Bayesian design for dichotomous repeated measurements with autocorrelation

In medicine and health sciences, binary outcomes are often measured repeatedly to study their change over time. A problem for such studies is that designs with an optimal efficiency for some parameter values may not be efficient for other values. To handle this problem, we propose Bayesian designs which formally account for the uncertainty in the parameter values for a mixed logistic model which allows quadratic changes over time. Bayesian D-optimal allocations of time points are computed for different priors, costs, covariance structures and values of the autocorrelation. Our results show that the optimal number of time points increases with the subject-to-measurement cost ratio, and that neither the optimal number of time points nor the optimal allocations of time points appear to depend strongly on the prior, the covariance structure or on the size of the autocorrelation. It also appears that for subject-to-measurement cost ratios up to five, four equidistant time points, and for larger cost ratios, five or six equidistant time points are highly efficient. Our results are compared with the actual design of a respiratory infection study in Indonesia and it is shown that, selection of a Bayesian optimal design will increase efficiency, especially for small cost ratios.