Estimating mean survival time: when is it possible?

TL;DR

This paper demonstrates that mean survival time can be estimated using a linear model with unbounded covariates, even when traditional conditions are not met, supported by theoretical analysis and simulations.

Contribution

It introduces a novel approach showing mean survival time is estimable from a linear model with unbounded covariates, relaxing traditional assumptions.

Findings

Mean survival time is estimable with unbounded covariates regardless of follow-up length.

Linear models outperform Cox models under heavy censoring and short follow-up.

Simulation results confirm theoretical findings and practical advantages.

Abstract

For right censored survival data, it is well known that the mean survival time can be consistently estimated when the support of the censoring time contains the support of the survival time. In practice, however, this condition can be easily violated because the follow-up of a study is usually within a finite window. In this article we show that the mean survival time is still estimable from a linear model when the support of some covariate(s) with nonzero coefficient(s) is unbounded regardless of the length of follow-up. This implies that the mean survival time can be well estimated when the covariate range is wide in practice. The theoretical finding is further verified for finite samples by simulation studies. Simulations also show that, when both models are correctly specified, the linear model yields reasonable mean square prediction errors and outperforms the Cox model, particularly with heavy censoring and short follow-up time.