Sample size and classification error for Bayesian change-point models with unlabelled sub-groups and incomplete...

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Statistical Modeling

Background:

• Many biological and medical processes exhibit changes in trajectory over time.
• Investigating these shape changes, particularly at specific time points (change-points), requires robust study designs.
• Existing models often lack the flexibility to handle subgroup differences and missing data inherent in longitudinal studies.

Purpose of the Study:

• To develop and evaluate a statistical model for detecting change-points in trajectories with distinct subgroups and missing data.
• To assess the impact of sample size on the accuracy of estimating underlying shapes, detecting change-points, and classifying subgroups.
• To provide guidance on study design for investigating processes with potential trajectory shifts.

Main Methods:

• Utilized fixed-effect change-point models, specifically broken-stick models, extended to accommodate two subgroups (change vs. no change).
• Incorporated a missingness model to handle incomplete follow-up data.
• Conducted a simulation study to examine the relationship between sample size and model performance.
• Employed a Bayesian framework with Markov chain Monte Carlo (MCMC) techniques for analysis.

Main Results:

• Even with modest sample sizes (N=500, 50 past change-point), change-points can be reliably detected and estimated.
• The model effectively handles subgroups with different trajectories and accounts for missing data.
• Accuracy of shape estimation and subgroup classification is influenced by sample size and observation error.

Conclusions:

• The proposed extended broken-stick model is suitable for analyzing longitudinal data with change-points, distinct subgroups, and missing observations.
• Effective change-point detection and estimation are achievable even in moderately sized studies.
• The findings offer valuable insights for designing future studies investigating dynamic processes in medicine and ecology.