In longitudinal studies, observations are often obtained at subject-specific observation times. Those times can be continuous times, not at a set of prespecified times. Frequently the observation times may be related to the outcome measure or other auxiliary variables that are related to the outcome measure but undesirable to condition upon in the regression model for outcome. Regression analysis unadjusted for such sampling designs yield biased estimates. Based on estimating equations, we propose a class of estimators in generalized linear regression models that can handle biased sampling under continuous observation times. We call those estimators ``inverse--intensity rate--ratio--weighted'' (IIRR) estimators. The proposed estimators are simple and easily computed as they are readily available in many statistical software packages. We integrate counting processes techniques with longitudinal data settings. We leave stochastic structure of the outcome completely unspecified. Covariates modeling the association in the regression model for outcome as well as covariates predicting the observation times can contain lagged outcome or lagged covariates. The estimators are root n consistent and asymptotically normal. We avoid estimation of the infinite--dimensional baseline sampling intensity. The finite sample performance of the proposed estimation procedure is investigated in a simulation study. Finally, we illustrate our approach with a data set from a health services research study that was subject to high noncompliance to predefined visit times.
Longitudinal Data Analysis and Time Series
Buzkova, Petra and Lumley, Thomas, "Longitudinal Data Analysis for Generalized Linear Models under Irregular, Biased Sampling: Situations with Follow-up Dependent on Outcome or Auxiliary Outcome-related Variables" (September 2005). UW Biostatistics Working Paper Series. Working Paper 262.