Regression with a right-censored predictor using inverse probability weighting methods

In a longitudinal study, measures of key variables might be incomplete or partially recorded due to drop-out, loss to follow-up, or early termination of the study occurring before the advent of the event of interest. In this paper, we focus primarily on the implementation of a regression model with a randomly censored predictor. We examine, particularly, the use of inverse probability weighting methods in a generalized linear model (GLM), when the predictor of interest is right-censored, to adjust for censoring. To improve the performance of the complete-case analysis and prevent selection bias, we consider three different weighting schemes: inverse censoring probability weights, Kaplan-Meier weights, and Cox proportional hazards weights. We use Monte Carlo simulation studies to evaluate and compare the empirical properties of different weighting estimation methods. Finally, we apply these methods to the Framingham Heart Study data as an illustrative example to estimate the relationship between age of onset of a clinically diagnosed cardiovascular event and low-density lipoprotein among cigarette smokers.