• MAX3;
  • efficiency robustness;
  • covariates;
  • case-control study


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. Genet. Epidemiol. 2011. © 2011 Wiley Periodicals, Inc. 35:695-705, 2011