Propensity Score Estimation in the Presence of Length-biased Sampling: A Nonparametric Adjustment Approach

The pervasive use of prevalent cohort studies on disease duration increasingly calls for an appropriate methodology to account for the biases that invariably accompany samples formed by such data. It is well-known, for example, that subjects with shorter lifetime are less likely to be present in such studies. Moreover, certain covariate values could be preferentially selected into the sample, being linked to the long-term survivors. The existing methodology for estimating the propensity score using data collected on prevalent cases requires the correct conditional survival/hazard function given the treatment and covariates. This requirement can be alleviated if the disease under study has stationary incidence, the so-called stationarity assumption. We propose a nonparametric adjustment technique based on a weighted estimating equation for estimating the propensity score which does not require modeling the conditional survival/hazard function when the stationarity assumption holds. The estimator's large-sample properties are established and its small-sample behavior is studied via simulation. The estimated propensity score is utilized to estimate the survival curves.