Flexible omnibus test in 1:M matched case-crossover study with measurement error in covariate

The matched case-crossover study design is used in public health, biomedical, and epidemiological research with clustered binary outcomes. Conditional logistic regression is commonly used for analysis because any effects associated with the matching covariates by stratum can be removed. However, some matching covariates often play an important role as effect modifications, causing incorrect statistical testing. The covariates in such studies are often measured with error, so that not accounting for this error can also lead to incorrect inferences for all covariates in the model. However, the methods available for simultaneously evaluating effect modification by matching covariates as well as assessing and characterizing error-in-covariates are limited. In this paper, we propose a flexible omnibus test for testing (1) the significance of a functional association between the clustered binary outcomes and covariates with the measurement error, (2) the existence of effect modifications by matching covariates, and (3) the significance of an interaction effect between the measurement error covariate and other covariates, without specifying the functional forms for these testings. The proposed omnibus test has the flexibility to allow inferences on various hypothesis settings. The advantages of the proposed flexible omnibus test are demonstrated through simulation studies and 1:4 bidirectional matched data analyses from an epidemiology study.