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The goals in clinical and cohort studies often include evaluation of theassociation of a time-dependent binary treatment or exposure with a survivaloutcome. Recently, several impactful studies targeted the association betweenaspirin-taking and survival following colorectal cancer diagnosis. Due tosurgery, aspirin-taking value is zero at baseline and may change its value toone at some time point. Estimating this association is complicated by havingonly intermittent measurements on aspirin-taking. Naive, commonly-used, methodscan lead to substantial bias. We present a class of calibration models for thedistribution of the time of status change of the binary covariate. Estimatesobtained from these models are then incorporated into the proportional hazardpartial likelihood in a natural way. We develop nonparametric, semiparametricand parametric calibration models, and derive asymptotic theory for the methodsthat we implement in the aspirin and colorectal cancer study. Our methodologyallows to include additional baseline variables in the calibration models forthe status change time of the binary covariate. We further develop a risk-setcalibration approach that is more useful in settings in which the associationbetween the binary covariate and survival is strong.

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