A joint modeling approach to data with informative cluster size: robustness to the cluster size model.

In many biomedical and epidemiological studies, data are often clustered due to longitudinal follow up or repeated sampling. While in some clustered data the cluster size is pre-determined, in others it may be correlated with the outcome of subunits, resulting in informative cluster size. When the cluster size is informative, standard statistical procedures that ignore cluster size may produce biased estimates. One attractive framework for modeling data with informative cluster size is the joint modeling approach in which a common set of random effects are shared by both the outcome and cluster size models. In addition to making distributional assumptions on the shared random effects, the joint modeling approach needs to specify the cluster size model. Questions arise as to whether the joint modeling approach is robust to misspecification of the cluster size model. In this paper, we studied both asymptotic and finite-sample characteristics of the maximum likelihood estimators in joint models when the cluster size model is misspecified. We found that using an incorrect distribution for the cluster size may induce small to moderate biases, while using a misspecified functional form for the shared random parameter in the cluster size model results in nearly unbiased estimation of outcome model parameters. We also found that there is little efficiency loss under this model misspecification. A developmental toxicity study was used to motivate the research and to demonstrate the findings.