Effect of Dropout on the Efficiency of Ds-Optimal Designs for Linear Mixed Models

Optimal designs are a class of experimental designs that are efficient with respect to some statistical criterion. Two types of optimal designs are considered in the study. D-optimal designs are designs that minimize the generalized variance of a model's estimated parameters. Ds-optimal designs are a class of D-optimal experimental designs that are useful when the researcher is interested in estimating a subset of parameters in a given model. For a specific parameter, Ds-optimal designs would be more efficient than D-optimal designs. Although the loss in efficiency of D-optimal designs relative to Ds-optimal designs have been examined in the past literature, past research did not consider the cases where there are missing observations.;Given that missing observations are ubiquitous in longitudinal studies due to dropout, the current study examines the loss in efficiency when D-optimal designs are used instead of Ds-optimal designs for data with missing observations. Results indicate that in general, location of Ds-optimal design points with dropout will shift closer towards the location of the D-optimal designs with complete data, compared to D-optimal design points with dropout. The D-optimal design with complete data corresponds with the smallest variance covariance matrix. For the data with dropout, the variance covariance matrix of the Ds-optimal design is closer in size to that of D-optimal design with complete data compared to that of D-optimal design with dropout. For both designs with dropout, efficiency loss is moderate.