D‐optimal cohort designs for linear mixed‐effects models

The D-optimality criterion is used to construct optimal designs for different numbers of independent cohorts, which constitute a number of repeated measurements per subject over time. A cost function for longitudinal data is proposed, and the optimality criterion is optimized taking into account the cost of the study. First, an optimal number of design points for a given number of cohorts and cost was identified. Then, an optimal number of cohorts is identified by comparing the relative efficiencies (REs). A numerical study shows that for models describing the trend of a continuous outcome over time by polynomials, the most efficient number of repeated measurements is equal to the sum of the total number of cohorts and the degree of the polynomial in the model. REs of a purely longitudinal cohort design with only one cohort, and mixed longitudinal and cross-sectional cohort designs with more cohorts are compared. The results show that a purely longitudinal cohort design with only one cohort of subjects measured at the optimal time points is the most efficient design. The findings in this paper show that one can obtain a highly efficient design for parameter estimation with only a few repeated measurements. The results of this study will reduce the cost of data collection and ease the logistical burdens in cohort studies.