Optimal Design In Multi-State Models For Clinical Trials

Abstract

Clinical trials are crucial for medical research and evidence-based healthcare. Tradition- ally focused on simple outcomes, many health conditions need more complex analysis to capture various patient states. Multi-state models address this by representing dynamic health transitions as a stochastic process. This research focuses on designing optimal experiments for multi-state models in survival data (i.e. time-to-event data), specifically exploring D-, weighted A-, and Ds- optimal designs for simple two-state model and competing risks model. Both complete (non-censored) data and type-I censored data scenarios with varying levels of censoring are considered. The aim is to optimise clinical trial designs within the multi-state model framework to achieve the most accurate parameter estimation. For the simple multi-state model, random data from the Weibull regression model fits into a nonlinear survival model. For competing risk models, bootstrap sampling methods improve precision and speed. An exchange algorithm constructs exact optimal designs, accommodating both censored and non-censored data. The sample covariance matrix of parameter estimators is derived, and an exchange algorithm is implemented to construct exact optimal designs for both the simple two-state model and the competing risks three-state model. These designs accommodate both censored and non-censored data. Extensive experiments using the developed algorithm, with various initial designs and prior points, consistently show that the optimal design typically includes points at the extremes, with proportions dependent on the optimality criterion and censoring percentage. The convergence of different designs to the same optimal design across experiments provides strong evidence of the optimality of the reported design.