On determination of sample size in hierarchical binomial models

Area of Science:

• Biostatistics
• Statistical Modeling
• Hierarchical Models

Background:

• Hierarchical designs are crucial for analyzing data with nested structures, such as patients within institutions.
• Understanding the impact of cluster size and prior distributions is essential for accurate statistical inference.

Purpose of the Study:

• To develop and compare two- and three-stage hierarchical models for discrete response data.
• To provide methods for sample size calculations in multi-institutional studies using these models.
• To evaluate the appropriateness of discharge planning rates in a congestive heart failure patient cohort.

Main Methods:

• Utilized a two-stage model with binomial distribution and a beta distribution for success probabilities.
• Employed a three-stage model incorporating gamma distributions for beta distribution parameters.
• Applied Markov Chain Monte Carlo (MCMC) and Monte Carlo simulations to compute posterior interval lengths.
• Characterized various prior distributions and generated tables for cluster size (n) and number of clusters (k).

Main Results:

• The study provides a framework for sample size determination under both two- and three-stage hierarchical models.
• Demonstrated methods for calculating sample sizes applicable to real-world multi-institutional health studies.
• Offered insights into the performance of different prior distributions within the hierarchical framework.

Conclusions:

• The developed hierarchical models and sample size calculation methods are valuable for designing multi-institutional studies.
• The findings are directly applicable to evaluating health outcomes, such as discharge planning rates for congestive heart failure patients.
• This research enhances the statistical toolkit for complex hierarchical data analysis in healthcare settings.