32 research outputs found
Efficient treatment allocation in two-way nested designs
No full textThe usual treatment allocation in randomized trials and their factorial and nested extensions is balanced, that is, with equal sample size in each treatment arm. This is optimal only when the variances and study costs are the same in both treatment arms, or when the ratio of treatment-specific variances is equal to the ratio of treatment-specific costs. Focusing on 2x2 cluster randomized trials with a quantitative outcome, this entry shows the effects of heterogeneity of variance and costs on the optimal treatment allocation. Essentially, that allocation assigns a larger part of the sample to the treatment arm with the larger variance and the lower costs. Since outcome variances are unknown in the design stage of a trial, references are given to robust design
SamP2CeT: an interactive computer program for sample size and power calculation for two-level cost-effectiveness trials
No full textThe cost-effectiveness of interventions (e.g. new medical therapies or health care technologies) is often evaluated in randomized clinical trials, where individuals are nested within clusters, for instance patients within general practices. In such two-level cost-effectiveness trials, one can randomly assign treatments to individuals within clusters (multicentre trial) or to entire clusters (cluster randomized trial). Such trials need careful planning to evaluate the cost-effectiveness of interventions within the available research resources. The optimal number of clusters and the optimal number of subjects per cluster for both types of cost-effectiveness trials can be determined by using optimal design theory. However, the construction of the optimal design requires information on model parameters, which may be unknown at the planning stage of a trial. To overcome this problem, a maximin strategy is employed. We have developed a computer program SamP2CeT in R to perform these sample size calculations. SamP2CeT provides a graphical user interface which enables the researchers to optimize the numbers of clusters and subjects per cluster in their cost-effectiveness trial as a function of study costs and outcome variances. In case of insufficient knowledge on model parameters, SamP2CeT also provides safe numbers of clusters and subjects per cluster, based on a maximin strategy. SamP2CeT can be used to calculate the smallest budget needed for a user-specified power level, the largest power attainable with a user-specified budget, and also has the facility to calculate the power for a user-specified design. Recent methodological developments on sample size and power calculation for two-level cost-effectiveness trials have been implemented in SamP2CeT. This program is user-friendly, as illustrated for two published cost-effectiveness trials
Calculating sample sizes for cluster randomized trials: We can keep it simple and efficient!
No full textAbstractObjectiveSimple guidelines for calculating efficient sample sizes in cluster randomized trials with unknown intraclass correlation (ICC) and varying cluster sizes.MethodsA simple equation is given for the optimal number of clusters and sample size per cluster. Here, optimal means maximizing power for a given budget or minimizing total cost for a given power. The problems of cluster size variation and specification of the ICC of the outcome are solved in a simple yet efficient way.ResultsThe optimal number of clusters goes up, and the optimal sample size per cluster goes down as the ICC goes up or as the cluster-to-person cost ratio goes down. The available budget, desired power, and effect size only affect the number of clusters and not the sample size per cluster, which is between 7 and 70 for a wide range of cost ratios and ICCs. Power loss because of cluster size variation is compensated by sampling 10% more clusters. The optimal design for the ICC halfway the range of realistic ICC values is a good choice for the first stage of a two-stage design. The second stage is needed only if the first stage shows the ICC to be higher than assumed.ConclusionEfficient sample sizes for cluster randomized trials are easily computed, provided the cost per cluster and cost per person are specified
Maximin design of cluster randomized trials with heterogeneous costs and variances
No full textCluster randomized trials evaluate the effect of a treatment on persons nested within clusters, with clusters being randomly assigned to treatment. The optimal sample size at the cluster and person level depends on the study cost per cluster and per person, and the outcome variance at the cluster and the person level. The variances are unknown in the design stage and can differ between treatment arms. As a solution, this paper presents a Maximin design that maximizes the minimum relative efficiency (relative to the optimal design) over the variance parameter space, for trials with two treatment arms and a quantitative outcome. This maximin relative efficiency design (MMRED) is compared with a published Maximin design which maximizes the minimum efficiency (MMED). Both designs are also compared with the optimal designs for homogeneous costs and variances (balanced design) and heterogeneous costs and homogeneous variances (cost-conscious design), for a range of variances based upon three published trials. Whereas the MMED is balanced under high uncertainty about the treatment-to-control variance ratio, the MMRED then tends towards a balanced budget allocation between arms, leading to an unbalanced sample size allocation if costs are heterogeneous, similar to the cost-conscious design. Further, the MMRED corresponds to an optimal design for an intraclass correlation (ICC) in the lower half of the assumed ICC range (optimistic), whereas the MMED is the optimal design for the maximum ICC within the ICC range (pessimistic). Attention is given to the effect of the Welch-Satterthwaite degrees of freedom for treatment effect testing on the design efficiencies
D-optimality of unequal versus equal cluster sizes for mixed effects linear regression analysis of randomized trials with clusters in one treatment arm
No full textThe efficiency loss due to varying cluster sizes in trials where treatments induce clustering of observations in one of the two treatment arms is examined. Such designs may arise when comparing group therapy to a condition with only medication or a condition not involving any kind of treatment. For maximum likelihood estimation in a mixed effects linear regression, asymptotic relative efficiencies (RE) of unequal versus equal cluster sizes in terms of the D-criterion and Ds-criteria are derived. A Monte Carlo simulation for small sample sizes shows these asymptotic REs to be very accurate for the Ds-criterion of the fixed effects and rather accurate for the D-criterion. Taylor approximations of the asymptotic REs turn out to be accurate and can be used to predict the efficiency loss when planning a trial. The RE usually will be more than 0.94 and, when planning sample sizes, multiplying both the number of clusters in one arm and the number of persons in the other arm by 1/RE is the most cost-efficient way of regaining the efficiency loss.Asymptotic relative efficiency Clustering effects of treatments D-criterion Ds-criterion Optimal design Varying cluster sizes
Commuting travel mode choice among office workers: Comparing an Extended Theory of Planned Behavior model between regions and organizational sectors
No full textLittle is known about how contextual factors influence psychosocial determinants of travel mode choice. The reported study examined the effect of organizational sector and geographical region on an Extended Theory of Planned Behavior (TPB) model of commuting travel mode choice. Multigroup structural equation model analyses were conducted to test for sectoral and regional differences using survey data from office workers of four organizations. The results indicate that intention was very strongly related to commuting travel mode choice. Attitude, descriptive norm, and perceived control were also consistently associated with intentions. Personal norm, injunctive norm, and habit did not have (consistent) significant effects on intention or behavior in the overall models of short-distance and long-distance commuting. Most commute-related beliefs varied between organizational sectors and regions. The relevance of psychosocial determinants in the extended TPB model was generally similar across sectors and regions, except for the effect of injunctive norm which differed between regions. The results suggest that organizational-level as well as regional-level interventions have potential to change commuting travel mode choice. Transforming attitude, descriptive norm and perceived control is likely to be equally useful across contexts, although the potential for change in psychosocial determinants might vary between contexts. (C) 2015 Hong Kong Society for Transportation Studies. Published by Elsevier Ltd. All rights reserved
Optimal two-stage sampling for mean estimation in multilevel populations when cluster size is informative
No full textTo estimate the mean of a quantitative variable in a hierarchical population, it is logistically convenient to sample in two stages (two-stage sampling), i.e. selecting first clusters, and then individuals from the sampled clusters. Allowing cluster size to vary in the population and to be related to the mean of the outcome variable of interest (informative cluster size), the following competing sampling designs are considered: sampling clusters with probability proportional to cluster size, and then the same number of individuals per cluster; drawing clusters with equal probability, and then the same percentage of individuals per cluster; and selecting clusters with equal probability, and then the same number of individuals per cluster. For each design, optimal sample sizes are derived under a budget constraint. The three optimal two-stage sampling designs are compared, in terms of efficiency, with each other and with simple random sampling of individuals. Sampling clusters with probability proportional to size is recommended. To overcome the dependency of the optimal design on unknown nuisance parameters, maximin designs are derived. The results are illustrated, assuming probability proportional to size sampling of clusters, with the planning of a hypothetical survey to compare adolescent alcohol consumption between France and Italy
Efficient treatment allocation in 2x2 multicenter trials when costs and variances are heterogeneous
No full textAt 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 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 multicenter trial on lifestyle improvement of patients in general practices
Efficient design of cluster randomized trials with treatment-dependent costs and treatment-dependent unknown variances
No full textCluster randomized trials evaluate the effect of a treatment on persons nested within clusters, where treatment is randomly assigned to clusters. Current equations for the optimal sample size at the cluster and person level assume that the outcome variances and/or the study costs are known and homogeneous between treatment arms. This paper presents efficient yet robust designs for cluster randomized trials with treatment-dependent costs and treatment-dependent unknown variances, and compares these with 2 practical designs. First, the maximin design (MMD) is derived, which maximizes the minimum efficiency (minimizes the maximum sampling variance) of the treatment effect estimator over a range of treatment-to-control variance ratios. The MMD is then compared with the optimal design for homogeneous variances and costs (balanced design), and with that for homogeneous variances and treatment-dependent costs (cost-considered design). The results show that the balanced design is the MMD if the treatment-to control cost ratio is the same at both design levels (cluster, person) and within the range for the treatment-to-control variance ratio. It still is highly efficient and better than the cost-considered design if the cost ratio is within the range for the squared variance ratio. Outside that range, the cost-considered design is better and highly efficient, but it is not the MMD. An example shows sample size calculation for the MMD, and the computer code (SPSS and R) is provided as supplementary material. The MMD is recommended for trial planning if the study costs are treatment-dependent and homogeneity of variances cannot be assumed
