Bayesian design for dichotomous repeated measurements with autocorrelation

Area of Science:

• Medicine and Health Sciences
• Biostatistics
• Epidemiology

Background:

• Repeatedly measured binary outcomes are common in health research.
• Traditional study designs may lack efficiency across various parameter values.
• Uncertainty in parameter values poses a challenge for optimal study design.

Purpose of the Study:

• Propose Bayesian designs to address parameter uncertainty in repeated binary outcome studies.
• Develop a mixed logistic model allowing for quadratic changes over time.
• Compute Bayesian D-optimal allocations of time points.

Main Methods:

• Utilized a mixed logistic model with quadratic time trends.
• Calculated Bayesian D-optimal allocations considering various priors, costs, and covariance structures.
• Assessed the impact of autocorrelation on optimal design.

Main Results:

• Optimal number of time points increases with the subject-to-measurement cost ratio.
• Optimal design is robust to prior specifications, covariance structures, and autocorrelation levels.
• Four equidistant time points are efficient for cost ratios up to five; five or six for higher ratios.

Conclusions:

• Bayesian optimal designs offer increased efficiency for longitudinal studies with binary outcomes.
• Equidistant time points are generally efficient, with the number depending on cost ratios.
• Application to a respiratory infection study highlights potential efficiency gains.