The impact of violation of the proportional hazards assumption on the discrimination of the Cox proportional hazards model

Background — The Cox proportional hazards regression model is frequently used to estimate an individual’s probability of experiencing an outcome within a specified prediction horizon. A key assumption of this model is that of proportional hazards. An important component of validating a prediction model is assessing its discrimination. Discrimination refers to the ability of predicted risk to separate those who do and do not experience the event. The impact of violation of the proportional hazards assumption on the discrimination of risk estimates obtained from a Cox model has not been examined.

Methods — We used Monte Carlo simulations to assess the impact of the magnitude of the violation of the proportional hazards assumption on the discrimination of a Cox model as assessed using the time-varying area under the curve and on predictive accuracy as assessed using the time-varying index of predictive accuracy.

Results — Compared to settings in which the proportional hazards assumption was satisfied, discrimination and predictive accuracy decreased in settings in which the log-hazard ratio was positively associated with time. Conversely, compared to settings in which the proportional hazards assumption was satisfied, discrimination and predictive accuracy increased in settings in which the log-hazard ratio was negatively associated with time. Compared with the use of a Cox regression model, the use of accelerated failure time parametric survival models, Royston and Parmar’s spline-based parametric survival models, and generalized linear models using pseudo-observations did not result in estimates with improved discrimination or predictive accuracy in settings in which the proportional hazards assumption was violated.

Conclusions — Violation of the proportional hazards assumption had an effect on the discrimination of predictions obtained using a Cox regression model.