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Design and analysis of trials with a partially nested design and a binary outcome measure.

ABSTRACT: Where treatments are administered to groups of patients or delivered by therapists, outcomes for patients in the same group or treated by the same therapist may be more similar, leading to clustering. Trials of such treatments should take account of this effect. Where such a treatment is compared with an un-clustered treatment, the trial has a partially nested design. This paper compares statistical methods for this design where the outcome is binary. Investigation of consistency reveals that a random coefficient model with a random effect for group or therapist is not consistent with other methods for a null treatment effect, and so this model is not recommended for this design. Small sample performance of a cluster-adjusted test of proportions, a summary measures test and logistic generalised estimating equations and random intercept models are investigated through simulation. The expected treatment effect is biased for the logistic models. Empirical test size of two-sided tests is raised only slightly, but there are substantial biases for one-sided tests. Three formulae are proposed for calculating sample size and power based on (i) the difference of proportions, (ii) the log-odds ratio or (iii) the arc-sine transformation of proportions. Calculated power from these formulae is compared with empirical power from a simulations study. Logistic models appeared to perform better than those based on proportions with the likelihood ratio test performing best in the range of scenarios considered. For these analyses, the log-odds ratio method of calculation of power gave an approximate lower limit for empirical power.

SUBMITTER: Roberts C

PROVIDER: S-EPMC4949566 | biostudies-literature | 2016 May

REPOSITORIES: biostudies-literature

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Design and analysis of trials with a partially nested design and a binary outcome measure.

Roberts Chris C Batistatou Evridiki E Roberts Stephen A SA

Statistics in medicine 20151215 10

Where treatments are administered to groups of patients or delivered by therapists, outcomes for patients in the same group or treated by the same therapist may be more similar, leading to clustering. Trials of such treatments should take account of this effect. Where such a treatment is compared with an un-clustered treatment, the trial has a partially nested design. This paper compares statistical methods for this design where the outcome is binary. Investigation of consistency reveals that a ...[more]

PMID: 26670388

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Project description:BACKGROUND:In individually randomised trials we might expect interventions delivered in groups or by care providers to result in clustering of outcomes for participants treated in the same group or by the same care provider. In partially nested randomised controlled trials (pnRCTs) this clustering only occurs in one trial arm, commonly the intervention arm. It is important to measure and account for between-cluster variability in trial design and analysis. We compare analysis approaches for pnRCTs with continuous outcomes, investigating the impact on statistical inference of cluster sizes, coding of the non-clustered arm, intracluster correlation coefficient (ICCs), and differential variance between intervention and control arm, and provide recommendations for analysis. METHODS:We performed a simulation study assessing the performance of six analysis approaches for a two-arm pnRCT with a continuous outcome. These include: linear regression model; fully clustered mixed-effects model with singleton clusters in control arm; fully clustered mixed-effects model with one large cluster in control arm; fully clustered mixed-effects model with pseudo clusters in control arm; partially nested homoscedastic mixed effects model, and partially nested heteroscedastic mixed effects model. We varied the cluster size, number of clusters, ICC, and individual variance between the two trial arms. RESULTS:All models provided unbiased intervention effect estimates. In the partially nested mixed-effects models, methods for classifying the non-clustered control arm had negligible impact. Failure to account for even small ICCs resulted in inflated Type I error rates and over-coverage of confidence intervals. Fully clustered mixed effects models provided poor control of the Type I error rates and biased ICC estimates. The heteroscedastic partially nested mixed-effects model maintained relatively good control of Type I error rates, unbiased ICC estimation, and did not noticeably reduce power even with homoscedastic individual variances across arms. CONCLUSIONS:In general, we recommend the use of a heteroscedastic partially nested mixed-effects model, which models the clustering in only one arm, for continuous outcomes similar to those generated under the scenarios of our simulations study. However, with few clusters (3-6), small cluster sizes (5-10), and small ICC (?0.05) this model underestimates Type I error rates and there is no optimal model.

Project description:BackgroundIn phase II trials, the most efficacious dose is usually not known. Moreover, given limited resources, it is difficult to robustly identify a dose while also testing for a signal of efficacy that would support a phase III trial. Recent designs have sought to be more efficient by exploring multiple doses through the use of adaptive strategies. However, the added flexibility may potentially increase the risk of making incorrect assumptions and reduce the total amount of information available across the dose range as a function of imbalanced sample size.MethodsTo balance these challenges, a novel placebo-controlled design is presented in which a restricted Bayesian response adaptive randomization (RAR) is used to allocate a majority of subjects to the optimal dose of active drug, defined as the dose with the lowest probability of poor outcome. However, the allocation between subjects who receive active drug or placebo is held constant to retain the maximum possible power for a hypothesis test of overall efficacy comparing the optimal dose to placebo. The design properties and optimization of the design are presented in the context of a phase II trial for subarachnoid hemorrhage.ResultsFor a fixed total sample size, a trade-off exists between the ability to select the optimal dose and the probability of rejecting the null hypothesis. This relationship is modified by the allocation ratio between active and control subjects, the choice of RAR algorithm, and the number of subjects allocated to an initial fixed allocation period. While a responsive RAR algorithm improves the ability to select the correct dose, there is an increased risk of assigning more subjects to a worse arm as a function of ephemeral trends in the data. A subarachnoid treatment trial is used to illustrate how this design can be customized for specific objectives and available data.ConclusionsBayesian adaptive designs are a flexible approach to addressing multiple questions surrounding the optimal dose for treatment efficacy within the context of limited resources. While the design is general enough to apply to many situations, future work is needed to address interim analyses and the incorporation of models for dose response.

Project description:OBJECTIVE:Randomised controlled trials (RCT) are the gold standard to provide unbiased data. However, when patients have a treatment preference, randomisation may influence participation and outcomes (eg, external and internal validity). The aim of this study was to assess the influence of patients' preference in RCTs by analysing partially randomised patient preference trials (RPPT); an RCT and preference cohort combined. DESIGN:Systematic review and meta-analyses. DATA SOURCES:MEDLINE, Embase, PsycINFO and the Cochrane Library. ELIGIBILITY CRITERIA FOR SELECTING STUDIES:RPPTs published between January 2005 and October 2018 reporting on allocation of patients to randomised and preference cohorts were included. DATA EXTRACTION AND SYNTHESIS:Two independent reviewers extracted data. The main outcomes were the difference in external validity (participation and baseline characteristics) and internal validity (lost to follow-up, crossover and the primary outcome) between the randomised and the preference cohort within each RPPT, compared in a meta-regression using a Wald test. Risk of bias was not assessed, as no quality assessment for RPPTs has yet been developed. RESULTS:In total, 117 of 3734 identified articles met screening criteria and 44 were eligible (24 873 patients). The participation rate in RPPTs was >95% in 14 trials (range: 48%-100%) and the randomisation refusal rate was >50% in 26 trials (range: 19%-99%). Higher education, female, older age, race and prior experience with one treatment arm were characteristics of patients declining randomisation. The lost to follow-up and cross-over rate were significantly higher in the randomised cohort compared with the preference cohort. Following the meta-analysis, the reported primary outcomes were comparable between both cohorts of the RPPTs, mean difference 0.093 (95% CI -0.178 to 0.364, p=0.502). CONCLUSIONS:Patients' preference led to a substantial proportion of a specific patient group refusing randomisation, while it did not influence the primary outcome within an RPPT. Therefore, RPPTs could increase external validity without compromising the internal validity compared with RCTs. PROSPERO REGISTRATION NUMBER:CRD42019094438.

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Design and analysis of trials with a partially nested design and a binary outcome measure.

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Design and analysis of trials with a partially nested design and a binary outcome measure.

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