Regression for Left‐Truncated and Right‐Censored Data: A Semiparametric Sieve Likelihood Approach

ABSTRACT Cohort studies of the onset of a disease often encounter left‐truncation on the event time of interest in addition to right‐censoring due to variable enrollment times of study participants. Analysis of such event time data can be biased if left‐truncation is not handled properly. We propose a semiparametric sieve likelihood approach for fitting a linear regression model to data where the response variable is subject to both left‐truncation and right‐censoring. We show that the estimators of regression coefficients are consistent, asymptotically normal and semiparametrically efficient. Extensive simulation studies show the effectiveness of the method across a wide variety of error distributions. We further illustrate the method by analyzing datasets from the Canadian Study of Health and Aging and The 90+ Study for aging and dementia.