Testing the fit of the logistic model for matched case-control studies

With numerous statistical packages being easily available to conduct the logistic regression analysis, assessment for the goodness-of-fit in the logistic case-control studies becomes more important in practice. While various methods for model checking in conventional case-control studies have been proposed in the literature, methods for checking model adequacy with matched case-control data get relatively less attention. In this study, we propose an omnibus goodness-of-fit test to assess adequacy of the conditional logistic model for matched case-control data. The proposed test can be either constructed based on the discrepancy between two moment estimations or derived to be a score-type test under a general random-effects model. Computation of the proposed test is quite simple in which it does not need to partition the covariate space or to estimate p-value of the test via simulations. The asymptotic null distribution and power calculation of the test are derived under a sequence of alternatives. Empirical type I error rates and powers of the test are performed by simulation studies. An example has been used to illustrate the proposed method as well.