The Impact of Violation of the Proportional Hazards Assumption on the Calibration of the Cox Proportional Hazards Model

Abstract

The Cox proportional hazards regression model is frequently used to develop clinical prediction models for time-to-event outcomes, allowing clinicians to estimate an individual's risk of experiencing the outcome within specified time horizons (e.g., estimate an individual's 10-year risk of death). The Cox regression model models the association between covariates and the hazard of the outcome. A key assumption of the Cox model is the proportional hazards assumption: the ratio of the hazard function for any two individuals is constant over time, and the ratio is a function of only their covariates and the regression coefficients. Calibration is an important aspect of the validation of clinical prediction models. Calibration refers to the concordance between predicted and observed risk. The impact of the violation of the proportional hazards assumption on the calibration of clinical prediction models developed using the Cox model has not been examined. We conducted a set of Monte Carlo simulations to assess the impact of the magnitude of the violation of the proportional hazards assumption on the calibration of the Cox model. We compared the calibration of predictions obtained using a Cox regression model that ignored the violation of the proportional hazards assumption with those obtained using accelerated failure time (AFT) models, Royston and Parmar's spline-based parametric survival models, and generalized linear models using pseudo-observations. We found that violation of the proportional hazards assumption had negligible impact on the calibration of predictions obtained using a Cox model.

Keywords: Cox regression; Monte Carlo simulations; calibration; model validation; proportional hazards.