Events

We consider estimating the propensity score and survival curves from observational data when the data constitute a length-biased sample from the target population. Length-bias in survival data occurs in observational studies when, for example, subjects with shorter lifetimes are less likely to be present in the recorded data. As such, depending on the association between covariates and survival time, some covariates will be under- or over-represented in the observed sample. Cheng and Wang (2012) introduced a method that adjusts for this bias that requires the correct conditional survival/hazard function given the treatment and covariates. When the marginal causal effect is the parameter of interest, however, investigators may prefer not to specify the conditional hazard model. We introduce a non-parametric adjustment technique based on a weighted estimating equation for estimating the propensity score that does not require any modeling assumption for the conditional survival function. We also present a non-parametric method to estimate the survival curves. Large sample properties of the estimators are established and their small sample behavior is studied using simulations. We apply the proposed method to a set of length-biased survival data collected as part of the Canadian Study of Health and Aging (CSHA).