A randomized trial of expedited intra-arrest transfer versus more extended on-scene resuscitation for refractory out of hospital cardiac arrest: Rationale and design of the EVIDENCE trial.

BACKGROUND: Refractory Out of Hospital Cardiac Arrest (r-OHCA) is common and the benefit versus harm of intra-arrest transport of patients to hospital is not clear. OBJECTIVE: To assess the rate of survival to hospital discharge in adult patients with r-OHCA, initial rhythm pulseless ventricular tachycardia (VT)/ventricular fibrillation (VF) or Pulseless Electrical Activity (PEA) treated with 1 of 2 locally accepted standards of care:1 expedited transport from scene; or2 ongoing advanced life support (ALS) resuscitation on-scene. HYPOTHESIS: We hypothesize that expedited transport from scene in r-OHCA improves survival with favorable neurological status/outcome. METHODS/DESIGN: Phase III, multi-center, partially blinded, prospective, intention-to-treat, safety and efficacy clinical trial with contemporaneous registry of patient ineligible for the clinical trial. Eligible patients for inclusion are adults with witnessed r-OHCA; estimated age 18 to 70, assumed medical cause with immediate bystander cardiopulmonary resuscitation (CPR); initial rhythm of VF/pulseless VT, or PEA; no return of spontaneous circulation following 3 shocks and/or 15 minutes of professional on-scene resuscitation; with mechanical CPR available. Two hundred patients will be randomized in a 1:1 ratio to either expedited transport from scene or ongoing ALS at the scene of cardiac arrest. SETTING: Two urban regions in NSW Australia. OUTCOMES: Primary: survival to hospital discharge with cerebral performance category (CPC) 1 or 2. Secondary: safety, survival, prognostic factors, use of ECMO supported CPR and functional assessment at hospital discharge and 4 weeks and 6 months, quality of life, healthcare use and cost-effectiveness. CONCLUSIONS: The EVIDENCE trial will determine the potential risks and benefits of an expedited transport from scene of cardiac arrest.

Confidence distributions for treatment effects in clinical trials: Posteriors without priors.

An attractive feature of using a Bayesian analysis for a clinical trial is that knowledge and uncertainty about the treatment effect is summarized in a posterior probability distribution. Researchers often find probability statements about treatment effects highly intuitive and the fact that this is not accommodated in frequentist inference is a disadvantage. At the same time, the requirement to specify a prior distribution in order to obtain a posterior distribution is sometimes an artificial process that may introduce subjectivity or complexity into the analysis. This paper considers a compromise involving confidence distributions, which are probability distributions that summarize uncertainty about the treatment effect without the need for a prior distribution and in a way that is fully compatible with frequentist inference. The concept of a confidence distribution provides a posterior-like probability distribution that is distinct from, but exists in tandem with, the relative frequency interpretation of probability used in frequentist inference. Although they have been discussed for decades, confidence distributions are not well known among clinical trial statisticians and the goal of this paper is to discuss their use in analyzing treatment effects from randomized trials. As well as providing an introduction to confidence distributions, some illustrative examples relevant to clinical trials are presented, along with various case studies based on real clinical trials. It is recommended that trial statisticians consider presenting confidence distributions for treatment effects when reporting analyses of clinical trials.

Importance of sequential methods in meta-analysis: implications for postoperative mortality, delirium, and stroke management.

Trial sequential analysis is an adaptation of frequentist sequential methods that can be used to improve inferences from meta-analysis. Trial sequential analysis can help preserve type I and type II error rates at desired levels for analyses conducted before the required information size. Through three case studies recently published in the British Journal of Anaesthesia, we show how trial sequential analysis can inform the interpretation of meta-analyses. Limitations of trial sequential analysis, which also include those of the meta-analysis to which it is applied, must be carefully considered alongside its benefits.

Pre- and on-treatment lactate dehydrogenase as a prognostic and predictive biomarker in advanced non-small cell lung cancer.

BACKGROUND: The survival outcomes of patients with advanced non-small cell lung cancer (NSCLC) treated with immune checkpoint inhibitors (ICIs) are variable. This study investigated whether pre- and on-treatment lactate dehydrogenase (LDH) could better prognosticate and select patients for ICI therapy. METHODS: Using data from the POPLAR and OAK trials of atezolizumab versus docetaxel in previously treated advanced NSCLC, the authors assessed the prognostic and predictive value of pretreatment LDH (less than or equal to vs greater than the upper limit of normal). They further examined changes in on-treatment LDH by performing landmark analyses and estimated overall survival (OS) distributions according to the LDH level stratified by the response category (complete response [CR]/partial response [PR] vs stable disease [SD]). They repeated pretreatment analyses in subgroups defined by the programmed death ligand 1 (PD-L1) status. RESULTS: This study included 1327 patients with available pretreatment LDH. Elevated pretreatment LDH was associated with an adverse prognosis regardless of treatment (hazard ratio [HR] for atezolizumab OS, 1.49; P = .0001; HR for docetaxel OS, 1.30; P = .004; P for treatment by LDH interaction = .28). Findings for elevated pretreatment LDH were similar for patients with positive PD-L1 expression treated with atezolizumab. Persistently elevated on-treatment LDH was associated with a 1.3- to 2.8-fold increased risk of death at weeks 6, 12, 18, and 24 regardless of treatment. Elevated LDH at 6 weeks was associated with significantly shorter OS regardless of radiological response (HR for CR/PR, 2.10; P = .04; HR for SD, 1.50; P < .01), with similar findings observed at 12 weeks. CONCLUSIONS: In previously treated advanced NSCLC, elevated pretreatment LDH is an independent adverse prognostic marker. There is no evidence that pretreatment LDH predicts ICI benefit. Persistently elevated on-treatment LDH is associated with worse OS despite radiologic response.

The validity of progression-free survival 2 as a surrogate trial end point for overall survival.

BACKGROUND: Overall survival (OS) is the gold-standard end point for oncology trials. However, the availability of multiple therapeutic options after progression and crossover to receive investigational agents confound and delay OS data maturation. Progression-free survival 2 (PFS-2), defined as the time from randomization to progression on first subsequent therapy, has been proposed as a surrogate for OS. Using a meta-analytic approach, the authors aimed to assess the association between OS and PFS-2 and compare this with progression-free survival 1 (PFS-1) and the objective response rate (ORR). METHODS: An electronic literature search was performed to identify randomized trials of systemic therapies in advanced solid tumors that reported PFS-2 as a prespecified end point. Correlations between OS and PFS-2, OS and PFS-1, and OS and ORR as hazard ratios (HRs) or odds ratios (ORs) were assessed via linear regression weighted by trial size. RESULTS: Thirty-eight trials were included, and they comprised 19,031 patients across 8 tumor types. PFS-2 displayed a moderate correlation with OS (r = 0.67; 95% confidence interval [CI], 0.08-0.69). Conversely, correlations of ORR (r = 0.12; 95% CI, 0.00-0.13) and PFS-1 (r = 0.21; 95% CI, 0.00-0.33) were poor. The findings for PFS-2 were consistent for subgroup analyses by treatment type (immunotherapy vs nonimmunotherapy: r = 0.67 vs 0.67), survival post progression (<12 vs ≥12 months: r = 0.86 vs 0.79), and percentage not receiving subsequent treatment (<50% vs ≥50%: r = 0.70 vs 0.63). CONCLUSIONS: Across diverse tumors and therapies, the treatment effect on PFS-2 correlated moderately with the treatment effect on OS. PFS-2 performed consistently better than PFS-1 and ORR, regardless of postprogression treatment and postprogression survival. PFS-2 should be included as a key trial end point in future randomized trials of solid tumors.

Distributional regression in clinical trials: treatment effects on parameters other than the mean.

BACKGROUND: The classical linear model is widely used in the analysis of clinical trials with continuous outcomes. However, required model assumptions are frequently not met, resulting in estimates of treatment effect that can be inefficient and biased. In addition, traditional models assess treatment effect only on the mean response, and not on other aspects of the response, such as the variance. Distributional regression modelling overcomes these limitations. The purpose of this paper is to demonstrate its usefulness for the analysis of clinical trials, and superior performance to that of traditional models. METHODS: Distributional regression models are demonstrated, and contrasted with normal linear models, on data from the LIPID randomized controlled trial, which compared the effects of pravastatin with placebo in patients with coronary heart disease. Systolic blood pressure (SBP) and the biomarker midregional pro-adrenomedullin (MR-proADM) were analysed. Treatment effect was estimated in models that used response distributions more appropriate than the normal (Box-Cox-t and Johnson's Su for MR-proADM and SBP, respectively), applied censoring below the detection limit of MR-proADM, estimated treatment effect on distributional parameters other than the mean, and included random effects for longitudinal observations. A simulation study was conducted to compare the performance of distributional regression models with normal linear regression, under conditions mimicking the LIPID study. The R package gamlss (Generalized Additive Models for Location, Scale and Shape), which implements maximum likelihood estimation for distributional regression modelling, was used throughout. RESULTS: In all cases the distributional regression models fit the data well, in contrast to poor fits obtained for traditional models; for MR-proADM a small but significant treatment effect on the mean was detected by the distributional regression model and not the normal model; and for SBP a beneficial treatment effect on the variance was demonstrated. In the simulation study distributional models strongly outperformed normal models when the response variable was non-normal and heterogeneous; and there was no disadvantage introduced by the use of distributional regression modelling when the response satisfied the normal linear model assumptions. CONCLUSIONS: Distributional regression models are a rich framework, largely untapped in the clinical trials world. We have demonstrated a sample of the capabilities of these models for the analysis of trials. If interest lies in accurate estimation of treatment effect on the mean, or other distributional features such as variance, the use of distributional regression modelling will yield superior estimates to traditional normal models, and is strongly recommended. TRIAL REGISTRATION: The LIPID trial was retrospectively registered on ANZCTR on 27/04/2016, registration number ACTRN12616000535471 .

PD-L1 expression as a prognostic marker in patients treated with chemotherapy for metastatic non-small-cell lung cancer.

Background: In metastatic non-small-cell lung cancer (mNSCLC), PD-L1 expression is associated with benefit from immune checkpoint inhibitor (ICI) therapy. However, the significance of PD-L1 expression in chemotherapy-treated patients is uncertain. Methods: Using the chemotherapy control arm of first-line randomized trials, a meta-analysis of the association between efficacy outcomes and PD-L1 status was performed, stratified by assay due to inter-assay differences. Results: Across 12 trials and 4378 patients, overall survival (OS) was superior in high PD-L1 versus negative tumors and low versus negative according to 22C3/28-8 assays. When classified by SP142 assay, no significant difference in response or survival was seen between PD-L1 groups. Conclusion: In mNSCLC, high PD-L1-expressing tumors are associated with longer OS and improved objective rate when treated with chemotherapy. Inter-assay variability impacts outcome results.

Biomarkers are naturally occurring cancer traits that can predict certain events. PD-L1 expression is a biomarker used in advanced lung cancer to predict benefit from immunotherapy. However, the association between PD-L1expression and chemotherapy is unclear. The authors analyzed data from 14 large clinical trials and found that PD-L1 expression could also be used to define a type of lung cancer that responds better to chemotherapy.

Analysis of adaptive platform trials using a network approach.

BACKGROUND: Adaptive platform trials allow randomized controlled comparisons of multiple treatments using a common infrastructure and the flexibility to adapt key design features during the study. Nonetheless, they have been criticized due to the potential for time trends in the underlying risk level of the population. Such time trends lead to confounding between design features and risk level, which may introduce bias favoring one or more treatments. This is particularly true when experimental treatments are not all randomized during the same time period as the control, leading to the potential for bias from non-concurrent controls. METHODS: Two analysis methods addressing this bias are stratification and adjustment. Stratification uses only comparisons between treatment cohorts randomized during identical time periods and does not use non-concurrent randomizations. Adjustment uses a modeled analysis including time period adjustment, allowing all data to be used, even from periods without concurrent randomization. We show that these competing approaches may be embedded in a common framework using network meta-analysis principles. We interpret the stages between adaptations in a platform trial as separate fixed design trials. This allows platform trials to be viewed as networks of direct randomized comparisons and indirect non-randomized comparisons. Network meta-analysis methodology can be re-purposed to aggregate the total information from a platform trial and to transparently decompose this total information into direct randomized evidence and indirect non-randomized evidence. This allows sensitivity to indirect information to be assessed and the two analysis methods to be clearly compared. RESULTS: Simulations of platform trials were analyzed using a network approach implemented in the netmeta package in R. The results demonstrated bias of unadjusted methods in the presence of time trends in risk level. Adjustment and stratification were both unbiased when direct evidence and indirect evidence were consistent. Network tests of inconsistency may be used to diagnose inconsistency when it exists. In an illustrative network analysis of one of the treatment comparisons from the STAMPEDE platform trial in metastatic prostate cancer, indirect comparisons using non-concurrent controls were inconsistent with the information from direct randomized comparisons. This supports the primary analysis approach of STAMPEDE, which used only direct randomized comparisons. CONCLUSION: Network meta-analysis provides a natural methodology for analyzing the network of direct and indirect treatment comparisons from a platform trial. Such analyses provide transparent separation of direct and indirect evidence, allowing assessment of the impact of non-concurrent controls. We recommend time-stratified analysis of concurrently controlled comparisons for primary analyses, with time-adjusted analyses incorporating non-concurrent controls reserved for secondary analyses. However, regardless of which methodology is used, a network analysis provides a useful supplement to the primary analysis.

Estimating age-specific COVID-19 fatality risk and time to death by comparing population diagnosis and death patterns: Australian data.

BACKGROUND: Mortality is a key component of the natural history of COVID-19 infection. Surveillance data on COVID-19 deaths and case diagnoses are widely available in the public domain, but they are not used to model time to death because they typically do not link diagnosis and death at an individual level. This paper demonstrates that by comparing the unlinked patterns of new diagnoses and deaths over age and time, age-specific mortality and time to death may be estimated using a statistical method called deconvolution. METHODS: Age-specific data were analysed on 816 deaths among 6235 cases over age 50 years in Victoria, Australia, from the period January through December 2020. Deconvolution was applied assuming logistic dependence of case fatality risk (CFR) on age and a gamma time to death distribution. Non-parametric deconvolution analyses stratified into separate age groups were used to assess the model assumptions. RESULTS: It was found that age-specific CFR rose from 2.9% at age 65 years (95% CI:2.2 - 3.5) to 40.0% at age 95 years (CI: 36.6 - 43.6). The estimated mean time between diagnosis and death was 18.1 days (CI: 16.9 - 19.3) and showed no evidence of varying by age (heterogeneity P = 0.97). The estimated 90% percentile of time to death was 33.3 days (CI: 30.4 - 36.3; heterogeneity P = 0.85). The final age-specific model provided a good fit to the observed age-stratified mortality patterns. CONCLUSIONS: Deconvolution was demonstrated to be a powerful analysis method that could be applied to extensive data sources worldwide. Such analyses can inform transmission dynamics models and CFR assessment in emerging outbreaks. Based on these Australian data it is concluded that death from COVID-19 occurs within three weeks of diagnosis on average but takes five weeks in 10% of fatal cases. Fatality risk is negligible in the young but rises above 40% in the elderly, while time to death does not seem to vary by age.

Recurrent time-to-event models with ordinal outcomes.

A model to accommodate time-to-event ordinal outcomes was proposed by Berridge and Whitehead. Very few studies have adopted this approach, despite its appeal in incorporating several ordered categories of event outcome. More recently, there has been increased interest in utilizing recurrent events to analyze practical endpoints in the study of disease history and to help quantify the changing pattern of disease over time. For example, in studies of heart failure, the analysis of a single fatal event no longer provides sufficient clinical information to manage the disease. Similarly, the grade/frequency/severity of adverse events may be more important than simply prolonged survival in studies of toxic therapies in oncology. We propose an extension of the ordinal time-to-event model to allow for multiple/recurrent events in the case of marginal models (where all subjects are at risk for each recurrence, irrespective of whether they have experienced previous recurrences) and conditional models (subjects are at risk of a recurrence only if they have experienced a previous recurrence). These models rely on marginal and conditional estimates of the instantaneous baseline hazard and provide estimates of the probabilities of an event of each severity for each recurrence over time. We outline how confidence intervals for these probabilities can be constructed and illustrate how to fit these models and provide examples of the methods, together with an interpretation of the results.

Using recurrent time-to-event models with multinomial outcomes to generate toxicity profiles.

Most clinical studies, which investigate the impact of therapy simultaneously, record the frequency of adverse events in order to monitor safety of the intervention. Study reports typically summarise adverse event data by tabulating the frequencies of the worst grade experienced but provide no details of the temporal profiles of specific types of adverse events. Such 'toxicity profiles' are potentially important tools in disease management and in the assessment of newer therapies including targeted treatments and immunotherapy where different types of toxicity may be more common at various times during long-term drug exposure. Toxicity profiles of commonly experienced adverse events occurring due to exposure to long-term treatment could assist in evaluating the costs of the health care benefits of therapy. We show how to generate toxicity profiles using an adaptation of the ordinal time-to-event model comprising of a two-step process, involving estimation of the multinomial response probabilities using multinomial logistic regression and combining these with recurrent time to event hazard estimates to produce cumulative event probabilities for each of the multinomial adverse event response categories. Such a model permits the simultaneous assessment of the risk of events over time and provides cumulative risk probabilities for each type of adverse event response. The method can be applied more generally by using different models to estimate outcome/response probabilities. The method is illustrated by developing toxicity profiles for three distinct types of adverse events associated with two treatment regimens for patients with advanced breast cancer.

Uric acid predicts long-term cardiovascular risk in type 2 diabetes but does not mediate the benefits of fenofibrate: The FIELD study.

AIM: To explore the relationship between baseline uric acid (UA) levels and long-term cardiovascular events in adults with type 2 diabetes (T2D) and to determine whether the cardioprotective effects of fenofibrate are partly mediated through its UA-lowering effects. METHODS: Data from the Fenofibrate Intervention and Event Lowering in Diabetes (FIELD) trial were utilized, comprising 9795 adults with T2D randomly allocated to treatment with fenofibrate or matching placebo. Plasma UA was measured before and after a 6-week, active fenofibrate run-in phase in all participants. Cox proportional hazards models were used to explore the relationships between baseline UA, pre-to-post run-in reductions in UA and long-term cardiovascular outcomes. RESULTS: Mean baseline plasma UA was 0.33 mmol/L (SD 0.08). Baseline UA was a significant predictor of long-term cardiovascular events, with every 0.1 mmol/L higher UA conferring a 21% increase in event rate (HR 1.21, 95% CI 1.13-1.29, P < .001). This remained significant after adjustment for treatment allocation, cardiovascular risk factors and renal function. The extent of UA reduction during fenofibrate run-in was also a significant predictor of long-term cardiovascular events, with every 0.1 mmol/L greater reduction conferring a 14% lower long-term risk (HR 0.86, 95% CI 0.76-0.97, P = .015). This effect was not modified by treatment allocation (Pinteraction = .77). CONCLUSIONS: UA is a strong independent predictor of long-term cardiovascular risk in adults with T2D. Although greater reduction in UA on fenofibrate is predictive of lower cardiovascular risk, this does not appear to mediate the cardioprotective effects of fenofibrate.

Benchmarking single-arm studies against historical controls from non-small cell lung cancer trials - an empirical analysis of bias.

Background: Recent trials of novel agents in 'rare' molecular subtypes of non-small cell lung cancer (NSCLC) have used single-arm trial designs and benchmarked outcomes against historical controls. We assessed the consistency of historical control outcomes using docetaxel data from published NSCLC randomized controlled trials (RCTs).Material and methods: Advanced NSCLC RCTs including a docetaxel monotherapy arm were included. Heterogeneity in tumor objective response rates (ORRs), progression-free survival (PFS) and overall survival (OS), and correlations between outcomes and year of trial commencement were assessed.Results: Among 63 trials (N = 10,633) conducted between 2000 and 2017, ORR ranged from 0% to 26% (I2 = 76.1%, pheterogeneity < .0001). Mean of the median PFS was 3.0 months (range: 1.4-6.4), 3-month PFS ranged from 25% to 85% (I2 = 86.0%, pheterogeneity < .0001). Mean of the median OS was 9.1 months (range: 4.7-22.9), 9-month OS ranged from 23% to 79% (I2 = 83.0%, pheterogeneity < .0001). Each later year of trial commencement was associated with 0.3% (p = .046), 0.5% (p = .11) and 0.9% (p = .001) improvement in ORR, 3-month PFS and 9-month OS rates, respectively.Conclusions: There was significant heterogeneity and an improving trend in docetaxel outcomes across trials conducted over 20 years. Benchmarking biomarker-targeted agents against historical controls may not be a valid approach to replace RCTs. Innovative study designs involving a concurrent control arm should be considered.

Pulse Oximeter Saturation Targeting and Oximeter Changes in the Benefits of Oxygen Saturation Targeting (BOOST)-II Australia and BOOST-II UK Oxygen Trials.

Infants in the Australian and UK Benefits of Oxygen Saturation Targeting-II trials treated using revised oximeters spent more time within their planned pulse oximeter saturation target ranges than infants treated using the original oximeters (P < .001). This may explain the larger mortality difference seen with revised oximeters. If so, average treatment effects from the Neonatal Oxygen Prospective Meta-analysis trials may be underestimates.

Predictive value of PD-L1 and other clinical factors for chemoimmunotherapy in advanced non-small-cell lung cancer.

We investigate if PD-L1 expression and other clinical characteristics predict chemoimmunotherapy (CIT) benefits versus chemotherapy in advanced non-small-cell lung cancer. We performed a meta-analysis of randomized controlled trials of CIT versus chemotherapy identified through electronic searches. In seven randomized controlled trials (n = 4170), CIT prolonged progression-free survival over chemotherapy (hazard ratio [HR]: 0.62; 95% CI: 0.58-0.67; p < 0.00001). The treatment benefits differed between PD-L1-high (HR: 0.41; 95% CI: 0.34-0.49) and PD-L1 low (HR: 0.63; 95% CI: 0.55-0.72; interaction-p = 0.00002) and PD-L1-high and PD-L1-negative (HR: 0.72; 95% CI: 0.65-0.80; interaction-p < 0.00001). Similar benefits were observed regardless of gender, EGFR/ALK status and histological subtype. PD-L1 status is predictive of CIT benefit and may assist patient selection and design of future trials.

Design of clinical trials involving multiple hypothesis tests with a common control.

Randomized clinical trials comparing several treatments to a common control are often reported in the medical literature. For example, multiple experimental treatments may be compared with placebo, or in combination therapy trials, a combination therapy may be compared with each of its constituent monotherapies. Such trials are typically designed using a balanced approach in which equal numbers of individuals are randomized to each arm, however, this can result in an inefficient use of resources. We provide a unified framework and new theoretical results for optimal design of such single-control multiple-comparator studies. We consider variance optimal designs based on D-, A-, and E-optimality criteria, using a general model that allows for heteroscedasticity and a range of effect measures that include both continuous and binary outcomes. We demonstrate the sensitivity of these designs to the type of optimality criterion by showing that the optimal allocation ratios are systematically ordered according to the optimality criterion. Given this sensitivity to the optimality criterion, we argue that power optimality is a more suitable approach when designing clinical trials where testing is the objective. Weighted variance optimal designs are also discussed, which, like power optimal designs, allow the treatment difference to play a major role in determining allocation ratios. We illustrate our methods using two real clinical trial examples taken from the medical literature. Some recommendations on the use of optimal designs in single-control multiple-comparator trials are also provided.

Estimation of adjusted rate differences using additive negative binomial regression.

Rate differences are an important effect measure in biostatistics and provide an alternative perspective to rate ratios. When the data are event counts observed during an exposure period, adjusted rate differences may be estimated using an identity-link Poisson generalised linear model, also known as additive Poisson regression. A problem with this approach is that the assumption of equality of mean and variance rarely holds in real data, which often show overdispersion. An additive negative binomial model is the natural alternative to account for this; however, standard model-fitting methods are often unable to cope with the constrained parameter space arising from the non-negativity restrictions of the additive model. In this paper, we propose a novel solution to this problem using a variant of the expectation-conditional maximisation-either algorithm. Our method provides a reliable way to fit an additive negative binomial regression model and also permits flexible generalisations using semi-parametric regression functions. We illustrate the method using a placebo-controlled clinical trial of fenofibrate treatment in patients with type II diabetes, where the outcome is the number of laser therapy courses administered to treat diabetic retinopathy. An R package is available that implements the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

Methods for exploring treatment effect heterogeneity in subgroup analysis: an application to global clinical trials.

Multi-country randomised clinical trials (MRCTs) are common in the medical literature, and their interpretation has been the subject of extensive recent discussion. In many MRCTs, an evaluation of treatment effect homogeneity across countries or regions is conducted. Subgroup analysis principles require a significant test of interaction in order to claim heterogeneity of treatment effect across subgroups, such as countries in an MRCT. As clinical trials are typically underpowered for tests of interaction, overly optimistic expectations of treatment effect homogeneity can lead researchers, regulators and other stakeholders to over-interpret apparent differences between subgroups even when heterogeneity tests are insignificant. In this paper, we consider some exploratory analysis tools to address this issue. We present three measures derived using the theory of order statistics, which can be used to understand the magnitude and the nature of the variation in treatment effects that can arise merely as an artefact of chance. These measures are not intended to replace a formal test of interaction but instead provide non-inferential visual aids, which allow comparison of the observed and expected differences between regions or other subgroups and are a useful supplement to a formal test of interaction. We discuss how our methodology differs from recently published methods addressing the same issue. A case study of our approach is presented using data from the Study of Platelet Inhibition and Patient Outcomes (PLATO), which was a large cardiovascular MRCT that has been the subject of controversy in the literature. An R package is available that implements the proposed methods.