Optimal designs for epidemiologic longitudinal studies with binary outcomes

Juha Mehtala ,Kari Auranen and Sangita Kulathina have a new paper in Statistical Methods in Medical Research. This considers optimal design of panel studies for binary stochastic processes which are assumed to be time-homogeneous Markov. Optimality is assessed based on the trace of the expected Fisher information. The authors also consider a two-phase design where the time spacing is improved upon after the first stage.

This paper, and also the paper by Hwang and Brookmeyer, restrict attention to equally spaced designs. Potentially, there may be efficiency gains from having unequally spaced observations particularly if equilibrium is not assumed at time 0. Moreover, an adaptive "doctor's care" type design where the gap to the next clinic visit depends on the current state is also likely to give some efficiency gains. There has been relatively little work on design for multi-state models. Clearly the efficiency gains achieved in practice depend on the accuracy of the initial assumptions about the true parameter values, although if a two-phase approach is possible it can militate against this. In complicated studies a simple relationship between expected parameter values and optimal design may not exist but may nevertheless be calculable by bespoke numerical optimization. Perhaps the main problem is that studies are rarely designed with an eventual multi-state model analysis in mind.