In longitudinal studies observations are often obtained at continuous subject-specific times. Frequently the availability of outcome data may be related to the outcome measure or other covariates that are related to the outcome measure. Under such biased sampling designs unadjusted regression analysis yield biased estimates. Building on the work of Lin & Ying (2001) that integrates counting processes techniques with longitudinal data settings we propose a class of estimators that can handle biased sampling. We call those estimators ``inverse--intensity--rate--ratio--weighted'' (IIRR) estimators. Of major focus is a mean--response model where we examine the marginal effect of the covariate X at time t on the mean of the response Y at that time. The proposed class of closed-form estimators are root n-consistent and asymptotically normal and do not require estimating any infinite--dimensional parameters. The estimators and estimators of their variance are relatively simple and computationally feasible. Simulation studies demonstrate that asymptotic approximations are accurate for moderate sample sizes. %Also, when comparing squared error, the proposed estimators are largely favored when compared to the Lin and Ying estimates or the GEE estimates. We illustrate our approach using data from a health service research study with extreme noncompliance to the scheduled visits that can not be explained by the intervention assignment alone.


Longitudinal Data Analysis and Time Series