Study design, rationale and methods of the Revitalising Informal Settlements and their Environments (RISE) study: a cluster randomised controlled trial to evaluate environmental and human health impacts of a water-sensitive intervention in informal settlements in Indonesia and Fiji

INTRODUCTION

Increasing urban populations have led to the growth of informal settlements, with contaminated environments linked to poor human health through a range of interlinked pathways. Here, we describe the design and methods for the Revitalising Informal Settlements and their Environments (RISE) study, a transdisciplinary randomised trial evaluating impacts of an intervention to upgrade urban informal settlements in two Asia-Pacific countries.

METHODS AND ANALYSIS

RISE is a cluster randomised controlled trial among 12 settlements in Makassar, Indonesia, and 12 in Suva, Fiji. Six settlements in each country have been randomised to receive the intervention at the outset; the remainder will serve as controls and be offered intervention delivery after trial completion. The intervention involves a water-sensitive approach, delivering site-specific, modular, decentralised infrastructure primarily aimed at improving health by decreasing exposure to environmental faecal contamination. Consenting households within each informal settlement site have been enrolled, with longitudinal assessment to involve health and well-being surveys, and human and environmental sampling. Primary outcomes will be evaluated in children under 5 years of age and include prevalence and diversity of gastrointestinal pathogens, abundance and diversity of antimicrobial resistance (AMR) genes in gastrointestinal microorganisms and markers of gastrointestinal inflammation. Diverse secondary outcomes include changes in microbial contamination; abundance and diversity of pathogens and AMR genes in environmental samples; impacts on ecological biodiversity and microclimates; mosquito vector abundance; anthropometric assessments, nutrition markers and systemic inflammation in children; caregiver-reported and self-reported health symptoms and healthcare utilisation; and measures of individual and community psychological, emotional and economic well-being. The study aims to provide proof-of-concept evidence to inform policies on upgrading of informal settlements to improve environments and human health and well-being.

ETHICS

Study protocols have been approved by ethics boards at Monash University, Fiji National University and Hasanuddin University.

TRIAL REGISTRATION NUMBER

ACTRN12618000633280; Pre-results.

Methods used to meta-analyse results from interrupted time series studies: A methodological systematic review protocol

Background: Systematic reviews are used to inform healthcare decision making. In reviews that aim to examine the effects of organisational, policy change or public health interventions, or exposures, evidence from interrupted time series (ITS) studies may be included. A core component of many systematic reviews is meta-analysis, which is the statistical synthesis of results across studies. There is currently a lack of guidance informing the choice of meta-analysis methods for combining results from ITS studies, and there have been no studies examining the meta-analysis methods used in practice. This study therefore aims to describe current meta-analysis methods used in a cohort of reviews of ITS studies.

Methods: We will identify the 100 most recent reviews (published between 1 January 2000 and 11 October 2019) that include meta-analyses of ITS studies from a search of eight electronic databases covering several disciplines (public health, psychology, education, economics). Study selection will be undertaken independently by two authors. Data extraction will be undertaken by one author, and for a random sample of the reviews, two authors. From eligible reviews we will extract details at the review level including discipline, type of interruption and any tools used to assess the risk of bias / methodological quality of included ITS studies; at the meta-analytic level we will extract type of outcome, effect measure(s), meta-analytic methods, and any methods used to re-analyse the individual ITS studies. Descriptive statistics will be used to summarise the data.

Conclusions: This review will describe the methods used to meta-analyse results from ITS studies. Results from this review will inform future methods research examining how different meta-analysis methods perform, and ultimately, the development of guidance.

Extending the I-squared statistic to describe treatment effect heterogeneity in cluster, multi-centre randomized trials and individual patient data meta-analysis

Treatment effect heterogeneity is commonly investigated in meta-analyses to identify if treatment effects vary across studies. When conducting an aggregate level data meta-analysis it is common to describe the magnitude of any treatment effect heterogeneity using the I-squared statistic, which is an intuitive and easily understood concept. The effect of a treatment might also vary across clusters in a cluster randomized trial, or across centres in multi-centre randomized trial, and it can be of interest to explore this at the analysis stage. In cross-over trials and other randomized designs, in which clusters or centres are exposed to both treatment and control conditions, this treatment effect heterogeneity can be identified. Here we derive and evaluate a comparable I-squared measure to describe the magnitude of heterogeneity in treatment effects across clusters or centres in randomized trials. We further show how this methodology can be used to estimate treatment effect heterogeneity in an individual patient data meta-analysis.

Creating effective interrupted time series graphs: Review and recommendations

Introduction

Interrupted Time Series (ITS) studies may be used to assess the impact of an interruption, such as an intervention or exposure. The data from such studies are particularly amenable to visual display and, when clearly depicted, can readily show the short‐ and long‐term impact of an interruption. Further, well‐constructed graphs allow data to be extracted using digitizing software, which can facilitate their inclusion in systematic reviews and meta‐analyses.

Aim

We provide recommendations for graphing ITS data, examine the properties of plots presented in ITS studies, and provide examples employing our recommendations.

Methods and results

Graphing recommendations from seminal data visualization resources were adapted for use with ITS studies. The adapted recommendations cover plotting of data points, trend lines, interruptions, additional lines and general graph components. We assessed whether 217 graphs from recently published (2013‐2017) ITS studies met our recommendations and found that 130 graphs (60%) had clearly distinct data points, 100 (46%) had trend lines, and 161 (74%) had a clearly defined interruption. Accurate data extraction (requiring distinct points that align with axis tick marks and labels that allow the points to be interpreted) was possible in only 72 (33%) graphs.

Conclusion

We found that many ITS graphs did not meet our recommendations and could be improved with simple changes. Our proposed recommendations aim to achieve greater standardization and improvement in the display of ITS data, and facilitate re‐use of the data in systematic reviews and meta‐analyses.

Application of data visualization recommendations can improve quality of interrupted time series graphs.

Well‐designed graphs accurately depict time series data, any impact of the interruption, and the results of the analysis.

Well‐designed graphs facilitate data extraction for use in systematic reviews and reproducibility.

An assessment of graphs included in interrupted time series studies (published between 2013 and 2017) found that graphs often do not meet core graphing recommendations.

Opportunities and challenges of clustering, crossing over, and using registry data in the PEPTIC trial

The Proton Pump Inhibitors (PPIs) versus Histamine-2 Receptor Blockers (H2RBs) for Ulcer Prophylaxis Therapy in the Intensive Care Unit (ICU) (PEPTIC) trial is the largest randomised clinical trial ever conducted in the field of intensive care medicine. The potential clinical implications of the trial have been the subject of a previous editorial. Here we focus on the implications of the study for clinical trial science and on the opportunities the study provides for exploratory analyses that will potentially shed further light on the relative safety and efficacy of using PPIs or H2RBs for stress ulcer prophylaxis in the critically ill.

A Stepped Wedge Cluster-Randomized Trial Assessing the Impact of a Riverbank Filtration Intervention to Improve Access to Safe Water on Health in Rural India

Sustainable and low-cost methods for delivery of safe drinking water in resource-limited settings remain suboptimal, which contributes to global diarrhea morbidity. We aimed to assess whether delivery of riverbank filtration-treated water to newly installed water storage tanks (improved quality and access, intervention condition) reduced reported diarrhea in comparison to delivery of unfiltered river water (improved access alone, control condition) in rural Indian villages. We used a stepped wedge cluster-randomized trial (SW-CRT) design involving four clusters (villages). Selection criteria included village size, proximity to a river, and lack of existing or planned community-level safe water sources. All adults and children were eligible for enrollment. All villages started in the control condition and were sequentially randomized to receive the intervention at 3-month intervals. Our primary outcome was 7-day-period prevalence of self- or caregiver-reported diarrhea, measured at 3-month intervals (five time points). Analysis was by intention to treat. Because blinding was not possible, we incorporated questions about symptoms unrelated to water consumption to check response validity (negative control symptoms). We measured outcomes in 2,222 households (9,836 participants). We did not find a measurable reduction in diarrhea post-intervention (RR: 0.98 [95% CI: 0.24-4.09]); possible explanations include low intervention uptake, availability of other safe water sources, low baseline diarrheal prevalence, and reporting fatigue. Our study highlights both the difficulties in evaluating the impact of real-world interventions and the potential for an optimized SW-CRT design to address budgetary, funding, and logistical constraints inherent in such evaluations.

Household Water Storage Management, Hygiene Practices, and Associated Drinking Water Quality in Rural India

Household drinking water storage is commonly practiced in rural India. Fecal contamination may be introduced at the water source, during collection, storage, or access. Within a trial of a community-level water supply intervention, we conducted five quarterly household-level surveys to collect information about water, sanitation, and hygiene practices in rural India. In a random subsample of households, we tested stored drinking water samples for Escherichia coli, concurrently observing storage and access practices. We conducted 9961 surveys and collected 3296 stored water samples. Stored water samples were frequently contaminated with E. coli (69%), and E. coli levels were the highest during the wet season. Most households contributing two or more drinking water samples had detectable E. coli in some (47%) or all (44%) samples. Predictors of stored water contamination with E. coli included consumption of river water and open defecation; consumption of reverse osmosis-treated water and safe water access practices appeared to be protective. Until households can be reached with on-premises continuous safe water supplies, suboptimal household water storage practices are likely to continue. Improvements to source water quality alone are unlikely to prevent exposure to contaminated drinking water unless attention is also given to improving household water storage, access, and sanitation practices.

Sample size and power calculations for open cohort longitudinal cluster randomized trials

When calculating sample size or power for stepped wedge or other types of longitudinal cluster randomized trials, it is critical that the planned sampling structure be accurately specified. One common assumption is that participants will provide measurements in each trial period, that is, a closed cohort, and another is that each participant provides only one measurement during the course of the trial. However some studies have an "open cohort" sampling structure, where participants may provide measurements in variable numbers of periods. To date, sample size calculations for longitudinal cluster randomized trials have not accommodated open cohorts. Feldman and McKinlay (1994) provided some guidance, stating that the participant-level autocorrelation could be varied to account for the degree of overlap in different periods of the study, but did not indicate precisely how to do so. We present sample size and power formulas that allow for open cohorts and discuss the impact of the degree of "openness" on sample size and power. We consider designs where the number of participants in each cluster will be maintained throughout the trial, but individual participants may provide differing numbers of measurements. Our results are a unification of closed cohort and repeated cross-sectional sample results of Hooper et al (2016), and indicate precisely how participant autocorrelation of Feldman and McKinlay should be varied to account for an open cohort sampling structure. We discuss different types of open cohort sampling schemes and how open cohort sampling structure impacts on power in the presence of decaying within-cluster correlations and autoregressive participant-level errors.

Effect of Stress Ulcer Prophylaxis With Proton Pump Inhibitors vs Histamine-2 Receptor Blockers on In-Hospital Mortality Among ICU Patients Receiving Invasive Mechanical Ventilation: The PEPTIC Randomized Clinical Trial

IMPORTANCE

Proton pump inhibitors (PPIs) or histamine-2 receptor blockers (H2RBs) are often prescribed for patients as stress ulcer prophylaxis drugs in the intensive care unit (ICU). The comparative effect of these drugs on mortality is unknown.

OBJECTIVE

To compare in-hospital mortality rates using PPIs vs H2RBs for stress ulcer prophylaxis.

DESIGN, SETTING, AND PARTICIPANTS

Cluster crossover randomized clinical trial conducted at 50 ICUs in 5 countries between August 2016 and January 2019. Patients requiring invasive mechanical ventilation within 24 hours of ICU admission were followed up for 90 days at the hospital.

INTERVENTIONS

Two stress ulcer prophylaxis strategies were compared (preferential use with PPIs vs preferential use with H2RBs). Each ICU used each strategy sequentially for 6 months in random order; 25 ICUs were randomized to the sequence with use of PPIs and then use of H2RBs and 25 ICUs were randomized to the sequence with use of H2RBs and then use of PPIs (13 436 patients randomized by site to PPIs and 13 392 randomized by site to H2RBs).

MAIN OUTCOMES AND MEASURES

The primary outcome was all-cause mortality within 90 days during index hospitalization. Secondary outcomes were clinically important upper gastrointestinal bleeding, Clostridioides difficile infection, and ICU and hospital lengths of stay.

RESULTS

Among 26 982 patients who were randomized, 154 opted out, and 26 828 were analyzed (mean [SD] age, 58 [17.0] years; 9691 [36.1%] were women). There were 26 771 patients (99.2%) included in the mortality analysis; 2459 of 13 415 patients (18.3%) in the PPI group died at the hospital by day 90 and 2333 of 13 356 patients (17.5%) in the H2RB group died at the hospital by day 90 (risk ratio, 1.05 [95% CI, 1.00 to 1.10]; absolute risk difference, 0.93 percentage points [95% CI, -0.01 to 1.88] percentage points; P = .054). An estimated 4.1% of patients randomized by ICU site to PPIs actually received H2RBs and an estimated 20.1% of patients randomized by ICU site to H2RBs actually received PPIs. Clinically important upper gastrointestinal bleeding occurred in 1.3% of the PPI group and 1.8% of the H2RB group (risk ratio, 0.73 [95% CI, 0.57 to 0.92]; absolute risk difference, -0.51 percentage points [95% CI, -0.90 to -0.12 percentage points]; P = .009). Rates of Clostridioides difficile infection and ICU and hospital lengths of stay were not significantly different by treatment group. One adverse event (an allergic reaction) was reported in 1 patient in the PPI group.

CONCLUSIONS AND RELEVANCE

Among ICU patients requiring mechanical ventilation, a strategy of stress ulcer prophylaxis with use of proton pump inhibitors vs histamine-2 receptor blockers resulted in hospital mortality rates of 18.3% vs 17.5%, respectively, a difference that did not reach the significance threshold. However, study interpretation may be limited by crossover in the use of the assigned medication.

TRIAL REGISTRATION

anzctr.org.au Identifier: ACTRN12616000481471.

Long-term effects of alcohol consumption on cognitive function: a systematic review and dose-response analysis of evidence published between 2007 and 2018

BACKGROUND

Understanding the long-term health effects of low to moderate alcohol consumption is important for establishing thresholds for minimising the lifetime risk of harm. Recent research has elucidated the dose-response relationship between alcohol and cardiovascular outcomes, showing an increased risk of harm at levels of intake previously thought to be protective. The primary objective of this review was to examine (1) whether there is a dose-response relationship between levels of alcohol consumption and long-term cognitive effects, and (2) what the effects are of different levels of consumption.

METHODS

The review was conducted according to a pre-specified protocol. Eligible studies were those published 2007 onwards that compared cognitive function among people with different levels of alcohol consumption (measured ≥ 6 months prior to first follow-up of cognition). Major cognitive impairment was excluded. Searches were limited to MEDLINE, Embase and PsycINFO (January 2007 to April 2018). Screening, data extraction, and risk of bias assessment (ROBINS-I) were piloted by three authors, then completed by a single author and checked by a second. Analyses were undertaken to identify and characterise dose-response relationships between levels of alcohol consumption and cognition. Certainty of evidence was assessed using GRADE.

RESULTS

We included 27 cohort studies (from 4786 citations). Eighteen studies examined the effects of alcohol consumption at different levels (risk of bias 16 serious, 2 critical). Ten studies provided data for dose-response analysis. The pooled dose-response relationship showed a maximum standardised mean difference (SMD) indicating slightly better cognition among women with moderate alcohol consumption compared to current non-drinkers (SMD 0.18, 95%CI 0.02 to 0.34, at 14.4 grams/day; 5 studies, very low certainty evidence), and a trivial difference for men (SMD 0.05, 95% CI 0.00 to 0.10, at 19.4 grams/day; 6 studies, very low certainty evidence).

CONCLUSIONS

Major limitations in the design and reporting of included studies made it impossible to discern if the effects of 'lower' levels of alcohol intake are due to bias. Further review of the evidence is unlikely to resolve this issue without meta-analysis of individual patient data from cohort studies that address biases in the selection of participants and classification of alcohol consumption.

Sustained adherence to a Mediterranean diet and physical activity on all-cause mortality in the Melbourne Collaborative Cohort Study: application of the g-formula

Background

Adherence to a traditional Mediterranean diet has been associated with lower mortality and cardiovascular disease risk. The relative importance of diet compared to other lifestyle factors and effects of dietary patterns over time remains unknown.

Methods

We used the parametric G-formula to account for time-dependent confounding, in order to assess the relative importance of diet compared to other lifestyle factors and effects of dietary patterns over time. We included healthy Melbourne Collaborative Cohort Study participants attending a visit during 1995–1999. Questionnaires assessed diet and physical activity at each of three study waves. Deaths were identified by linkage to national registries. We estimated mortality risk over approximately 14 years (1995–2011).

Results

Of 22,213 participants, 2163 (9.7%) died during 13.6 years median follow-up. Sustained high physical activity and adherence to a Mediterranean-style diet resulted in an estimated reduction in all-cause mortality of 1.82 per 100 people (95% confidence interval (CI): 0.03, 3.6). The population attributable fraction was 13% (95% CI: 4, 23%) for sustained high physical activity, 7% (95% CI: − 3, 17%) for sustained adherence to a Mediterranean-style diet and 18% (95% CI: 0, 36%) for their combination.

Conclusions

A small reduction in mortality may be achieved by sustained elevated physical activity levels in healthy middle-aged adults, but there may be comparatively little gain from increasing adherence to a Mediterranean-style diet.

Effect decomposition through multiple causally nonordered mediators in the presence of exposure-induced mediator-outcome confounding

Avin et al (2005) showed that, in the presence of exposure-induced mediator-outcome confounding, decomposing the total causal effect (TCE) using standard conditional exchangeability assumptions is not possible even under a nonparametric structural equation model with all confounders observed. Subsequent research has investigated the assumptions required for such a decomposition to be identifiable and estimable from observed data. One approach was proposed by VanderWeele et al (2014). They decomposed the TCE under three different scenarios: (1) treating the mediator and the exposure-induced confounder as joint mediators; (2) generating path-specific effects albeit without distinguishing between multiple distinct paths through the exposure-induced confounder; and (3) using so-called randomised interventional analogues where sampling values from the distribution of the mediator within the levels of the exposure effectively marginalises over the exposure-induced confounder. In this paper, we extend their approach to the case where there are multiple mediators that do not influence each other directly but which are all influenced by an exposure-induced mediator-outcome confounder. We provide a motivating example and results from a simulation study based on from our work in dental epidemiology featuring the 1982 Pelotas Birth Cohort in Brazil.

The perioperative administration of dexamethasone and infection (PADDI) trial protocol: rationale and design of a pragmatic multicentre non-inferiority study

INTRODUCTION

The intraoperative administration of dexamethasone for prophylaxis against postoperative nausea and vomiting is a common and recommended practice. The safety of the administration of this immunosuppressive agent at a time of significant immunological disruption has not been rigorously evaluated in terms of infective complications.

METHODS/ANALYSIS

This is a pragmatic, multicentre, randomised, controlled, non-inferiority trial. A total of 8880 patients undergoing elective major surgery will be enrolled. Participants will be randomly allocated to receive either dexamethasone 8 mg or placebo intravenously following the induction of anaesthesia in a 1:1 ratio, stratified by centre and diabetes status. Patient enrolment into the trial is ongoing. The primary outcome is surgical site infection at 30 days following surgery, defined according to the Centre for Disease Control criteria.

ETHICS/DISSEMINATION

The PADDI trial has been approved by the ethics committees of over 45 participating sites in Australia, New Zealand, Hong Kong, South Africa and the Netherlands. The trial has been endorsed by the Australia and New Zealand College of Anaesthetists Clinical Trials Network and the Australian Society for Infectious Diseases Clinical Research Network. Participant recruitment began in March 2016 and is expected to be complete in mid-2019. Publication of the results of the PADDI trial is anticipated to occur in early 2020.

TRIAL REGISTRATION NUMBER

ACTRN12614001226695.

How many times should a cluster randomized crossover trial cross over?

Trial planning requires making efficient yet practical design choices. In a cluster randomized crossover trial, clusters of subjects cross back and forth between implementing the control and intervention conditions over the course of the trial, with each crossover marking the start of a new period. If it is possible to set up such a trial with more crossovers, a pertinent question is whether there are efficiency gains from clusters crossing over more frequently, and if these gains are substantial enough to justify the added complexity and cost of implementing more crossovers. We seek to determine the optimal number of crossovers for a fixed trial duration, and then identify other highly efficient designs by allowing the total number of clusters to vary and imposing thresholds on maximum cost and minimum statistical power. Our results pertain to trials with continuous recruitment and a continuous primary outcome, with the treatment effect estimated using a linear mixed model. To account for the similarity between subjects' outcomes within a cluster, we assume a correlation structure in which the correlation decays gradually in a continuous manner as the time between subjects' measurements increases. The optimal design is characterized by crossovers between the control and intervention conditions with each successive subject. However, this design is neither practical nor cost-efficient to implement, nor is it necessary: the gains in efficiency increase sharply in moving from a two-period to a four-period trial design, but approach an asymptote for the scenarios considered as the number of crossovers continues to increase.

Information content of stepped-wedge designs when treatment effect heterogeneity and/or implementation periods are present

Stepped-wedge cluster randomized trials, which randomize clusters of subjects to treatment sequences in which clusters switch from control to intervention conditions, are being conducted with increasing frequency. Due to the real-world nature of this design, methodological and implementation challenges are ubiquitous. To account for such challenges, more complex statistical models to plan studies and analyze data are required. In this paper, we consider stepped-wedge trials that accommodate treatment effect heterogeneity across clusters, implementation periods during which no data are collected, or both treatment effect heterogeneity and implementation periods. Previous work has shown that the sequence-period cells of a stepped-wedge design contribute unequal amounts of information to the estimation of the treatment effect. In this paper, we extend that work by considering the amount of information available for the estimation of the treatment effect in each sequence-period cell, sequence, and period of stepped-wedge trials with more complex designs and outcome models. When either treatment effect heterogeneity and/or implementation periods are present, the pattern of information content of sequence-period cells tends to be clustered around the times of the switch from control to intervention condition, similarly to when these complexities are absent. However, the presence and degree of treatment effect heterogeneity and the number of implementation periods can influence the information content of periods and sequences markedly.

Design characteristics and statistical methods used in interrupted time series studies evaluating public health interventions: protocol for a review

INTRODUCTION

An interrupted time series (ITS) design is an important observational design used to examine the effects of an intervention or exposure. This design has particular utility in public health where it may be impracticable or infeasible to use a randomised trial to evaluate health system-wide policies, or examine the impact of exposures (such as earthquakes). There have been relatively few studies examining the design characteristics and statistical methods used to analyse ITS designs. Further, there is a lack of guidance to inform the design and analysis of ITS studies.This is the first study in a larger project that aims to provide tools and guidance for researchers in the design and analysis of ITS studies. The objectives of this study are to (1) examine and report the design characteristics and statistical methods used in a random sample of contemporary ITS studies examining public health interventions or exposures that impact on health-related outcomes, and (2) create a repository of time series data extracted from ITS studies. Results from this study will inform the remainder of the project which will investigate the performance of a range of commonly used statistical methods, and create a repository of input parameters required for sample size calculation.

METHODS AND ANALYSIS

We will collate 200 ITS studies evaluating public health interventions or the impact of exposures. ITS studies will be identified from a search of the bibliometric database PubMed between the years 2013 and 2017, combined with stratified random sampling. From eligible studies, we will extract study characteristics, details of the statistical models and estimation methods, effect metrics and parameter estimates. Further, we will extract the time series data when available. We will use systematic review methods in the screening, application of inclusion and exclusion criteria, and extraction of data. Descriptive statistics will be used to summarise the data.

ETHICS AND DISSEMINATION

Ethics approval is not required since information will only be extracted from published studies. Dissemination of the results will be through peer-reviewed publications and presentations at conferences. A repository of data extracted from the published ITS studies will be made publicly available.

Accounting for a decaying correlation structure in cluster randomized trials with continuous recruitment

A requirement for calculating sample sizes for cluster randomized trials (CRTs) conducted over multiple periods of time is the specification of a form for the correlation between outcomes of subjects within the same cluster, encoded via the within-cluster correlation structure. Previously proposed within-cluster correlation structures have made strong assumptions; for example, the usual assumption is that correlations between the outcomes of all pairs of subjects are identical ("uniform correlation"). More recently, structures that allow for a decay in correlation between pairs of outcomes measured in different periods have been suggested. However, these structures are overly simple in settings with continuous recruitment and measurement. We propose a more realistic "continuous-time correlation decay" structure whereby correlations between subjects' outcomes decay as the time between these subjects' measurement times increases. We investigate the use of this structure on trial planning in the context of a primary care diabetes trial, where there is evidence of decaying correlation between pairs of patients' outcomes over time. In particular, for a range of different trial designs, we derive the variance of the treatment effect estimator under continuous-time correlation decay and compare this to the variance obtained under uniform correlation. For stepped wedge and cluster randomized crossover designs, incorrectly assuming uniform correlation will underestimate the required sample size under most trial configurations likely to occur in practice. Planning of CRTs requires consideration of the most appropriate within-cluster correlation structure to obtain a suitable sample size.

Correction to: Effectiveness of a new model of primary care management on knee pain and function in patients with knee osteoarthritis: Protocol for THE PARTNER STUDY

After the publication of this protocol [1], our collaborator Prima Health solutions advised us of their intent to withdraw from the study.

Power and sample size requirements for GEE analyses of cluster randomized crossover trials

The cluster randomized crossover design has been proposed to improve efficiency over the traditional parallel cluster randomized design, which often involves a limited number of clusters. In recent years, the cluster randomized crossover design has been increasingly used to evaluate the effectiveness of health care policy or programs, and the interest often lies in quantifying the population-averaged intervention effect. In this paper, we consider the two-treatment two-period crossover design, and develop sample size procedures for continuous and binary outcomes corresponding to a population-averaged model estimated by generalized estimating equations, accounting for both within-period and interperiod correlations. In particular, we show that the required sample size depends on the correlation parameters through an eigenvalue of the within-cluster correlation matrix for continuous outcomes and through two distinct eigenvalues of the correlation matrix for binary outcomes. We demonstrate that the empirical power corresponds well with the predicted power by the proposed formulae for as few as eight clusters, when outcomes are analyzed using the matrix-adjusted estimating equations for the correlation parameters concurrently with a suitable bias-corrected sandwich variance estimator.

Inference for the treatment effect in multiple-period cluster randomised trials when random effect correlation structure is misspecified

Multiple-period cluster randomised trials, such as stepped wedge or cluster cross-over trials, are being conducted with increasing frequency. In the design and analysis of these trials, it is necessary to specify the form of the within-cluster correlation structure, and a common assumption is that the correlation between the outcomes of any pair of subjects within a cluster is identical. More complex models that allow for correlations within a cluster to decay over time have recently been suggested. However, most software packages cannot fit these models. As a result, practitioners may choose a simpler model. We analytically examine the impact of incorrectly omitting a decay in correlation on the variance of the treatment effect estimator and show that misspecification of the within-cluster correlation structure can lead to incorrect conclusions regarding estimated treatment effects for stepped wedge and cluster crossover trials.

Information content of cluster-period cells in stepped wedge trials

Stepped wedge and other multiple-period cluster randomized trials, which collect data from multiple clusters across multiple time periods, are being conducted with increasing frequency; statistical research into these designs has not kept apace. In particular, some stepped wedge designs with missing cluster-period "cells" have been proposed without any formal justification. Indeed there are no general guidelines regarding which cells of a stepped wedge design contribute the least information toward estimation of the treatment effect, and correspondingly which may be preferentially omitted. In this article, we define a metric of the information content of cluster-period cells, entire treatment sequences, and entire periods of the standard stepped wedge design as the increase in variance of the estimator of the treatment effect when that cell, sequence, or period is omitted. We show that the most information-rich cells are those that occur immediately before or after treatment switches, but also that there are additional cells that contribute almost as much to the estimation of the treatment effect. However, the information content patterns depend on the assumed correlation structure for the repeated measurements within a cluster.