Non-sequential augmentation strategies to address separation in logistic regression

Previous research on small sample multi-factor D-optimal designs for the logistic regression model has demonstrated that these designs are prone to encountering separation, a phenomenon where the responses are completely or quasi-completely separable by a hyperplane in the design space. Separation causes the non-existence of maximum likelihood parameter estimates and represents a serious problem for model fitting purposes. In this paper, several non-sequential design augmentation strategies, where additional experimental trials are performed following an initial experiment that has encountered separation, are investigated. Small local and Bayesian D-optimal initial designs are generated for several representative logistic regression models, and a Monte Carlo simulation methodology is then used to investigate the effectiveness of each augmentation strategy in eliminating separation. Results of the simulation study show that augmenting design runs (trials) in regions of maximum prediction variance (MPV) is the most effective strategy for eliminating separation. However, MPV augmentation tends to produce designs with lower D-efficiencies. The paper illustrates that MPV augmentation reliably eliminates separation and can be used in practice to obtain usable parameter estimates for the logistic regression model.