Semiparametric analysis of transformation models with dependently left-truncated and right-censored data

In transplant studies, the patients must survive long enough to receive a transplant, which induces left-truncation. The assumption of independence between failure and truncation times may not hold since a longer transplant waiting time can be associated with a worse survivorship. To take dependence into consideration, we utilize a semiparametric transformation model, where the truncation time is both a truncated variable and a predictor of the time to failure. Using the inverse-probability-weighted (IPW) approach, we propose an IPW estimator of the marginal distribution of waiting time. Simulation studies are conducted to investigate finite sample performance of the proposed estimator. We also apply our methods to bone marrow and heart transplant data.