Comparison of stopped Cox regression with direct methods such as pseudo-values and binomial regression

Abstract

By far the most popular model to obtain survival predictions for individual patients is the Cox model. The Cox model does not make any assumptions on the underlying hazard, but it relies heavily on the proportional hazards assumption. The most common ways to circumvent this robustness problem are 1) to categorize patients based on their prognostic risk score and to base predictions on Kaplan-Meier curves for the risk categories, or 2) to include interactions with the covariates and suitable functions of time. Robust estimators of the $t_0$-year survival probabilities can also be obtained from a “stopped Cox” regression model, in which all observations are administratively censored at $t_0$. Other recent approaches to solve this robustness problem, originally proposed in the context of competing risks, are pseudo-values and direct binomial regression, based on unbiased estimating equations. In this paper stopped Cox regression is compared with these direct approaches. This is done by means of a simulation study to assess the biases of the different approaches and an analysis of breast cancer data to get some feeling for the performance in practice. The tentative conclusion is that stopped Cox and direct models agree well if the follow-up is not too long. There are larger differences for long-term follow-up data. There stopped Cox might be more efficient, but less robust.