The case-time-control design: further assumptions and conditions.

The case-time-control design is a strategy that was developed to tackle the problem of confounding by indication in the nonexperimental assessment of intended or known effects of drugs. By using subjects as their own controls, the case-time-control design, under an explicitly defined model, eliminates the biasing effect of unmeasured confounding factors in the situation where exposure varies over time. The correct application of this design is based on a specific model that contains inherent assumptions and imposes certain conditions for the approach to be valid. In a recent article, Greenland questioned the validity of the case-time-control design by presenting several "counterexamples." In this paper, we review the assumptions inherent to the validity of the case-time-control model. We show that the presumed counterexamples are not what they are claimed to be, simply because they do not conform to the logistic model explicitly underlying the case-time-control approach. These examples are shown to arise from an alternative model that includes a confounder by period interaction, a term expressly avoided in the case-time-control model. When the data from these examples are modified to satisfy the correct model, the resulting case-time-control estimates of the treatment odds ratio are exactly 2, the true treatment effect. We clarify the necessity of this assumption in the context of matching in epidemiology. We also discuss briefly the assumptions of conditional independence and carryover effects.