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.

Advancing randomized controlled trial methodologies: The place of innovative trial design in eating disorders research.

Randomized controlled trials can be used to generate evidence on the efficacy and safety of new treatments in eating disorders research. Many of the trials previously conducted in this area have been deemed to be of low quality, in part due to a number of practical constraints. This article provides an overview of established and more innovative clinical trial designs, accompanied by pertinent examples, to highlight how design choices can enhance flexibility and improve efficiency of both resource allocation and participant involvement. Trial designs include individually randomized, cluster randomized, and designs with randomizations at multiple time points and/or addressing several research questions (master protocol studies). Design features include the use of adaptations and considerations for pragmatic or registry-based trials. The appropriate choice of trial design, together with rigorous trial conduct, reporting and analysis, can establish high-quality evidence to advance knowledge in the field. It is anticipated that this article will provide a broad and contemporary introduction to trial designs and will help researchers make informed trial design choices for improved testing of new interventions in eating disorders. PUBLIC SIGNIFICANCE: There is a paucity of high quality randomized controlled trials that have been conducted in eating disorders, highlighting the need to identify where efficiency gains in trial design may be possible to advance the eating disorder research field. We provide an overview of some key trial designs and features which may offer solutions to practical constraints and increase trial efficiency.

Comparison of statistical methods used to meta-analyse results from interrupted time series studies: an empirical study.

BACKGROUND: The Interrupted Time Series (ITS) is a robust design for evaluating public health and policy interventions or exposures when randomisation may be infeasible. Several statistical methods are available for the analysis and meta-analysis of ITS studies. We sought to empirically compare available methods when applied to real-world ITS data. METHODS: We sourced ITS data from published meta-analyses to create an online data repository. Each dataset was re-analysed using two ITS estimation methods. The level- and slope-change effect estimates (and standard errors) were calculated and combined using fixed-effect and four random-effects meta-analysis methods. We examined differences in meta-analytic level- and slope-change estimates, their 95% confidence intervals, p-values, and estimates of heterogeneity across the statistical methods. RESULTS: Of 40 eligible meta-analyses, data from 17 meta-analyses including 282 ITS studies were obtained (predominantly investigating the effects of public health interruptions (88%)) and analysed. We found that on average, the meta-analytic effect estimates, their standard errors and between-study variances were not sensitive to meta-analysis method choice, irrespective of the ITS analysis method. However, across ITS analysis methods, for any given meta-analysis, there could be small to moderate differences in meta-analytic effect estimates, and important differences in the meta-analytic standard errors. Furthermore, the confidence interval widths and p-values for the meta-analytic effect estimates varied depending on the choice of confidence interval method and ITS analysis method. CONCLUSIONS: Our empirical study showed that meta-analysis effect estimates, their standard errors, confidence interval widths and p-values can be affected by statistical method choice. These differences may importantly impact interpretations and conclusions of a meta-analysis and suggest that the statistical methods are not interchangeable in practice.

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.

Evaluation of statistical methods used to meta-analyse results from interrupted time series studies: A simulation study.

Interrupted time series (ITS) are often meta-analysed to inform public health and policy decisions but examination of the statistical methods for ITS analysis and meta-analysis in this context is limited. We simulated meta-analyses of ITS studies with continuous outcome data, analysed the studies using segmented linear regression with two estimation methods [ordinary least squares (OLS) and restricted maximum likelihood (REML)], and meta-analysed the immediate level- and slope-change effect estimates using fixed-effect and (multiple) random-effects meta-analysis methods. Simulation design parameters included varying series length; magnitude of lag-1 autocorrelation; magnitude of level- and slope-changes; number of included studies; and, effect size heterogeneity. All meta-analysis methods yielded unbiased estimates of the interruption effects. All random effects meta-analysis methods yielded coverage close to the nominal level, irrespective of the ITS analysis method used and other design parameters. However, heterogeneity was frequently overestimated in scenarios where the ITS study standard errors were underestimated, which occurred for short series or when the ITS analysis method did not appropriately account for autocorrelation. The performance of meta-analysis methods depends on the design and analysis of the included ITS studies. Although all random effects methods performed well in terms of coverage, irrespective of the ITS analysis method, we recommend the use of effect estimates calculated from ITS methods that adjust for autocorrelation when possible. Doing so will likely to lead to more accurate estimates of the heterogeneity variance.

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.

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.

The impact of iterative removal of low-information cluster-period cells from a stepped wedge design.

BACKGROUND: Standard stepped wedge trials, where clusters switch from the control to the intervention condition in a staggered manner, can be costly and burdensome. Recent work has shown that the amount of information contributed by each cluster in each period differs, with some cluster-periods contributing a relatively small amount of information. We investigate the patterns of the information content of cluster-period cells upon iterative removal of low-information cells, assuming a model for continuous outcomes with constant cluster-period size, categorical time period effects, and exchangeable and discrete-time decay intracluster correlation structures. METHODS: We sequentially remove pairs of "centrosymmetric" cluster-period cells from an initially complete stepped wedge design which contribute the least amount of information to the estimation of the treatment effect. At each iteration, we update the information content of the remaining cells, determine the pair of cells with the lowest information content, and repeat this process until the treatment effect cannot be estimated. RESULTS: We demonstrate that as more cells are removed, more information is concentrated in the cells near the time of the treatment switch, and in "hot-spots" in the corners of the design. For the exchangeable correlation structure, removing the cells from these hot-spots leads to a marked reduction in study precision and power, however the impact of this is lessened for the discrete-time decay structure. CONCLUSIONS: Removing cluster-period cells distant from the time of the treatment switch may not lead to large reductions in precision or power, implying that certain incomplete designs may be almost as powerful as complete designs.

Prehospital Tranexamic Acid for Severe Trauma.

BACKGROUND: Whether prehospital administration of tranexamic acid increases the likelihood of survival with a favorable functional outcome among patients with major trauma and suspected trauma-induced coagulopathy who are being treated in advanced trauma systems is uncertain. METHODS: We randomly assigned adults with major trauma who were at risk for trauma-induced coagulopathy to receive tranexamic acid (administered intravenously as a bolus dose of 1 g before hospital admission, followed by a 1-g infusion over a period of 8 hours after arrival at the hospital) or matched placebo. The primary outcome was survival with a favorable functional outcome at 6 months after injury, as assessed with the use of the Glasgow Outcome Scale-Extended (GOS-E). Levels on the GOS-E range from 1 (death) to 8 ("upper good recovery" [no injury-related problems]). We defined survival with a favorable functional outcome as a GOS-E level of 5 ("lower moderate disability") or higher. Secondary outcomes included death from any cause within 28 days and within 6 months after injury. RESULTS: A total of 1310 patients were recruited by 15 emergency medical services in Australia, New Zealand, and Germany. Of these patients, 661 were assigned to receive tranexamic acid, and 646 were assigned to receive placebo; the trial-group assignment was unknown for 3 patients. Survival with a favorable functional outcome at 6 months occurred in 307 of 572 patients (53.7%) in the tranexamic acid group and in 299 of 559 (53.5%) in the placebo group (risk ratio, 1.00; 95% confidence interval [CI], 0.90 to 1.12; P = 0.95). At 28 days after injury, 113 of 653 patients (17.3%) in the tranexamic acid group and 139 of 637 (21.8%) in the placebo group had died (risk ratio, 0.79; 95% CI, 0.63 to 0.99). By 6 months, 123 of 648 patients (19.0%) in the tranexamic acid group and 144 of 629 (22.9%) in the placebo group had died (risk ratio, 0.83; 95% CI, 0.67 to 1.03). The number of serious adverse events, including vascular occlusive events, did not differ meaningfully between the groups. CONCLUSIONS: Among adults with major trauma and suspected trauma-induced coagulopathy who were being treated in advanced trauma systems, prehospital administration of tranexamic acid followed by an infusion over 8 hours did not result in a greater number of patients surviving with a favorable functional outcome at 6 months than placebo. (Funded by the Australian National Health and Medical Research Council and others; PATCH-Trauma ClinicalTrials.gov number, NCT02187120.).

Sample size for partially nested designs and other nested or crossed designs with a continuous outcome when adjusted for baseline.

In a randomized controlled trial, outcomes of different subjects may be independent at baseline, but correlated at a follow-up measurement due to treatment. This treatment-related clustering at follow-up can arise for instance because the treatment is given in a group or because subjects are treated individually but by the same therapist (therapist effect). There is substantial literature on the design and analysis of such trials when estimation of the intervention effect is based on a follow-up measurement (eg, directly after treatment or at a later time point). However, often the baseline measurement of the outcome is highly correlated with the follow-up measurement, and this information can be used in the analysis. For a randomized design with a baseline and a follow-up measurement, we compare sample size requirements for analyses with and without adjustment for this baseline measure. We show that adjusting for baseline reduces required sample size. This reduction depends on the variance of the difference between arms at baseline, the variance of this difference at follow-up, and the correlation between the two. From this, we derive sample size formulas for partially or fully nested designs, and cluster randomized trials with treatment as a partially or fully cross-classified factor. Also, we discuss situations where clusters are already present at baseline or where treatment by cluster interaction is present. For the partially nested design, we work out practical design considerations (eg, use of content-matter input, design factors and optimal allocation ratio) and investigate small sample properties of the sample size formula.

Effect estimates can be accurately calculated with data digitally extracted from interrupted time series graphs.

Interrupted time series (ITS) studies are frequently used to examine the impact of population-level interventions or exposures. Systematic reviews with meta-analyses including ITS designs may inform public health and policy decision-making. Re-analysis of ITS may be required for inclusion in meta-analysis. While publications of ITS rarely provide raw data for re-analysis, graphs are often included, from which time series data can be digitally extracted. However, the accuracy of effect estimates calculated from data digitally extracted from ITS graphs is currently unknown. Forty-three ITS with available datasets and time series graphs were included. Time series data from each graph was extracted by four researchers using digital data extraction software. Data extraction errors were analysed. Segmented linear regression models were fitted to the extracted and provided datasets, from which estimates of immediate level and slope change (and associated statistics) were calculated and compared across the datasets. Although there were some data extraction errors of time points, primarily due to complications in the original graphs, they did not translate into important differences in estimates of interruption effects (and associated statistics). Using digital data extraction to obtain data from ITS graphs should be considered in reviews including ITS. Including these studies in meta-analyses, even with slight inaccuracy, is likely to outweigh the loss of information from non-inclusion.

Mental health and wellbeing of health and aged care workers in Australia, May 2021 - June 2022: a longitudinal cohort study.

OBJECTIVES: To assess the mental health and wellbeing of health and aged care workers in Australia during the second and third years of the coronavirus disease 2019 (COVID-19) pandemic, overall and by occupation group. DESIGN, SETTING, PARTICIPANTS: Longitudinal cohort study of health and aged care workers (ambulance, hospitals, primary care, residential aged care) in Victoria: May-July 2021 (survey 1), October-December 2021 (survey 2), and May-June 2022 (survey 3). MAIN OUTCOME MEASURES: Proportions of respondents (adjusted for age, gender, socio-economic status) reporting moderate to severe symptoms of depression (Patient Health Questionnaire-9, PHQ-9), anxiety (Generalized Anxiety Disorder scale, GAD-7), or post-traumatic stress (Impact of Event Scale-6, IES-6), burnout (abbreviated Maslach Burnout Inventory, aMBI), or high optimism (10-point visual analogue scale); mean scores (adjusted for age, gender, socio-economic status) for wellbeing (Personal Wellbeing Index-Adult, PWI-A) and resilience (Connor Davidson Resilience Scale 2, CD-RISC-2). RESULTS: A total of 1667 people responded to at least one survey (survey 1, 989; survey 2, 1153; survey 3, 993; response rate, 3.3%). Overall, 1211 survey responses were from women (72.6%); most respondents were hospital workers (1289, 77.3%) or ambulance staff (315, 18.9%). The adjusted proportions of respondents who reported moderate to severe symptoms of depression (survey 1, 16.4%; survey 2, 22.6%; survey 3, 19.2%), anxiety (survey 1, 8.8%; survey 2, 16.0%; survey 3, 11.0%), or post-traumatic stress (survey 1, 14.6%; survey 2, 35.1%; survey 3, 14.9%) were each largest for survey 2. The adjusted proportions of participants who reported moderate to severe symptoms of burnout were higher in surveys 2 and 3 than in survey 1, and the proportions who reported high optimism were smaller in surveys 2 and 3 than in survey 1. Adjusted mean scores for wellbeing and resilience were similar at surveys 2 and 3 and lower than at survey 1. The magnitude but not the patterns of change differed by occupation group. CONCLUSION: Burnout was more frequently reported and mean wellbeing and resilience scores were lower in mid-2022 than in mid-2021 for Victorian health and aged care workers who participated in our study. Evidence-based mental health and wellbeing programs for workers in health care organisations are needed. TRIAL REGISTRATION: Australian New Zealand Clinical Trials Registry: ACTRN12621000533897 (observational study; retrospective).

Effect of atorvastatin on skeletal muscles of patients with knee osteoarthritis: Post-hoc analysis of a randomised controlled trial.

Objective: Populations with knee osteoarthritis (KOA) are at increased risk of cardiovascular disease, due to higher prevalence of risk factors including dyslipidaemia, where statins are commonly prescribed. However, the effect of statins on muscles and symptoms in this population is unknown. Thus, this study examined the effect of atorvastatin on muscle properties in patients with symptomatic KOA. Design: Post-hoc analysis of a 2-year multicentre randomised, double-blind, placebo-controlled trial. Setting: Australian community. Participants: Participants aged 40-70 years (mean age 55.7 years, 55.6% female) with KOA who met the American College of Rheumatology clinical criteria received atorvastatin 40 mg daily (n = 151) or placebo (n = 153). Main outcome measures: Levels of creatinine kinase (CK), aspartate transaminase (AST), and alanine transaminase (ALT) at 1, 6, 12, and 24 months; muscle strength (by dynamometry) at 12 and 24 months; vastus medialis cross-sectional area (CSA) on magnetic resonance imaging at 24 months; and self-reported myalgia. Results: There were no significant between-group differences in CK and AST at all timespoints. The atorvastatin group had higher ALT than placebo group at 1 (median 26 vs. 21, p = 0.004) and 6 (25 vs. 22, p = 0.007) months without significant between-group differences at 12 and 24 months. Muscle strength increased in both groups at 24 months without between-group differences [mean 8.2 (95% CI 3.5, 12.9) vs. 5.9 (1.3, 10.4), p = 0.49]. Change in vastus medialis CSA at 24 months favoured the atorvastatin group [0.11 (-0.10, 0.31) vs. -0.23 (-0.43, -0.03), p = 0.02] but of uncertain clinical significance. There was a trend for more myalgia in the atorvastatin group (8/151 vs. 2/153, p = 0.06) over 2 years, mostly occurring within 6 months (7/151 vs. 1/153, p = 0.04). Conclusions: In those with symptomatic KOA, despite a trend for more myalgia, there was no clear evidence of an adverse effect of atorvastatin on muscles, including those most relevant to knee joint health.

The batched stepped wedge design: A design robust to delays in cluster recruitment.

Stepped wedge designs are an increasingly popular variant of longitudinal cluster randomized trial designs, and roll out interventions across clusters in a randomized, but step-wise fashion. In the standard stepped wedge design, assumptions regarding the effect of time on outcomes may require that all clusters start and end trial participation at the same time. This would require ethics approvals and data collection procedures to be in place in all clusters before a stepped wedge trial can start in any cluster. Hence, although stepped wedge designs are useful for testing the impacts of many cluster-based interventions on outcomes, there can be lengthy delays before a trial can commence. In this article, we introduce "batched" stepped wedge designs. Batched stepped wedge designs allow clusters to commence the study in batches, instead of all at once, allowing for staggered cluster recruitment. Like the stepped wedge, the batched stepped wedge rolls out the intervention to all clusters in a randomized and step-wise fashion: a series of self-contained stepped wedge designs. Provided that separate period effects are included for each batch, software for standard stepped wedge sample size calculations can be used. With this time parameterization, in many situations including when linear models are assumed, sample size calculations reduce to the setting of a single stepped wedge design with multiple clusters per sequence. In these situations, sample size calculations will not depend on the delays between the commencement of batches. Hence, the power of batched stepped wedge designs is robust to unexpected delays between batches.

Evaluating the performance of Bayesian and restricted maximum likelihood estimation for stepped wedge cluster randomized trials with a small number of clusters.

BACKGROUND: Stepped wedge trials are an appealing and potentially powerful cluster randomized trial design. However, they are frequently implemented with a small number of clusters. Standard analysis methods for these trials such as a linear mixed model with estimation via maximum likelihood or restricted maximum likelihood (REML) rely on asymptotic properties and have been shown to yield inflated type I error when applied to studies with a small number of clusters. Small-sample methods such as the Kenward-Roger approximation in combination with REML can potentially improve estimation of the fixed effects such as the treatment effect. A Bayesian approach may also be promising for such multilevel models but has not yet seen much application in cluster randomized trials. METHODS: We conducted a simulation study comparing the performance of REML with and without a Kenward-Roger approximation to a Bayesian approach using weakly informative prior distributions on the intracluster correlation parameters. We considered a continuous outcome and a range of stepped wedge trial configurations with between 4 and 40 clusters. To assess method performance we calculated bias and mean squared error for the treatment effect and correlation parameters and the coverage of 95% confidence/credible intervals and relative percent error in model-based standard error for the treatment effect. RESULTS: Both REML with a Kenward-Roger standard error and degrees of freedom correction and the Bayesian method performed similarly well for the estimation of the treatment effect, while intracluster correlation parameter estimates obtained via the Bayesian method were less variable than REML estimates with different relative levels of bias. CONCLUSIONS: The use of REML with a Kenward-Roger approximation may be sufficient for the analysis of stepped wedge cluster randomized trials with a small number of clusters. However, a Bayesian approach with weakly informative prior distributions on the intracluster correlation parameters offers a viable alternative, particularly when there is interest in the probability-based inferences permitted within this paradigm.

Methodological systematic review recommends improvements to conduct and reporting when meta-analyzing interrupted time series studies.

OBJECTIVES: Interrupted Time Series (ITS) are a type of nonrandomized design commonly used to evaluate public health policy interventions, and the impact of exposures, at the population level. Meta-analysis may be used to combine results from ITS across studies (in the context of systematic reviews) or across sites within the same study. We aimed to examine the statistical approaches, methods, and completeness of reporting in reviews that meta-analyze results from ITS. STUDY DESIGN AND SETTINGS: Eight electronic databases were searched to identify reviews (published 2000-2019) that meta-analyzed at least two ITS. Characteristics of the included reviews, the statistical methods used to analyze the ITS and meta-analyze their results, effect measures, and risk of bias assessment tools were extracted. RESULTS: Of the 4213 identified records, 54 reviews were included. Nearly all reviews (94%) used two-stage meta-analysis, most commonly fitting a random effects model (69%). Among the 41 reviews that re-analyzed the ITS, linear regression (39%) and ARIMA (20%) were most commonly used; 38% adjusted for autocorrelation. The most common effect measure meta-analyzed was an immediate level-change (46/54). Reporting of the statistical methods and ITS characteristics was often incomplete. CONCLUSION: Improvement is needed in the conduct and reporting of reviews that meta-analyze results from ITS.

Is antibiotic treatment effective in the management of chronic low back pain with disc herniation? Study protocol for a randomised controlled trial.

BACKGROUND: There has been immense interest and debate regarding the effectiveness of antibiotic treatment for chronic low back pain. Two randomised controlled trials have examined the efficacy of antibiotics for chronic low back pain with disc herniation and Modic changes, but have reported conflicting results. The aim of this double-blind, randomised, placebo-controlled trial is to determine the efficacy of antibiotic treatment in a broader patient subgroup of chronic low back pain with disc herniation and investigate whether the presence of Modic changes predicts response to antibiotic therapy. METHODS: One hundred and seventy individuals with chronic low back pain will be recruited through hospital and private medical and allied health clinics; advertising in national, community and social media; and posting of flyers in community locations. They will be randomly allocated to receive either amoxicillin-clavulanate (500 mg/125 mg) twice per day for 90 days or placebo. The primary outcome measure of pain intensity will be assessed using the Low Back Pain Rating scale and a 100-mm visual analogue scale at 12 months. Secondary measures of self-reported low back disability and work absence and hindrance will also be examined, and an economic analysis will be conducted. Intention-to-treat analyses will be performed. DISCUSSION: There is uncertainty about whether antibiotic treatment is effective for chronic low back pain and, if effective, which patient subgroup is most likely to respond. We will conduct a clinical trial to investigate the efficacy of antibiotics compared with placebo in individuals with chronic low back pain and a disc herniation. Our findings will provide high-quality evidence to assist in answering these questions. TRIAL REGISTRATION: Australian New Zealand Clinical Trials Registry ACTRN12615000958583 . Registered on 11 September 2015.

Inference for the treatment effect in longitudinal cluster randomized trials when treatment effect heterogeneity is ignored.

In cluster-randomized trials, sometimes the effect of the intervention being studied differs between clusters, commonly referred to as treatment effect heterogeneity. In the analysis of stepped wedge and cluster-randomized crossover trials, it is possible to include terms in outcome regression models to allow for such treatment effect heterogeneity yet this is not frequently considered. Outside of some simulation studies of specific cases where the outcome is binary, the impact of failing to include terms for treatment effect heterogeneity on the variance of the treatment effect estimator is unknown. We analytically examine the impact of failing to include terms for treatment effect heterogeneity on the variance of the treatment effect estimator, when outcomes are continuous. Using analysis of variance and feasible generalized least squares we provide expressions for this variance. For both the cluster-randomized crossover design and the stepped wedge design, our analytic derivations indicate that failing to include treatment effect heterogeneity results in the estimates for variance of the treatment effect that are too small, leading to inflation of type I error rates. We therefore recommend assessing the sensitivity of sample size calculations and conclusions drawn from the analysis of cluster randomized trials to the inclusion of treatment effect heterogeneity.

Evaluation of statistical methods used in the analysis of interrupted time series studies: a simulation study.

BACKGROUND: Interrupted time series (ITS) studies are frequently used to evaluate the effects of population-level interventions or exposures. However, examination of the performance of statistical methods for this design has received relatively little attention. METHODS: We simulated continuous data to compare the performance of a set of statistical methods under a range of scenarios which included different level and slope changes, varying lengths of series and magnitudes of lag-1 autocorrelation. We also examined the performance of the Durbin-Watson (DW) test for detecting autocorrelation. RESULTS: All methods yielded unbiased estimates of the level and slope changes over all scenarios. The magnitude of autocorrelation was underestimated by all methods, however, restricted maximum likelihood (REML) yielded the least biased estimates. Underestimation of autocorrelation led to standard errors that were too small and coverage less than the nominal 95%. All methods performed better with longer time series, except for ordinary least squares (OLS) in the presence of autocorrelation and Newey-West for high values of autocorrelation. The DW test for the presence of autocorrelation performed poorly except for long series and large autocorrelation. CONCLUSIONS: From the methods evaluated, OLS was the preferred method in series with fewer than 12 points, while in longer series, REML was preferred. The DW test should not be relied upon to detect autocorrelation, except when the series is long. Care is needed when interpreting results from all methods, given confidence intervals will generally be too narrow. Further research is required to develop better performing methods for ITS, especially for short series.

Completeness of reporting and risks of overstating impact in cluster randomised trials: a systematic review.

Overstating the impact of interventions through incomplete or inaccurate reporting can lead to inappropriate scale-up of interventions with low impact. Accurate reporting of the impact of interventions is of great importance in global health research to protect scarce resources. In global health, the cluster randomised trial design is commonly used to evaluate complex, multicomponent interventions, and outcomes are often binary. Complete reporting of impact for binary outcomes means reporting both relative and absolute measures. We did a systematic review to assess reporting practices and potential to overstate impact in contemporary cluster randomised trials with binary primary outcome. We included all reports registered in the Cochrane Central Register of Controlled Trials of two-arm parallel cluster randomised trials with at least one binary primary outcome that were published in 2017. Of 73 cluster randomised trials, most (60 [82%]) showed incomplete reporting. Of 64 cluster randomised trials for which it was possible to evaluate, most (40 [63%]) reported results in such a way that impact could be overstated. Care is needed to report complete evidence of impact for the many interventions evaluated using the cluster randomised trial design worldwide.