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

Area of Science:

• Biostatistics
• Epidemiology
• Statistical Modeling

Background:

• Biomedical and epidemiological studies often involve clustered data from longitudinal follow-up or repeated sampling.
• Cluster size can be pre-determined or correlated with outcomes, leading to informative cluster size.
• Ignoring informative cluster size in standard statistical methods can bias estimates.

Purpose of the Study:

• To investigate the robustness of joint modeling approaches to cluster size model misspecification.
• To assess the impact of misspecifying the cluster size model on parameter estimation in joint models.
• To evaluate both asymptotic and finite-sample properties of maximum likelihood estimators under misspecification.

Main Methods:

• Utilized a joint modeling framework sharing common random effects for outcome and cluster size models.
• Investigated misspecification of the cluster size model's distribution and functional form.
• Analyzed asymptotic and finite-sample characteristics of maximum likelihood estimators.
• Applied findings to a developmental toxicity study.

Main Results:

• Misspecification of the cluster size distribution can lead to small to moderate biases.
• Misspecifying the functional form of the shared random parameter in the cluster size model results in nearly unbiased outcome model parameters.
• Little efficiency loss was observed even with model misspecification.

Conclusions:

• Joint modeling approaches demonstrate robustness to certain types of cluster size model misspecification, particularly regarding functional form.
• Careful consideration of distributional assumptions in cluster size models is important, though functional form misspecification appears less critical for outcome parameter estimation.
• The findings support the utility of joint modeling in handling informative cluster sizes in complex data structures.