A Note on the Estimate of Treatment Effect from a Cox Regression Model When the Proportionality Assumption Is Violated

ABSTRACT

Cox proportional hazards regression model has been widely used to estimate the effect of a prognostic factor on a time-to-event outcome. In a survey of survival analyses in cancer journals, it was found that only 5% of studies using Cox proportional hazards model attempted to verify the underlying assumption. Usually an estimate of the treatment effect from fitting a Cox model was reported without validation of the proportionality assumption. It is not clear how such an estimate should be interpreted if the proportionality assumption is violated. In this article, we show that the estimate of treatment effect from a Cox regression model can be interpreted as a weighted average of the log-scaled hazard ratio over the duration of study. A hypothetic example is used to explain the weights.