Efficient treatment allocation in two-way nested designs

Optimal allocation to treatments in a sequential multiple assignment randomized trial

One of the main questions in the design of a trial is how many subjects should be assigned to each treatment condition. Previous research has shown that equal randomization is not necessarily the best choice. We study the optimal allocation for a novel trial design, the sequential multiple assignment randomized trial, where subjects receive a sequence of treatments across various stages. A subject's randomization probabilities to treatments in the next stage depend on whether he or she responded to treatment in the current stage. We consider a prototypical sequential multiple assignment randomized trial design with two stages. Within such a design, many pairwise comparisons of treatment sequences can be made, and a multiple-objective optimal design strategy is proposed to consider all such comparisons simultaneously. The optimal design is sought under either a fixed total sample size or a fixed budget. A Shiny App is made available to find the optimal allocations and to evaluate the efficiency of competing designs. As the optimal design depends on the response rates to first-stage treatments, maximin optimal design methodology is used to find robust optimal designs. The proposed methodology is illustrated using a sequential multiple assignment randomized trial example on weight loss management.

Optimal allocations for two treatment comparisons within the proportional odds cumulative logits model

This paper studies optimal treatment allocations for two treatment comparisons when the outcome is ordinal and analyzed by a proportional odds cumulative logits model. The variance of the treatment effect estimator is used as optimality criterion. The optimal design is sought so that this variance is minimal for a given total sample size or a given budget, meaning that the power for the test on treatment effect is maximal, or it is sought so that a required power level is achieved at a minimal total sample size or budget. Results are presented for three, five and seven ordered response categories, three treatment effect sizes and a skewed, bell-shaped or polarized distribution of the response probabilities. The optimal proportion subjects in the intervention condition decreases with the number of response categories and the costs for the intervention relative to those for the control. The relation between the optimal proportion and effect size depends on the distribution of the response probabilities. The widely used balanced design is not always the most efficient; its efficiency as compared to the optimal design decreases with increasing cost ratio. The optimal design is highly robust to misspecification of the response probabilities and treatment effect size. The optimal design methodology is illustrated using two pharmaceutical examples. A Shiny app is available to find the optimal treatment allocation, to evaluate the efficiency of the balanced design and to study the relation between budget or sample size and power.

Optimal Design in Hierarchical Random Effect Models for Individual Prediction with Application in Precision Medicine

Hierarchical random effect models are used for different purposes in clinical research and other areas. In general, the main focus is on population parameters related to the expected treatment effects or group differences among all units of an upper level (e.g. subjects in many settings). Optimal design for estimation of population parameters are well established for many models. However, optimal designs for the prediction for the individual units may be different. Several settings are identified in which individual prediction may be of interest. In this paper, we determine optimal designs for the individual predictions, e.g. in multi-cluster trials or in trials that investigate a new treatment in a number of different subpopulations, and compare them to a conventional balanced design with respect to treatment allocation. Our investigations show that in the case of uncorrelated cluster intercepts and cluster treatments the optimal allocations are far from being balanced if the treatment effects vary strongly as compared to the residual error and more subjects should be recruited to the active (new) treatment. Nevertheless, efficiency loss may be limited resulting in a moderate sample size increase when individual predictions are foreseen with a balanced allocation.

Efficient treatment allocation in 2 × 2 multicenter trials when costs and variances are heterogeneous

At the design stage of a study, it is crucial to compute the sample size needed for treatment effect estimation with maximum precision and power. The optimal design depends on the costs, which may be known at the design stage, and on the outcome variances, which are unknown. A balanced design, optimal for homogeneous costs and variances, is typically used. An alternative to the balanced design is a design optimal for the known and possibly heterogeneous costs, and homogeneous variances, called costs considering design. Both designs suffer from loss of efficiency, compared with optimal designs for heterogeneous costs and variances. For 2 × 2 multicenter trials, we compute the relative efficiency of the balanced and the costs considering designs, relative to the optimal designs. We consider 2 heterogeneous costs and variance scenarios (in 1 scenario, 2 treatment conditions have small and 2 have large costs and variances; in the other scenario, 1 treatment condition has small, 2 have intermediate, and 1 has large costs and variances). Within these scenarios, we examine the relative efficiency of the balanced design and of the costs considering design as a function of the extents of heterogeneity of the costs and of the variances and of their congruence (congruent when the cheapest treatment has the smallest variance, incongruent when the cheapest treatment has the largest variance). We find that the costs considering design is generally more efficient than the balanced design, and we illustrate this theory on a 2 × 2 multicenter trial on lifestyle improvement of patients in general practices.

Efficient treatment allocation in 2 × 2 cluster randomized trials, when costs and variances are heterogeneous

Typically, clusters and individuals in cluster randomized trials are allocated across treatment conditions in a balanced fashion. This is optimal under homogeneous costs and outcome variances. However, both the costs and the variances may be heterogeneous. Then, an unbalanced allocation is more efficient but impractical as the outcome variance is unknown in the design stage of a study. A practical alternative to the balanced design could be a design optimal for known and possibly heterogeneous costs and homogeneous variances. However, when costs and variances are heterogeneous, both designs suffer from loss of efficiency, compared with the optimal design. Focusing on cluster randomized trials with a 2 × 2 design, the relative efficiency of the balanced design and of the design optimal for heterogeneous costs and homogeneous variances is evaluated, relative to the optimal design. We consider two heterogeneous scenarios (two treatment arms with small, and two with large, costs or variances, or one small, two intermediate, and one large costs or variances) at each design level (cluster, individual, and both). Within these scenarios, we compute the relative efficiency of the two designs as a function of the extents of heterogeneity of the costs and variances, and the congruence (the cheapest treatment has the smallest variance) and incongruence (the cheapest treatment has the largest variance) between costs and variances. We find that the design optimal for heterogeneous costs and homogeneous variances is generally more efficient than the balanced design and we illustrate this theory on a trial that examines methods to reduce radiological referrals from general practices. Copyright © 2016 John Wiley & Sons, Ltd.