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The pervasive use of prevalent cohort studies on disease duration,increasingly calls for appropriate methodologies to account for the biases thatinvariably accompany samples formed by such data. It is well-known, forexample, that subjects with shorter lifetime are less likely to be present insuch studies. Moreover, certain covariate values could be preferentiallyselected into the sample, being linked to the long-term survivors. The existingmethodology for estimation of the propensity score using data collected onprevalent cases requires the correct conditional survival/hazard function giventhe treatment and covariates. This requirement can be alleviated if the diseaseunder study has stationary incidence, the so-called stationarity assumption. Wepropose a nonparametric adjustment technique based on a weighted estimatingequation for estimating the propensity score which does not require modelingthe conditional survival/hazard function when the stationarity assumptionholds. Large sample properties of the estimator is established and its smallsample behavior is studied via simulation.

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