FDR），并且在所有有效FDR程序中具有最小的错误未发现率（FNR）。通过仿真研究和真实数据分析，我们进一步证明了我们的新颖程序相对于现有程序的优势。