A novel calibration framework for survival analysis when a binary covariate is measured at sparse time points

TL;DR

This paper introduces a new calibration framework for accurately estimating the effect of a time-dependent binary covariate, measured intermittently, on survival outcomes, addressing bias in traditional methods.

Contribution

It develops nonparametric, semiparametric, and parametric calibration models for the covariate change time, incorporating baseline variables and proposing a risk-set calibration approach.

Findings

Models improve bias correction in survival analysis with intermittent covariate data

Application to colorectal cancer study demonstrates practical utility

Theoretical properties of the estimators are established

Abstract

The goals in clinical and cohort studies often include evaluation of the association of a time-dependent binary treatment or exposure with a survival outcome. Recently, several impactful studies targeted the association between aspirin-taking and survival following colorectal cancer diagnosis. Due to surgery, aspirin-taking value is zero at baseline and may change its value to one at some time point. Estimating this association is complicated by having only intermittent measurements on aspirin-taking. Naive, commonly-used, methods can lead to substantial bias. We present a class of calibration models for the distribution of the time of status change of the binary covariate. Estimates obtained from these models are then incorporated into the proportional hazard partial likelihood in a natural way. We develop nonparametric, semiparametric and parametric calibration models, and derive asymptotic theory for the methods that we implement in the aspirin and colorectal cancer study. Our methodology allows to include additional baseline variables in the calibration models for the status change time of the binary covariate. We further develop a risk-set calibration approach that is more useful in settings in which the association between the binary covariate and survival is strong.