On Robust and Efficient Designs for Risk Estimation in Epidemiological Studies

Best (but oft forgotten) practices: Efficient sample sizes for commonly used trial designs

Designing studies such that they have a high level of power to detect an effect or association of interest is an important tool to improve the quality and reproducibility of findings from such studies. Since resources (research subjects, time, and money) are scarce, it is important to obtain sufficient power with minimum use of such resources. For commonly used randomized trials of the treatment effect on a continuous outcome, designs are presented that minimize the number of subjects or the amount of research budget when aiming for a desired power level. This concerns the optimal allocation of subjects to treatments and, in case of nested designs such as cluster-randomized trials and multicenter trials, also the optimal number of centers versus the number of persons per center. Since such optimal designs require knowledge of parameters of the analysis model that are not known in the design stage, in particular outcome variances, maximin designs are presented. These designs guarantee a prespecified power level for plausible ranges of the unknown parameters and minimize research costs for the worst-case values of these parameters. The focus is on a 2-group parallel design, the AB/BA crossover design, and cluster-randomized and multicenter trials with a continuous outcome. How to calculate sample sizes for maximin designs is illustrated for examples from nutrition. Several computer programs that are helpful in calculating sample sizes for optimal and maximin designs are discussed as well as some results on optimal designs for other types of outcomes.

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.

Maximin optimal designs for cluster randomized trials

We consider design issues for cluster randomized trials (CRTs) with a binary outcome where both unit costs and intraclass correlation coefficients (ICCs) in the two arms may be unequal. We first propose a design that maximizes cost efficiency (CE), defined as the ratio of the precision of the efficacy measure to the study cost. Because such designs can be highly sensitive to the unknown ICCs and the anticipated success rates in the two arms, a local strategy based on a single set of best guesses for the ICCs and success rates can be risky. To mitigate this issue, we propose a maximin optimal design that permits ranges of values to be specified for the success rate and the ICC in each arm. We derive maximin optimal designs for three common measures of the efficacy of the intervention, risk difference, relative risk and odds ratio, and study their properties. Using a real cancer control and prevention trial example, we ascertain the efficiency of the widely used balanced design relative to the maximin optimal design and show that the former can be quite inefficient and less robust to mis-specifications of the ICCs and the success rates in the two arms.

Optimal treatment allocation for placebo-treatment comparisons in trials with discrete-time survival endpoints

In many randomized controlled trials, treatment groups are of equal size, but this is not necessarily the best choice. This paper provides a methodology to calculate optimal treatment allocations for longitudinal trials when we wish to compare multiple treatment groups with a placebo group, and the comparisons may have unequal importance. The focus is on trials with a survival endpoint measured in discrete time. We assume the underlying survival process is Weibull and show that values for the parameters in the Weibull distribution have an impact on the optimal treatment allocation scheme in an interesting way. Additionally, we incorporate different cost considerations at the subject and measurement levels and determine the optimal number of time periods. We also show that when many events occur at the beginning of the trial, fewer time periods are more efficient. As an application, we revisit a risperidone maintenance treatment trial in schizophrenia and use our proposed methodology to redesign it and compare merits of our optimal design.

Higher order response adaptive urn designs for clinical trials with highly successful treatments

We consider a problem of reducing the expected number of treatment failures in trials where the probability of response to treatment is close to 1 and treatments are compared based on log odds ratio. We propose a new class of urn designs for randomization of patients in a clinical trial. The new urn designs target a number of allocation proportions including the allocation proportion that yields the same power as equal allocation but significantly less expected treatment failures. The new design is compared with the doubly adaptively biased coin design, the efficient randomized adaptive design and with equal allocation. The properties of the new class of designs are studied by embedding them into a family of continuous time stochastic processes.

An Introduction to Optimal Design

In this article we give an elementary introduction to optimal design for some basic statistical models. Research questions coming from a project on dyscalculia are used as illustrative examples throughout this article. First, basic design issues are considered for the t-test and simple regression and then extended to the general linear model. Finally, we will outline optimal designs for nonlinear statistical models. As a simple example, logistic regression with a binary explanatory variable is used.

Optimum treatment allocation rules under a variance heterogeneity model

We provide optimal treatment allocation schemes when the outcome variance varies across the treatment groups and our objectives are to estimate treatment effects with equal or unequal interest. Unlike other optimal designs, such as A-optimal designs, the proposed designs can be found without an iterative scheme. We evaluate robustness properties of the optimal designs to mis-specification in the expected variance from each group and identify situations when popular allocation schemes have poor efficiencies. An application to design a randomized rheumatoid arthritis trial is discussed, along with a potential application to design a cancer screening trial when the main outcome is a continuous variable.