Evaluation of Cox's model and logistic regression for matched case-control data with time-dependent covariates: a simulation study

Abstract

Case-control studies are typically analysed using the conventional logistic model, which does not directly account for changes in the covariate values over time. Yet, many exposures may vary over time. The most natural alternative to handle such exposures would be to use the Cox model with time-dependent covariates. However, its application to case-control data opens the question of how to manipulate the risk sets. Through a simulation study, we investigate how the accuracy of the estimates of Cox's model depends on the operational definition of risk sets and/or on some aspects of the time-varying exposure. We also assess the estimates obtained from conventional logistic regression. The lifetime experience of a hypothetical population is first generated, and a matched case-control study is then simulated from this population. We control the frequency, the age at initiation, and the total duration of exposure, as well as the strengths of their effects. All models considered include a fixed-in-time covariate and one or two time-dependent covariate(s): the indicator of current exposure and/or the exposure duration. Simulation results show that none of the models always performs well. The discrepancies between the odds ratios yielded by logistic regression and the 'true' hazard ratio depend on both the type of the covariate and the strength of its effect. In addition, it seems that logistic regression has difficulty separating the effects of inter-correlated time-dependent covariates. By contrast, each of the two versions of Cox's model systematically induces either a serious under-estimation or a moderate over-estimation bias. The magnitude of the latter bias is proportional to the true effect, suggesting that an improved manipulation of the risk sets may eliminate, or at least reduce, the bias.