Out of order: specification check sequencing in Cox models

The Cox duration model serves as the basis for more complex duration models like competing risks, repeated events, and multistate models. These models make a number of assumptions, many of which can be assessed empirically, sometimes for substantive ends. We use Monte Carlo simulations to show the order in which practitioners assess these assumptions can impact the model’s final specification, and ultimately, can produce misleading inferences. We focus on three assumptions regarding model specification decisions: proportional hazards (PH), stratified baseline hazards, and stratum-specific covariate effects. Our results suggest checking the PH assumption before checking for stratum-specific covariate effects tends to produce the correct final specification most frequently. We reexamine a recent study of the timing of GATT/WTO applications to illustrate our points.