Conditional survival given covariates and marginal survival

TL;DR

This paper explores how conditioning on a marginal survival function affects regression analysis of survival data, showing it offers no efficiency gain under proportional hazards but provides consistent estimates when the model is invalid.

Contribution

It introduces a conditional estimation method based on marginal survival, which remains consistent even when proportional hazards assumptions are violated.

Findings

No efficiency gain under valid proportional hazards models.

Conditional estimator is consistent when proportional hazards assumption fails.

Simulations demonstrate the estimator's robustness and interpretability.

Abstract

Assuming some regression model, it is common to study the conditional distribution of survival given covariates. Here, we consider the impact of further conditioning, specifically conditioning on a marginal survival function, known or estimated. We investigate to what purposes any such information can be used in a proportional or non-proportional hazards regression analysis of time on the covariates. It does not lead to any improvement in efficiency when the form of the assumed proportional hazards model is valid. However, when the proportional hazards model is not valid, the usual partial likelihood estimator is not consistent and depends heavily on the unknown censoring mechanism. In this case we show that the conditional estimate that we propose is consistent for a parameter that has a strong interpretation independent of censoring. Simulations and examples are provided.