Sample size estimation for stratified individual and cluster randomized trials with binary outcomes

A pilot randomised controlled trial assessing standard versus dermal patch-augmented rotator cuff repair found no adverse effects and suggest future trials need a minimum of 150 patients

PURPOSE

The aims of this pilot randomised controlled trial (RCT) were to assess the safety and efficacy of a human dermal allograft patch and assess the feasibility of a future RCT comparing retear rate and functional outcome 12 months following standard and augmented double-row rotator cuff repair.

METHODS

 A pilot RCT was conducted among patients undergoing arthroscopic repair of rotator cuff tear measuring between 1 and 5 cm. They were randomised to either augmented (double-row repair with human acellular dermal patch) or standard (double-row repair only). The primary outcome was rotator cuff retear determined on MRI scan at 12 months using the Sugaya's classification (grade 4 or 5). All adverse events were recorded. Functional assessment was performed at baseline and 3, 6, 9, and 12 months post-surgery using clinical outcome scores. Safety was assessed by complications and adverse effects, and feasibility by recruitment, follow-up rate and proof of concept statistical analyses of a future trial.

RESULTS

Between 2017 and 2019, 63 patients were considered for inclusion. Twenty-three patients were excluded, leaving 40 patients (20 per group) in the final study population. The mean tear sizes were 3.0 cm in the augmented and 2.4 cm in the standard group. There was one adhesive capsulitis in the augmented group, with no other adverse events. Retear was observed in 4/18 (22%) of patients in the augmented and 5/18 (28%) in the standard group. In both groups, functional outcome improved significantly which was clinically meaningful for all scores, with no difference between groups. Retear rate increased with tear size. Future trials are feasible but need a minimum total sample size of 150 patients.

CONCLUSION

 Clinically meaningful improved function without adverse effects was found with human acellular dermal patch-augmented cuff repairs.

LEVEL OF EVIDENCE

Level II.

The required size of cluster randomized trials of nonpharmaceutical interventions in epidemic settings

To control the SARS‐CoV‐2 pandemic and future pathogen outbreaks requires an understanding of which nonpharmaceutical interventions are effective at reducing transmission. Observational studies, however, are subject to biases that could erroneously suggest an impact on transmission, even when there is no true effect. Cluster randomized trials permit valid hypothesis tests of the effect of interventions on community transmission. While such trials could be completed in a relatively short period of time, they might require large sample sizes to achieve adequate power. However, the sample sizes required for such tests in outbreak settings are largely undeveloped, leaving unanswered the question of whether these designs are practical. We develop approximate sample size formulae and simulation‐based sample size methods for cluster randomized trials in infectious disease outbreaks. We highlight key relationships between characteristics of transmission and the enrolled communities and the required sample sizes, describe settings where trials powered to detect a meaningful true effect size may be feasible, and provide recommendations for investigators in planning such trials. The approximate formulae and simulation banks may be used by investigators to quickly assess the feasibility of a trial, followed by more detailed methods to more precisely size the trial. For example, we show that community‐scale trials requiring 220 clusters with 100 tested individuals per cluster are powered to identify interventions that reduce transmission by 40% in one generation interval, using parameters identified for SARS‐CoV‐2 transmission. For more modest treatment effects, or when transmission is extremely overdispersed, however, much larger sample sizes are required.

Allowing for stratification in sample size planning of two-arm trials with continuous or binary outcome: Overview and tutorial

More often than not, clinical trials and even nonclinical medical experiments have to be run with observational units sampled from populations to be assumed heterogeneous with respect to covariates associated with the outcome. Relevant covariates which are known prior to randomization are usually categorical in type, and the corresponding subpopulations are called strata. In contrast to randomization which in most cases is performed in a way ensuring approximately constant sample size ratios across the strata, sample size planning is rarely done taking stratification into account. This holds true although the statistical literature provides a reasonably rich repertoire of testing procedures for stratified comparisons between two treatments in a parallel group design. For all of them, at least approximate methods of power calculation are available from which algorithms or even closed-form formulae for required sample sizes can be derived. The objective of this tutorial is to give a systematic review of the most frequently applicable of these methods and to compare them in terms of their efficiency under standard settings. Based on the results, recommendations for the sample size planning of stratified two-arm trials are given.

Power and sample size calculations for cluster randomized trials with binary outcomes when intracluster correlation coefficients vary by treatment arm

BACKGROUND/AIMS

Generalized estimating equations are commonly used to fit logistic regression models to clustered binary data from cluster randomized trials. A commonly used correlation structure assumes that the intracluster correlation coefficient does not vary by treatment arm or other covariates, but the consequences of this assumption are understudied. We aim to evaluate the effect of allowing variation of the intracluster correlation coefficient by treatment or other covariates on the efficiency of analysis and show how to account for such variation in sample size calculations.

METHODS

We develop formulae for the asymptotic variance of the estimated difference in outcome between treatment arms obtained when the true exchangeable correlation structure depends on the treatment arm and the working correlation structure used in the generalized estimating equations analysis is: (i) correctly specified, (ii) independent, or (iii) exchangeable with no dependence on treatment arm. These formulae require a known distribution of cluster sizes; we also develop simplifications for the case when cluster sizes do not vary and approximations that can be used when the first two moments of the cluster size distribution are known. We then extend the results to settings with adjustment for a second binary cluster-level covariate. We provide formulae to calculate the required sample size for cluster randomized trials using these variances.

RESULTS

We show that the asymptotic variance of the estimated difference in outcome between treatment arms using these three working correlation structures is the same if all clusters have the same size, and this asymptotic variance is approximately the same when intracluster correlation coefficient values are small. We illustrate these results using data from a recent cluster randomized trial for infectious disease prevention in which the clusters are groups of households and modest in size (mean 9.6 individuals), with intracluster correlation coefficient values of 0.078 in the control arm and 0.057 in an intervention arm. In this application, we found a negligible difference between the variances calculated using structures (i) and (iii) and only a small increase (typically <5%) for the independent correlation structure (ii), and hence minimal effect on power or sample size requirements. The impact may be larger in other applications if there is greater variation in the ICC between treatment arms or with an additional covariate.

CONCLUSION

The common approach of fitting generalized estimating equations with an exchangeable working correlation structure with a common intracluster correlation coefficient across arms likely does not substantially reduce the power or efficiency of the analysis in the setting of a large number of small or modest-sized clusters, even if the intracluster correlation coefficient varies by treatment arm. Our formulae, however, allow formal evaluation of this and may identify situations in which variation in intracluster correlation coefficient by treatment arm or another binary covariate may have a more substantial impact on power and hence sample size requirements.

Snowball Sampling Study Design for Serosurveys Early in Disease Outbreaks

Serological surveys can provide evidence of cases that were not previously detected, depict the spectrum of disease severity, and estimate the proportion of asymptomatic infections. To capture these parameters, survey sample sizes may need to be very large, especially when the overall infection rate is still low. Therefore, we propose the use of "snowball sampling" to enrich serological surveys by testing contacts of infected persons identified in the early stages of an outbreak. For future emerging pandemics, this observational study sampling design can answer many key questions, such as estimation of the asymptomatic proportion of all infected cases, the probability of a given clinical presentation for a seropositive individual, or the association between characteristics of either the host or the infection and seropositivity among contacts of index individuals. We provide examples, in the context of the coronavirus disease 2019 (COVID-19) pandemic, of studies and analysis methods that use a snowball sample and perform a simulation study that demonstrates scenarios where snowball sampling can answer these questions more efficiently than other sampling schemes. We hope such study designs can be applied to provide valuable information to slow the present pandemic as it enters its next stage and in early stages of future pandemics.

Methods for dealing with unequal cluster sizes in cluster randomized trials: A scoping review

In a cluster-randomized trial (CRT), the number of participants enrolled often varies across clusters. This variation should be considered during both trial design and data analysis to ensure statistical performance goals are achieved. Most methodological literature on the CRT design has assumed equal cluster sizes. This scoping review focuses on methodology for unequal cluster size CRTs. EMBASE, Medline, Google Scholar, MathSciNet and Web of Science databases were searched to identify English-language articles reporting on methodology for unequal cluster size CRTs published until March 2021. We extracted data on the focus of the paper (power calculation, Type I error etc.), the type of CRT, the type and the range of parameter values investigated (number of clusters, mean cluster size, cluster size coefficient of variation, intra-cluster correlation coefficient, etc.), and the main conclusions. Seventy-nine of 5032 identified papers met the inclusion criteria. Papers primarily focused on the parallel-arm CRT (p-CRT, n = 60, 76%) and the stepped-wedge CRT (n = 14, 18%). Roughly 75% of the papers addressed trial design issues (sample size/power calculation) while 25% focused on analysis considerations (Type I error, bias, etc.). The ranges of parameter values explored varied substantially across different studies. Methods for accounting for unequal cluster sizes in the p-CRT have been investigated extensively for Gaussian and binary outcomes. Synthesizing the findings of these works is difficult as the magnitude of impact of the unequal cluster sizes varies substantially across the combinations and ranges of input parameters. Limited investigations have been done for other combinations of a CRT design by outcome type, particularly methodology involving binary outcomes-the most commonly used type of primary outcome in trials. The paucity of methodological papers outside of the p-CRT with Gaussian or binary outcomes highlights the need for further methodological development to fill the gaps.

School-Based Telemedicine Interventions for Asthma: A Systematic Review

BACKGROUND

School health systems are increasingly investing in telemedicine platforms to address acute and chronic illnesses. Asthma, the most common chronic illness in childhood, is of particular interest given its high burden on school absenteeism.

OBJECTIVE

Conduct a systematic review evaluating impact of school-based telemedicine programs on improving asthma-related outcomes.

DATA SOURCES

PubMed, Cochrane CENTRAL, CINAHL, ERIC, PsycINFO, Embase, and Google Scholar.

STUDY ELIGIBILITY CRITERIA

Original research, including quasi-experimental studies, without restriction on the type of telemedicine.

PARTICIPANTS

School-aged pediatric patients with asthma and their families.

INTERVENTIONS

School-based telemedicine.

STUDY APPRAISAL AND SYNTHESIS METHODS

Two authors independently screened each abstract, conducted full-text review, assessed study quality, and extracted information. A third author resolved disagreements.

RESULTS

Of 371 articles identified, 7 were included for the review. Outcomes of interest were asthma symptom-free days, asthma symptom frequency, quality of life, health care utilization, school absences, and spirometry. Four of 7 studies reported significant increases in symptom-free days and/or decrease in symptom frequency. Five of 6 reported increases in at least one quality-of-life metric, 2 of 7 reported a decrease in at least 1 health care utilization metric, 1 of 3 showed reductions in school absences, and 1 of 2 reported improvements in spirometry measures.

LIMITATIONS

Variability in intervention designs and outcome measures make comparisons and quantitative analyses across studies difficult. Only 2 of 7 studies were randomized controlled trials.

CONCLUSIONS AND IMPLICATIONS OF KEY FINDINGS

High-quality evidence supporting the use of school-based telemedicine programs to improve patient outcomes is limited. While available evidence suggests benefit, only 2 comparative trials were identified, and the contribution of telemedicine to these studies' results is unclear.