Sampling adjusted analysis of dynamic additive regression models for longitudinal data

We consider a modelling approach to longitudinal data that aims at estimati ng flexible covariate effects in a model where the sampling probabilities a re modelled explicitly, The joint modelling yields simple estimators that a re easy to compute and analyse, even if the sampling of the longitudinal re sponses interacts with the response level. An incorrect model for the sampl ing probabilities results in biased estimates. Non-representative sampling occurs, for example, if patients with an extreme development (based on extr eme values of the response) are called in for additional examinations and m easurements. We allow covariate effects to be time-varying or time-constant . Estimates of covariate effects are obtained by solving martingale equatio ns locally for the cumulative regression functions. Using Aalen's additive model for the sampling probabilities, we obtain simple expressions for the estimators and their asymptotic variances. The asymptotic distributions for the estimators of the non-parametric components as well as the parametric components of the model are derived drawing on general martingale results. Two applications are presented. We consider the growth of cystic fibrosis p atients and the prothrombin index for liver cirrhosis patients. The conclus ion about the growth of the cystic fibrosis patients is not altered when ad justing for a possible non-representativeness in the sampling, whereas we r each substantively different conclusions about the treatment effect for the Liver cirrhosis patients.