Sample size calculators for planning stepped-wedge cluster randomized trials: a review and comparison

Assessment of health promotion action for tuberculosis of end tuberculosis action plan (2019-2022) in China

BACKGROUND

Tuberculosis is a chronic infectious disease that endangers people's health, and China is a country with a high burden of tuberculosis. To accelerate the progress towards ending TB, the Chinese government implemented the End TB Action Plan (2019-2022), which consists of six actions. Among the End TB Action Plan, health promotion was conducted to improve the awareness of TB knowledge among Chinese people. The purpose of this study is to evaluate the effectiveness of implementing TB health promotion activities outlined in the End TB Action Plan, and to provide recommendations for future TB prevention and control plan.

METHODS

A cross-sectional study was conducted in nine Chinese provinces in 2022. A total of 11,920 Chinese people filled out the questionnaire. Logistic regression analysis was used to explore that overall awareness of TB core information is associated with whether they received TB health education.

RESULTS

The study involved 11,920 Chinese participants. The overall awareness rate of the core information of TB was 84.2%, which does not reach the 85% goal of the End TB Action Plan. The single awareness rate that TB is a chronic infectious disease and that the vast majority of TB patients can be cured were 75.3% and 76.0%. Participants who received TB health education had a higher awareness rate of TB core information. Participants who were elderly, retired or had a primary school education or below had poor awareness of the core information of TB. Participants who were elderly, lived in urban areas, were equipment operators or had a primary school education or below received less TB health education. Participants mainly received TB health education through TV (44.6%) and Internet (37.8%), preferred TV, broadcasts or movies (58.9%) and Internet advertising (54.7%). Participants preferred illustrated (46.2%) and audio-visual (44.8%) advertising materials. The common sources used to answer health-related questions on the internet were We-Medias (48.3%) and search engines (38.9%). Participants preferred to use short-form videos (66.8%) and illustrations (53.1%) to answer health-related questions.

CONCLUSIONS

Health promotion action for TB had a positive effect in China, but the awareness of TB was inadequate among Chinese people, and it is necessary to strengthen TB health education for those people. Moreover, TB prevention and control institutions should advertise TB more in audio-visual and illustrated forms on the Internet and audio-visual media. Health-related questions should be published in short-form video and illustrated forms in the We-Media and search engine more.

Sample Size Calculations for Stepped Wedge Designs with Treatment Effects that May Change with the Duration of Time under Intervention

The stepped wedge design is often used to evaluate interventions as they are rolled out across schools, health clinics, communities, or other clusters. Most models used in the design and analysis of stepped wedge trials assume that the intervention effect is immediate and constant over time following implementation of the intervention (the "exposure time"). This is known as the IT (immediate treatment effect) assumption. However, recent research has shown that using methods based on the IT assumption when the treatment effect varies over exposure time can give extremely misleading results. In this manuscript, we discuss the need to carefully specify an appropriate measure of the treatment effect when the IT assumption is violated and we show how a stepped wedge trial can be powered when it is anticipated that the treatment effect will vary as a function of the exposure time. Specifically, we describe how to power a trial when the exposure time indicator (ETI) model of Kenny et al. (Statistics in Medicine, 41, 4311-4339, 2022) is used and the estimand of interest is a weighted average of the time-varying treatment effects. We apply these methods to the ADDRESS-BP trial, a type 3 hybrid implementation study designed to address racial disparities in health care by evaluating a practice-based implementation strategy to reduce hypertension in African American communities.

Multilevel Intervention Stepped Wedge Designs (MLI-SWDs)

Multilevel interventions (MLIs) hold promise for reducing health inequities by intervening at multiple types of social determinants of health consistent with the socioecological model of health. In spite of their potential, methodological challenges related to study design compounded by a lack of tools for sample size calculation inhibit their development. We help address this gap by proposing the Multilevel Intervention Stepped Wedge Design (MLI-SWD), a hybrid experimental design which combines cluster-level (CL) randomization using a Stepped Wedge design (SWD) with independent individual-level (IL) randomization. The MLI-SWD is suitable for MLIs where the IL intervention has a low risk of interference between individuals in the same cluster, and it enables estimation of the component IL and CL treatment effects, their interaction, and the combined intervention effect. The MLI-SWD accommodates cross-sectional and cohort designs as well as both incomplete (clusters are not observed in every study period) and complete observation patterns. We adapt recent work using generalized estimating equations for SWD sample size calculation to the multilevel setting and provide an R package for power and sample size calculation. Furthermore, motivated by our experiences with the ongoing NC Works 4 Health study, we consider how to apply the MLI-SWD when individuals join clusters over the course of the study. This situation arises when unemployment MLIs include IL interventions that are delivered while the individual is unemployed. This extension requires carefully considering whether the study interventions will satisfy additional causal assumptions but could permit randomization in new settings.

Optimal designs using generalized estimating equations in cluster randomized crossover and stepped wedge trials

Cluster randomized crossover and stepped wedge cluster randomized trials are two types of longitudinal cluster randomized trials that leverage both the within- and between-cluster comparisons to estimate the treatment effect and are increasingly used in healthcare delivery and implementation science research. While the variance expressions of estimated treatment effect have been previously developed from the method of generalized estimating equations for analyzing cluster randomized crossover trials and stepped wedge cluster randomized trials, little guidance has been provided for optimal designs to ensure maximum efficiency. Here, an optimal design refers to the combination of optimal cluster-period size and optimal number of clusters that provide the smallest variance of the treatment effect estimator or maximum efficiency under a fixed total budget. In this work, we develop optimal designs for multiple-period cluster randomized crossover trials and stepped wedge cluster randomized trials with continuous outcomes, including both closed-cohort and repeated cross-sectional sampling schemes. Local optimal design algorithms are proposed when the correlation parameters in the working correlation structure are known. MaxiMin optimal design algorithms are proposed when the exact values are unavailable, but investigators may specify a range of correlation values. The closed-form formulae of local optimal design and MaxiMin optimal design are derived for multiple-period cluster randomized crossover trials, where the cluster-period size and number of clusters are decimal. The decimal estimates from closed-form formulae can then be used to investigate the performances of integer estimates from local optimal design and MaxiMin optimal design algorithms. One unique contribution from this work, compared to the previous optimal design research, is that we adopt constrained optimization techniques to obtain integer estimates under the MaxiMin optimal design. To assist practical implementation, we also develop four SAS macros to find local optimal designs and MaxiMin optimal designs.

Maintaining the validity of inference from linear mixed models in stepped-wedge cluster randomized trials under misspecified random-effects structures

Linear mixed models are commonly used in analyzing stepped-wedge cluster randomized trials. A key consideration for analyzing a stepped-wedge cluster randomized trial is accounting for the potentially complex correlation structure, which can be achieved by specifying random-effects. The simplest random effects structure is random intercept but more complex structures such as random cluster-by-period, discrete-time decay, and more recently, the random intervention structure, have been proposed. Specifying appropriate random effects in practice can be challenging: assuming more complex correlation structures may be reasonable but they are vulnerable to computational challenges. To circumvent these challenges, robust variance estimators may be applied to linear mixed models to provide consistent estimators of standard errors of fixed effect parameters in the presence of random-effects misspecification. However, there has been no empirical investigation of robust variance estimators for stepped-wedge cluster randomized trials. In this article, we review six robust variance estimators (both standard and small-sample bias-corrected robust variance estimators) that are available for linear mixed models in R, and then describe a comprehensive simulation study to examine the performance of these robust variance estimators for stepped-wedge cluster randomized trials with a continuous outcome under different data generators. For each data generator, we investigate whether the use of a robust variance estimator with either the random intercept model or the random cluster-by-period model is sufficient to provide valid statistical inference for fixed effect parameters, when these working models are subject to random-effect misspecification. Our results indicate that the random intercept and random cluster-by-period models with robust variance estimators performed adequately. The CR3 robust variance estimator (approximate jackknife) estimator, coupled with the number of clusters minus two degrees of freedom correction, consistently gave the best coverage results, but could be slightly conservative when the number of clusters was below 16. We summarize the implications of our results for the linear mixed model analysis of stepped-wedge cluster randomized trials and offer some practical recommendations on the choice of the analytic model.

Reconsidering stepped wedge cluster randomized trial designs with implementation periods: Fewer sequences or the parallel-group design with baseline and implementation periods are potentially more efficient

BACKGROUND/AIMS

When designing a cluster randomized trial, advantages and disadvantages of tentative designs must be weighed. The stepped wedge design is popular for multiple reasons, including its potential to increase power via improved efficiency relative to a parallel-group design. In many realistic settings, it will take time for clusters to fully implement the intervention. When designing the HEALing (Helping to End Addiction Long-termSM) Communities Study, implementation time was a major consideration, and we examined the efficiency and practicality of three designs. Specifically, a three-sequence stepped wedge design with implementation periods, a corresponding two-sequence modified design that is created by removing the middle sequence, and a parallel-group design with baseline and implementation periods. In this article, we study the relative efficiencies of these specific designs. More generally, we study the relative efficiencies of modified designs when the stepped wedge design with implementation periods has three or more sequences. We also consider different correlation structures.

METHODS

We compare efficiencies of stepped wedge designs with implementation periods consisting of three to nine sequences with a variety of corresponding designs. The three-sequence design is compared to the two-sequence modified design and to the parallel-group design with baseline and implementation periods analysed via analysis of covariance. Stepped wedge designs with implementation periods consisting of four or more sequences are compared to modified designs that remove all or a subset of 'middle' sequences. Efficiencies are based on the use of linear mixed effects models.

RESULTS

In the studied settings, the modified design is more efficient than the three-sequence stepped wedge design with implementation periods. The parallel-group design with baseline and implementation periods with analysis of covariance-based analysis is often more efficient than the three-sequence design. With respect to stepped wedge designs with implementation periods that are comprised of more sequences, there are often corresponding modified designs that improve efficiency. However, use of only the first and last sequences has the potential to be either relatively efficient or inefficient. Relative efficiency is impacted by the strength of the statistical correlation among outcomes from the same cluster; for example, the relative efficiencies of modified designs tend to be greater for smaller cluster auto-correlation values.

CONCLUSION

If a three-sequence stepped wedge design with implementation periods is being considered for a future cluster randomized trial, then a corresponding modified design using only the first and last sequences should be considered if sole focus is on efficiency. However, a parallel-group design with baseline and implementation periods and analysis of covariance-based analysis can be a practical, efficient alternative. For stepped wedge designs with implementation periods and a larger number of sequences, modified versions that remove 'middle' sequences should be considered. Due to the potential sensitivity of design efficiencies, statistical correlation should be carefully considered.

Intravesical Interferon Therapy vs Hyaluronic Acid for Pain Among Female Individuals With Interstitial Cystitis: A Randomized Clinical Trial

Importance

Interstitial cystitis (IC) is a debilitating condition. Although viral infection is a potential etiological cause, few studies have detected the effect of antiviral treatment.

Objective

To determine the efficacy and safety of intravesical interferon instillation compared with hyaluronic acid in female patients with IC.

Design, Setting, and Participants

This double-masked, randomized phase 2/3 clinical trial with parallel group design was implemented from October 2022 to April 2023 and had a 6-month follow-up period. The study was conducted at a single center. Eligible participants were female patients aged 18 to 70 years with a diagnosis of IC for more than 6 months. The last visit took place in October 2023. Data were analyzed between October and November 2023.

Intervention

Patients were randomized 1:1 to receive either intravesical instillation of interferon or hyaluronic acid.

Main Outcomes and Measures

The primary end point was change in visual analog scale pain score. Secondary end points included changes in voiding frequency, functional bladder capacity, symptom index, and global response assessment. Adverse events were closely monitored.

Results

Among the 52 patients, the mean (SD) age was 50.0 (14.1) years and they were randomized to either the interferon group (26 [50%]) or hyaluronic acid (26 [50%]). The visual analog pain score showed the interferon group decreased more significantly than hyaluronic acid (-1.3; 95% CI, -2.3 to -0.3; P = .02) at month 6, with 20 patients (77%) exhibiting a 30% or higher reduction in pain compared with baseline. Secondary end points of voiding frequency, functional bladder capacity, and nocturia episodes showed no significant difference between 2 therapies. However, interferon showed a significantly higher reduction in the Interstitial Cystitis Symptom Index (-3.0; 95% CI, -5.3 to -0.7; P = .01) and the Problem Index (-2.5; 95% CI, -4.5 to -0.4; P = .02) at month 6, with 22 patients (85%) presenting as moderately or markedly improved. The frequencies of adverse events were similar between 2 groups. Only 1 patient discontinued hyaluronic acid because of poor effectiveness.

Conclusions and Relevance

In this randomized clinical trial, female patients with IC could benefit from intravesical interferon therapy, without serious adverse events. These results offered hope for antiviral approaches in IC, but larger-scale, multicenter trials and long-term follow-up should be considered.

Trial Registration

ClinicalTrials.gov Identifier: NCT05912946.

Power calculation for detecting interaction effect in cross-sectional stepped-wedge cluster randomized trials: an important tool for disparity research

BACKGROUND

The stepped-wedge cluster randomized trial (SW-CRT) design has become popular in healthcare research. It is an appealing alternative to traditional cluster randomized trials (CRTs) since the burden of logistical issues and ethical problems can be reduced. Several approaches for sample size determination for the overall treatment effect in the SW-CRT have been proposed. However, in certain situations we are interested in examining the heterogeneity in treatment effect (HTE) between groups instead. This is equivalent to testing the interaction effect. An important example includes the aim to reduce racial disparities through healthcare delivery interventions, where the focus is the interaction between the intervention and race. Sample size determination and power calculation for detecting an interaction effect between the intervention status variable and a key covariate in the SW-CRT study has not been proposed yet for binary outcomes.

METHODS

We utilize the generalized estimating equation (GEE) method for detecting the heterogeneity in treatment effect (HTE). The variance of the estimated interaction effect is approximated based on the GEE method for the marginal models. The power is calculated based on the two-sided Wald test. The Kauermann and Carroll (KC) and the Mancl and DeRouen (MD) methods along with GEE (GEE-KC and GEE-MD) are considered as bias-correction methods.

RESULTS

Among three approaches, GEE has the largest simulated power and GEE-MD has the smallest simulated power. Given cluster size of 120, GEE has over 80% statistical power. When we have a balanced binary covariate (50%), simulated power increases compared to an unbalanced binary covariate (30%). With intermediate effect size of HTE, only cluster sizes of 100 and 120 have more than 80% power using GEE for both correlation structures. With large effect size of HTE, when cluster size is at least 60, all three approaches have more than 80% power. When we compare an increase in cluster size and increase in the number of clusters based on simulated power, the latter has a slight gain in power. When the cluster size changes from 20 to 40 with 20 clusters, power increases from 53.1% to 82.1% for GEE; 50.6% to 79.7% for GEE-KC; and 48.1% to 77.1% for GEE-MD. When the number of clusters changes from 20 to 40 with cluster size of 20, power increases from 53.1% to 82.1% for GEE; 50.6% to 81% for GEE-KC; and 48.1% to 79.8% for GEE-MD.

CONCLUSIONS

We propose three approaches for cluster size determination given the number of clusters for detecting the interaction effect in SW-CRT. GEE and GEE-KC have reasonable operating characteristics for both intermediate and large effect size of HTE.

Planning stepped wedge cluster randomized trials to detect treatment effect heterogeneity

Stepped wedge design is a popular research design that enables a rigorous evaluation of candidate interventions by using a staggered cluster randomization strategy. While analytical methods were developed for designing stepped wedge trials, the prior focus has been solely on testing for the average treatment effect. With a growing interest on formal evaluation of the heterogeneity of treatment effects across patient subpopulations, trial planning efforts need appropriate methods to accurately identify sample sizes or design configurations that can generate evidence for both the average treatment effect and variations in subgroup treatment effects. To fill in that important gap, this article derives novel variance formulas for confirmatory analyses of treatment effect heterogeneity, that are applicable to both cross-sectional and closed-cohort stepped wedge designs. We additionally point out that the same framework can be used for more efficient average treatment effect analyses via covariate adjustment, and allows the use of familiar power formulas for average treatment effect analyses to proceed. Our results further sheds light on optimal design allocations of clusters to maximize the weighted precision for assessing both the average and heterogeneous treatment effects. We apply the new methods to the Lumbar Imaging with Reporting of Epidemiology Trial, and carry out a simulation study to validate our new methods.

Sample size calculations for randomized controlled trials with repeatedly measured continuous variables as primary outcomes need improvements: a cross-sectional study

OBJECTIVES

Randomized controlled trials (RCTs) with repeatedly measured continuous variables as primary outcomes are common. Although statistical methodologies for calculating sample sizes in such trials have been extensively investigated, their practical application remains unclear. This study aims to provide an overview of sample size calculation methods for different research questions (e.g., key time point treatment effect, treatment effect change over time) and evaluate the adequacy of current practices in trial design.

STUDY DESIGN AND SETTING

We conducted a comprehensive search of PubMed to identify RCTs published in core journals in 2019 that utilized repeatedly measured continuous variables as their primary outcomes. Data were extracted using a predefined questionnaire including general study characteristics, primary outcomes, detailed sample size calculation methods, and methods for analyzing the primary outcome. We re-estimated the sample size for trials that provided all relevant parameters.

RESULTS

A total of 168 RCTs were included, with a median of four repeated measurements (interquartile range 3-6) per outcome. In 48 (28.6%) trials, the primary outcome used for sample size calculation differed from the one used in defining the primary outcomes. There were 90 (53.6%) trials exhibited inconsistencies between the hypotheses specified for sample size calculation and those specified for primary analysis. The statistical methods used for sample size calculation in 158 (94.0%) trials did not align with those used for primary analysis. Additionally, only 6 (3.6%) trials accounted for the number of repeated measurements, and 7 (4.2%) trials considered the correlation among these measurements when calculating the sample size. Furthermore, of the 128 (76.2%) trials that considered loss to follow-up, 33 (25.8%) used an incorrect formula (i.e., N∗(1+lose rate) for sample size adjustment. In 53 (49.5%) out of 107 trials, the re-estimated sample size was larger than the reported sample size.

CONCLUSION

The practice of sample size calculation for RCTs with repeatedly measured continuous variables as primary outcomes displayed significant deficiencies, with a notable proportion of trials failed to report essential parameters about repeated measurement required for sample size calculation. Our findings highlight the urgent need to use optimal sample size methods that align with the research hypothesis, primary analysis method, and the form of the primary outcome.

The staircase cluster randomised trial design: A pragmatic alternative to the stepped wedge

This article introduces the 'staircase' design, derived from the zigzag pattern of steps along the diagonal of a stepped wedge design schematic where clusters switch from control to intervention conditions. Unlike a complete stepped wedge design where all participating clusters must collect and provide data for the entire trial duration, clusters in a staircase design are only required to be involved and collect data for a limited number of pre- and post-switch periods. This could alleviate some of the burden on participating clusters, encouraging involvement in the trial and reducing the likelihood of attrition. Staircase designs are already being implemented, although in the absence of a dedicated methodology, approaches to sample size and power calculations have been inconsistent. We provide expressions for the variance of the treatment effect estimator when a linear mixed model for an outcome is assumed for the analysis of staircase designs in order to enable appropriate sample size and power calculations. These include explicit variance expressions for basic staircase designs with one pre- and one post-switch measurement period. We show how the variance of the treatment effect estimator is related to key design parameters and demonstrate power calculations for examples based on a real trial.

Does it decay? Obtaining decaying correlation parameter values from previously analysed cluster randomised trials

A frequently applied assumption in the analysis of data from cluster randomised trials is that the outcomes from all participants within a cluster are equally correlated. That is, the intracluster correlation, which describes the degree of dependence between outcomes from participants in the same cluster, is the same for each pair of participants in a cluster. However, recent work has discussed the importance of allowing for this correlation to decay as the time between the measurement of participants in a cluster increases. Incorrect omission of such a decay can lead to under-powered studies, and confidence intervals for estimated treatment effects can be too narrow or too wide, depending on the characteristics of the design. When planning studies, researchers often rely on previously reported analyses of trials to inform their choice of intracluster correlation. However, most reported analyses of clustered data do not incorporate a correlation decay. Thus, often all that is available are estimates of intracluster correlations obtained under the potentially incorrect assumption of no decay. In this article, we show that it is possible to use intracluster correlation values obtained from models that incorrectly omit a decay to inform plausible choices of decaying correlations. Our focus is on intracluster correlation estimates for continuous outcomes obtained by fitting linear mixed models with exchangeable or block-exchangeable correlation structures. We describe how plausible values for decaying correlations may be obtained given these estimated intracluster correlations. An online app is presented that allows users to obtain plausible values of the decay, which can be used at the trial planning stage to assess the sensitivity of sample size and power calculations to decaying correlation structures.

Comparing analytical strategies for balancing site-level characteristics in stepped-wedge cluster randomized trials: a simulation study

BACKGROUND

Stepped-wedge cluster randomized trials (SWCRTs) are a type of cluster-randomized trial in which clusters are randomized to cross-over to the active intervention sequentially at regular intervals during the study period. For SWCRTs, sequential imbalances of cluster-level characteristics across the random sequence of clusters may lead to biased estimation. Our study aims to examine the effects of balancing cluster-level characteristics in SWCRTs.

METHODS

To quantify the level of cluster-level imbalance, a novel imbalance index was developed based on the Spearman correlation and rank regression of the cluster-level characteristic with the cross-over timepoints. A simulation study was conducted to assess the impact of sequential cluster-level imbalances across different scenarios varying the: number of sites (clusters), sample size, number of cross-over timepoints, site-level intra-cluster correlation coefficient (ICC), and effect sizes. SWCRTs assumed either an immediate "constant" treatment effect, or a gradual "learning" treatment effect which increases over time after crossing over to the active intervention. Key performance metrics included the relative root mean square error (RRMSE) and relative mean bias.

RESULTS

Fully-balanced designs almost always had the highest efficiency, as measured by the RRMSE, regardless of the number of sites, ICC, effect size, or sample sizes at each time for SWCRTs with learning effect. A consistent decreasing trend of efficiency was observed by increasing RRMSE as imbalance increased. For example, for a 12-site study with 20 participants per site/timepoint and ICC of 0.10, between the most balanced and least balanced designs, the RRMSE efficiency loss ranged from 52.5% to 191.9%. In addition, the RRMSE was decreased for larger sample sizes, larger number of sites, smaller ICC, and larger effect sizes. The impact of pre-balancing diminished when there was no learning effect.

CONCLUSION

The impact of pre-balancing on preventing efficiency loss was easily observed when there was a learning effect. This suggests benefit of pre-balancing with respect to impacting factors of treatment effects.

Generalizing the information content for stepped wedge designs: A marginal modeling approach

Stepped wedge trials are increasingly adopted because practical constraints necessitate staggered roll-out. While a complete design requires clusters to collect data in all periods, resource and patient-centered considerations may call for an incomplete stepped wedge design to minimize data collection burden. To study incomplete designs, we expand the metric of information content to discrete outcomes. We operate under a marginal model with general link and variance functions, and derive information content expressions when data elements (cells, sequences, periods) are omitted. We show that the centrosymmetric patterns of information content can hold for discrete outcomes with the variance-stabilizing link function. We perform numerical studies under the canonical link function, and find that while the patterns of information content for cells are approximately centrosymmetric for all examined underlying secular trends, the patterns of information content for sequences or periods are more sensitive to the secular trend, and may be far from centrosymmetric.

Enhancing doctor-patient relationships in community health care institutions: the Patient Oriented Four Habits Model (POFHM) trial-a stepped wedge cluster randomized trial protocol

BACKGROUND

The poor relationship between doctors and patients is a long-standing, global problem. However, current interventions tend to focus on the training of physicians, while patient-targeted interventions still need to be improved. Considering that patients play a significant role in outpatient consultations, we developed a protocol to assess the effectiveness of the Patient Oriented Four Habits Model (POFHM) in improving doctor-patient relationships.

METHODS

A cross-sectional incomplete stepped-wedge cluster randomized trial design will be conducted in 8 primary healthcare institutions (PHCs). Following phase I of "usual care" as control measures for each PHC, either a patient- or doctor-only intervention will be implemented in phase II. In phase III, both patients and doctors will be involved in the intervention. This study will be conducted simultaneously in Nanling County and West Lake District. The primary outcomes will be evaluated after patients complete their visit: (1) patient literacy, (2) sense of control and (3) quality of doctor-patient communication. Finally, a mixed-effects model and subgroup analysis will be used to evaluate the effectiveness of the interventions.

DISCUSSION

Fostering good consultation habits for the patient is a potentially effective strategy to improve the quality of doctor-patient communication. This study evaluates the implementation process and develops a rigorous quality control manual using a theoretical domain framework under the collective culture of China. The results of this trial will provide substantial evidence of the effectiveness of patient-oriented interventions. The POFHM can benefit the PHCs and provide a reference for countries and regions where medical resources are scarce and collectivist cultures dominate.

TRIAL REGISTRATION

AsPredicted #107,282 on Sep 18, 2022; https://aspredicted.org/QST_MHW.

Accounting for complex intracluster correlations in longitudinal cluster randomized trials: a case study in malaria vector control

BACKGROUND

The effectiveness of malaria vector control interventions is often evaluated using cluster randomized trials (CRT) with outcomes assessed using repeated cross-sectional surveys. A key requirement for appropriate design and analysis of longitudinal CRTs is accounting for the intra-cluster correlation coefficient (ICC). In addition to exchangeable correlation (constant ICC over time), correlation structures proposed for longitudinal CRT are block exchangeable (allows a different within- and between-period ICC) and exponential decay (allows between-period ICC to decay exponentially). More flexible correlation structures are available in statistical software packages and, although not formally proposed for longitudinal CRTs, may offer some advantages. Our objectives were to empirically explore the impact of these correlation structures on treatment effect inferences, identify gaps in the methodological literature, and make practical recommendations.

METHODS

We obtained data from a parallel-arm CRT conducted in Tanzania to compare four different types of insecticide-treated bed-nets. Malaria prevalence was assessed in cross-sectional surveys of 45 households in each of 84 villages at baseline, 12-, 18- and 24-months post-randomization. We re-analyzed the data using mixed-effects logistic regression according to a prespecified analysis plan but under five different correlation structures as well as a robust variance estimator under exchangeable correlation and compared the estimated correlations and treatment effects. A proof-of-concept simulation was conducted to explore general conclusions.

RESULTS

The estimated correlation structures varied substantially across different models. The unstructured model was the best-fitting model based on information criteria. Although point estimates and confidence intervals for the treatment effect were similar, allowing for more flexible correlation structures led to different conclusions based on statistical significance. Use of robust variance estimators generally led to wider confidence intervals. Simulation results showed that under-specification can lead to coverage probabilities much lower than nominal levels, but over-specification is more likely to maintain nominal coverage.

CONCLUSION

More flexible correlation structures should not be ruled out in longitudinal CRTs. This may be particularly important in malaria trials where outcomes may fluctuate over time. In the absence of robust methods for selecting the best-fitting correlation structure, researchers should examine sensitivity of results to different assumptions about the ICC and consider robust variance estimators.

Power and sample size analysis for longitudinal mixed models of health in populations exposed to environmental contaminants: a tutorial

BACKGROUND

When evaluating the impact of environmental exposures on human health, study designs often include a series of repeated measurements. The goal is to determine whether populations have different trajectories of the environmental exposure over time. Power analyses for longitudinal mixed models require multiple inputs, including clinically significant differences, standard deviations, and correlations of measurements. Further, methods for power analyses of longitudinal mixed models are complex and often challenging for the non-statistician. We discuss methods for extracting clinically relevant inputs from literature, and explain how to conduct a power analysis that appropriately accounts for longitudinal repeated measures. Finally, we provide careful recommendations for describing complex power analyses in a concise and clear manner.

METHODS

For longitudinal studies of health outcomes from environmental exposures, we show how to [1] conduct a power analysis that aligns with the planned mixed model data analysis, [2] gather the inputs required for the power analysis, and [3] conduct repeated measures power analysis with a highly-cited, validated, free, point-and-click, web-based, open source software platform which was developed specifically for scientists.

RESULTS

As an example, we describe the power analysis for a proposed study of repeated measures of per- and polyfluoroalkyl substances (PFAS) in human blood. We show how to align data analysis and power analysis plan to account for within-participant correlation across repeated measures. We illustrate how to perform a literature review to find inputs for the power analysis. We emphasize the need to examine the sensitivity of the power values by considering standard deviations and differences in means that are smaller and larger than the speculated, literature-based values. Finally, we provide an example power calculation and a summary checklist for describing power and sample size analysis.

CONCLUSIONS

This paper provides a detailed roadmap for conducting and describing power analyses for longitudinal studies of environmental exposures. It provides a template and checklist for those seeking to write power analyses for grant applications.

A general method for calculating power for GEE analysis of complete and incomplete stepped wedge cluster randomized trials

Stepped wedge designs have uni-directional crossovers at randomly assigned time points (steps) where clusters switch from control to intervention condition. Incomplete stepped wedge designs are increasingly used in cluster randomized trials of health care interventions and have periods without data collection due to logistical, resource and patient-centered considerations. The development of sample size formulae for stepped wedge trials has primarily focused on complete designs and continuous responses. Addressing this gap, a general, fast, non-simulation based power procedure is proposed for generalized estimating equations analysis of complete and incomplete stepped wedge designs and its predicted power is compared to simulated power for binary and continuous responses. An extensive set of simulations for six and twelve clusters is based upon the Connect-Home trial with an incomplete stepped wedge design. Results show that empirical test size is well controlled using a t-test with bias-corrected sandwich variance estimator for as few as six clusters. Analytical power agrees well with a simulated power in scenarios with twelve clusters. For six clusters, analytical power is similar to simulated power with estimation using the correctly specified model-based variance estimator. To explore the impact of study design choice on power, the proposed fast GEE power method is applied to the Connect-Home trial design, four alternative incomplete stepped wedge designs and one complete design.