We propose a method for analysis of loglinear regression models for longitudinal data that are subject to continuous and irregular follow-up. Frequently, if the follow-up is irregular, 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. We examine the marginal association of the covariates X at time t and the logarithm of the mean of response Y at time t. We focus on semiparametric regression with unspecified baseline function of time. To predict the follow-up times we use a marginal rate model with arbitrary baseline intensity and possibly time-varying covariates Z. We avoid the estimation of infinitely dimensional baseline intensity of follow-up as well as the intercept function in the outcome model. Our estimation procedure is based on estimating equations. The proposed class of estimators are root n consistent and asymptotically normal. We present simulation studies that assess the performance of the estimator under finite samples. We illustrate our approach using data from a health services research study.


Longitudinal Data Analysis and Time Series