Properties of proportional-hazards score tests under misspecified regression models

The effects are investigated of misspecifying a proportional-hazards regression model on the associated partial-likelihood score test for comparing two randomized treatments in the presence of covariates. The asymptotic efficiency of the proportional-hazards score test, relative to the optimal partial-likelihood test, declines slowly as the hazard functions for the two treatments deviate from proportionality; the efficiency can be very low when the hazard functions cross or differ only at large survival times. Misspecification of the functional form of the regression portion of a proportional-hazards model introduces a quantitative treatment-covariate interaction. In the situations that we examine, based on a binary covariate, this misspecification usually results in only a minor drop in efficiency. The omission of a covariate that is balanced across treatments has a negligible effect on the size of the score test, but can substantially reduce power when the covariate effect is strong. The loss of power from mismodeling a balanced covariate is usually small.