Antineutrophil cytoplasmic antibody associated vasculitis (AAV) is extremely heterogeneous in clinical presentation and involves multiple organ systems. While the clinical presentation of AAV is diverse, we hypothesized that all AAV share common pathways and tested the hypothesis based on three different microarray studies of peripheral leukocytes, sinus and orbital inflammation disease. For the hypothesis testing we developed a two-component semiparametric mixture model to estimate the local false discovery rates from the $p$-values of three studies. The two pillars of the proposed approach are Efron’s empirical null principle and log-concave density estimation for the alternative distribution. Our method outperforms other existing methods, in particular when the proportion of null is not that high. It is robust against the misspecification of alternative distribution. A unique feature of our method is that it can be extended to compute the local false discovery rates by combining multiple lists of $p$-values.

中文翻译：

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从多个研究中估计局部错误发现率的半参数混合方法

抗中性粒细胞胞浆抗体相关性血管炎（AAV）在临床表现上极为不同，涉及多个器官系统。尽管AAV的临床表现是多种多样的，但我们假设所有AAV都具有共同的途径，并基于对外周白细胞，窦和眼眶炎症疾病的三项不同的微阵列研究对这一假设进行了检验。对于假设检验，我们开发了一种两成分半参数混合模型，可以根据三项研究的$ p $值估算局部错误发现率。提出的方法的两个支柱是Efron的经验空值原理和对数分布的对数凹面密度估计。我们的方法优于其他现有方法，特别是当null的比例不高时。它对替代分配的错误规范具有鲁棒性。我们方法的独特之处在于，它可以扩展为通过组合$ p $值的多个列表来计算本地错误发现率。