Duration Models, Stratified Hazards, and Proportional Hazard Testing

• In Event: Generalized Linear Models in Political Science

Abstract

Proportional hazards is a key assumption underlying several duration models, most notably the Cox semi-parametric duration model. Violating it can yield misleading inferences for any of the model’s covariates. Testing for the assumption is therefore crucial, and is typically done with residual-based diagnostics. However, the residual-based diagnostic is predicated on a key assumption: that the residuals’ variance is equal across each t’s riskset, amounting to a homoscedasticity assumption. This assumption is likely not met in the presence of stratified hazards, meaning the conclusions we draw about a covariate’s effect being proportional or not may be incorrect in the presence of stratification. We argue political scientists should be more attentive to this assumption, because several important duration model variants involve stratified hazards—namely, three different types of repeated event models, plus along with multistate models. We introduce a straightforward modification to the residual-based diagnostic that corrects for the potential violation, and provide commands in R and Stata to implement it. Importantly, the biostatistics literature is silent on how to address proportional hazards testing in models with shared frailty terms and/or clustered standard errors, as the standard modification in the literature is far less straightforward to implement in these situations. Our commands implement our modified correction for these models without issue, and we run simulations to show our modification can successfully detect PH violations in these settings. We also reanalyze several studies, implementing our correction, and show how the studies' results are affected.

Authors

• Shawna K. Metzger, University of Virginia

• Benjamin Thomas Jones, The University of Mississippi