Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, People's Republic of China.
Genet Epidemiol. 2011 Nov;35(7):695-705. doi: 10.1002/gepi.20620. Epub 2011 Aug 26.
The trend test under the additive model is commonly used when a case-control genetic association study is carried out. However, for many complex diseases, the underlying genetic models are unknown and a mis-specification of the genetic model may result in a substantial loss of power. MAX3 has been proposed as an efficiency robust test against genetic model uncertainty which takes the maximum absolute value of the trend test statistics under the recessive, additive, and dominant models. Besides its popularity, little attention has been paid to the adjustment of covariates in this test and existing approaches all depend on the estimators of parameters of interest which may be seriously biased if the individuals are divided into a large number of partial tables stratified by covariates. In this article, we propose a modified MAX3 test based on the Mantel-Haenszel test (MHT). This new test avoids estimating the nuisance parameters induced by the covariates; thus, it is valid under both large and small numbers of partial tables while still enjoys the property of efficiency robustness. The asymptotic distribution of the test under the null hypothesis of no association is also derived; thus the corresponding asymptotic P-value of the statistic can be easily calculated. Besides, we prove that this new test can be equally derived through a conditional likelihood. As a result, the original MAX3 based on the trend tests or the matching trend tests can be treated as a special case and generally incorporated into the newly proposed test. Simulation results show that the modified MAX3 can keep the correct size under the null hypothesis and is more efficiency robustness than any single MHT optimal for a specified genetic model under the alternative hypothesis. Two real examples corresponding to the large and small number of partial tables scenarios, respectively, are analyzed using the proposed method. A type 2 diabetes mellitus data set is also analyzed to evaluate the performance of the proposed test under the GWAS criteria.
当进行病例对照遗传关联研究时，通常使用加性模型下的趋势检验。然而，对于许多复杂疾病，潜在的遗传模型是未知的，遗传模型的错误指定可能导致大量的功效损失。MAX3 已被提议作为一种针对遗传模型不确定性的有效稳健检验，该检验采用了隐性、加性和显性模型下趋势检验统计量的最大绝对值。除了它的流行程度之外，很少有人关注这个检验中的协变量调整，现有的方法都依赖于感兴趣参数的估计量，如果将个体分为大量按协变量分层的部分表，这些估计量可能会严重偏差。在本文中，我们提出了一种基于 Mantel-Haenszel 检验（MHT）的修改后的 MAX3 检验。这个新的检验避免了估计由协变量引起的麻烦参数；因此，它在部分表数量大或小的情况下都是有效的，同时仍然具有效率稳健性的特性。在没有关联的零假设下，该检验的渐近分布也被推导出来；因此，可以很容易地计算出统计量的相应渐近 P 值。此外，我们证明这个新的检验也可以通过条件似然来得到。因此，基于趋势检验或匹配趋势检验的原始 MAX3 可以被视为一个特例，并通常被纳入新提出的检验中。模拟结果表明，在零假设下，修改后的 MAX3 可以保持正确的大小，并且在替代假设下，比任何针对特定遗传模型的单一 MHT 都更有效稳健。分别使用提出的方法分析了对应于部分表数量大或小的两个真实例子。还使用所提出的方法分析了一个 2 型糖尿病数据集，以评估该检验在 GWAS 标准下的性能。
