MODEL INCONSISTENCY, ILLUSTRATED BY THE COX PROPORTIONAL HAZARDS MODEL

We consider problems involving the comparison of two or more treatment s where we have the opportunity to adjust for relevant covariates eith er conditionally in a regression model or implicitly in repeated measu res data, for example, in crossover trials. It is seen that for data a rising from non-Normal distributions there is the possibility that mod els adjusting for covariates and those not adjusting for covariates wi ll be inconsistent, that is, at most one of the models can be valid. A lternatively, even if conditional and unconditional models are valid, parameters in each model may have different interpretations. We note t hat this presents difficulties for the specification and interpretatio n of the analysis. It is also clear that model validation is critical. Specific attention is paid to survival data analysed by the Cox propo rtional hazards model.