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.

Analysis of Nonconcurrent Controls in Adaptive Platform Trials: Separating Randomized and Nonrandomized Information.

Adaptive platform trials allow treatments to be added or dropped during the study, meaning that the control arm may be active for longer than the experimental arms. This leads to nonconcurrent controls, which provide nonrandomized information that may increase efficiency but may introduce bias from temporal confounding and other factors. Various methods have been proposed to control confounding from nonconcurrent controls, based on adjusting for time period. We demonstrate that time adjustment is insufficient to prevent bias in some circumstances where nonconcurrent controls are present in adaptive platform trials, and we propose a more general analytical framework that accounts for nonconcurrent controls in such circumstances. We begin by defining nonconcurrent controls using the concept of a concurrently randomized cohort, which is a subgroup of participants all subject to the same randomized design. We then use cohort adjustment rather than time adjustment. Due to flexibilities in platform trials, more than one randomized design may be in force at any time, meaning that cohort-adjusted and time-adjusted analyses may be quite different. Using simulation studies, we demonstrate that time-adjusted analyses may be biased while cohort-adjusted analyses remove this bias. We also demonstrate that the cohort-adjusted analysis may be interpreted as a synthesis of randomized and indirect comparisons analogous to mixed treatment comparisons in network meta-analysis. This allows the use of network meta-analysis methodology to separate the randomized and nonrandomized components and to assess their consistency. Whenever nonconcurrent controls are used in platform trials, the separate randomized and indirect contributions to the treatment effect should be presented.

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 .

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.

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.

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.

Lu-177 PSMA vs Comparator Treatments and Survival in Metastatic Castration-Resistant Prostate Cancer.

Importance: Observed treatment effects on overall survival (OS) differed substantially in the first 2 randomized clinical trials of lutetium Lu 177 vipivotide tetraxetan (Lu-177) prostate-specific membrane antigen (PSMA) in metastatic castration-resistant prostate cancer. Objective: To investigate factors associated with the observed difference in treatment effects on OS, including differences in the risk of crossover from randomized treatment after disease progression. Design, Setting, and Participants: This comparative effectiveness study used individual participant data from 2 randomized clinical trials, TheraP (A Randomised Phase 2 Trial of 177Lu-PSMA617 Theranostic Versus Cabazitaxel in Progressive Metastatic Castration Resistant Prostate Cancer [ANZUP Protocol 1603]) (n = 200), recruited from February 2018 to September 2019 in Australia, and published data from VISION (An International, Prospective, Open Label, Multicenter, Randomized Phase 3 Study of 177Lu-PSMA-617 in the Treatment of Patients With Progressive PSMA-Positive Metastatic Castration-Resistant Prostate Cancer) (n = 831), recruited from June 2018 to October 2019 in North America and Europe. Individual participant data for OS were reconstructed from VISION using the published survival curves. Data were analyzed February 6, 2018, to December 31, 2021, for TheraP and June 4, 2018, to January 27, 2021, for VISION. Interventions: TheraP randomized participants to receive treatment with Lu-177 PSMA or cabazitaxel. VISION randomized participants to receive treatment with or without Lu-177 PSMA in addition to physicians' choice of protocol-permitted treatments (PPT; approved hormonal treatments [such as abiraterone and enzalutamide], bisphosphonates, radiotherapy, denosumab, or glucocorticoids), excluding cabazitaxel. Main Outcomes and Measures: Patient characteristics, treatment protocols, and OS outcomes of the 2 trials were compared. Estimates of the effect on OS from TheraP were adjusted for crossover from randomly assigned treatment using a rank-preserving structural failure time model (RPSFTM) and inverse probability of censoring weights (IPCW) methods. Results: The 200 participants in TheraP and 831 participants in VISION were similar in age (median [range], 72 [49-86] vs 71 [40-94] years). Improved OS was observed in the comparator treatment group (cabazitaxel) in TheraP compared with VISION (PPT) (hazard ratio [HR], 0.53 [95% CI, 0.39-0.71]). The Lu-177 PSMA treatment groups in TheraP and VISION had similar OS (HR, 0.92 [95% CI, 0.70-1.19]). In TheraP, 20 of 101 participants in the cabazitaxel group crossed over to Lu-177 PSMA, while 32 of 99 participants in the Lu-177 PSMA arm crossed over to cabazitaxel. No statistically significant differences in OS between the Lu-177 PSMA and cabazitaxel groups of TheraP were observed after controlling for crossover to cabazitaxel: RPSFTM HR, 0.97 (95% CI, 0.60-1.58); IPCW HR, 0.92 (95% CI, 0.65-1.32); RPSFTM HR, 0.97 (95% CI, 0.60-1.58) and IPCW HR, 0.82 (95% CI, 0.54-1.24) for crossover to Lu-177 PSMA; RPSFTM HR, 0.96 (95% CI, 0.53-1.74) and IPCW HR, 0.82 (95% CI, 0.53-1.27) for crossover to either Lu-177 PSMA or cabazitaxel. Conclusions and Relevance: Findings of this secondary analysis of the TheraP and VISION randomized clinical trials suggest that the choice of comparator treatments (ie, cabazitaxel vs PPT) may explain the difference in the observed effect of Lu-177 PSMA on OS between the 2 trials. Causal inference methods such as RPSFTM and IPCW may help rule out crossover as a plausible explanation.

Challenges of estimating treatment effects after a positive interim analysis.

BACKGROUND: This research investigates why a beneficial treatment effect reported at the first interim analysis (IA) may diminish at a subsequent analysis (SA). We examined three challenges in interpreting treatment effects from randomized clinical trials (RCTs) after the first positive IA: overestimation bias; non-proportional hazards; and heterogeneity in recruitment. We investigate how a penalized estimation method can address overestimation bias, and discuss additional factors to consider when interpreting positive IA results. METHODS: We identified oncology RCTs reporting positive results at the initial IA and a SA for event-free (EFS) and overall survival (OS). We modeled: (1) the hazard ratio at IA (HRIA) versus its timing as measured by the information fraction (IF; i.e., events at IA versus total events sought); and (2), the ratio of HRIA to HRSA (rHR) versus the IF. This was repeated for HRIA adjusted for overestimation bias. Examples of the other two challenges were sought. RESULTS: Amongst 71 RCTs, HRIA were positively associated with the IF (slope: EFS 0.83, 95 % CI 0.44-1.22; OS 0.25, 95 % CI 0.10-0.41). HRIA tended to exaggerate HRSA, and more so the lower the IF (slope rHR versus IF: EFS 0.10, 95 % CI - 0.22 to 0.42; OS 0.26, 95 % CI 0.07-0.46). Adjusted HRIA did not exaggerate HRSA (slope rHR versus IF: EFS - 0.14, 95 % CI - 0.67 to 0.39; OS 0.02, 95 % CI - 0.26 to 0.30). Examples of two other challenges are shown. CONCLUSION: Overestimation bias, non-proportional hazards, and heterogeneity in recruitment and other important treatments should be considered when communicating estimates of treatment effects from positive IAs.

Relative risk regression: reliable and flexible methods for log-binomial models.

Relative risks (RRs) are generally considered preferable to odds ratios in prospective studies. However, unlike logistic regression for odds ratios, the standard log-binomial model for RR regression does not respect the natural parameter constraints and is therefore often subject to numerical instability. In this paper, we develop a reliable and flexible method for fitting log-binomial models. We use an Expectation-Maximization (EM) algorithm where the multiplicative event probability is viewed as the joint probability for a collection of latent binary outcomes. This gives a simple iterative scheme that provides stable convergence to the maximum likelihood estimate. In addition to reliability, the method offers some flexible generalizations, including models with unspecified isotonic regression functions. We examine the method's performance using simulations and data analyses of the age-specific RR of mortality following heart attack. These analyses demonstrate the potential for numerical instability in RR regression and show how this can be overcome using the proposed approach. Source code to implement the method in R is provided as supplementary material available at Biostatistics online.

Meta-analysis of clinical trials with early stopping: an investigation of potential bias.

Clinical trials that stop early for benefit have a treatment difference that overestimates the true effect. The consequences of this fact have been extensively debated in the literature. Some researchers argue that early stopping, or truncation, is an important source of bias in treatment effect estimates, particularly when truncated studies are incorporated into meta-analyses. Such claims are bound to lead some systematic reviewers to consider excluding truncated studies from evidence synthesis. We therefore investigated the implications of this strategy by examining the properties of sequentially monitored studies conditional on reaching the final analysis. As well as estimation bias, we studied information bias measured by the difference between standard measures of statistical information, such as sample size, and the actual information based on the conditional sampling distribution. We found that excluding truncated studies leads to underestimation of treatment effects and overestimation of information. Importantly, the information bias increases with the estimation bias, meaning that greater estimation bias is accompanied by greater overweighting in a meta-analysis. Simulations of meta-analyses confirmed that the bias from excluding truncated studies can be substantial. In contrast, when meta-analyses included truncated studies, treatment effect estimates were essentially unbiased. Previous analyses comparing treatment effects in truncated and non-truncated studies are shown not to be indicative of bias in truncated studies. We conclude that early stopping of clinical trials is not a substantive source of bias in meta-analyses and recommend that all studies, both truncated and non-truncated, be included in evidence synthesis.

Linear mixed models for investigating effect modification in subgroup meta-analysis.

Subgroup meta-analysis can be used for comparing treatment effects between subgroups using information from multiple trials. If the effect of treatment is differential depending on subgroup, the results could enable personalization of the treatment. We propose using linear mixed models for estimating treatment effect modification in aggregate data meta-analysis. The linear mixed models capture existing subgroup meta-analysis methods while allowing for additional features such as flexibility in modeling heterogeneity, handling studies with missing subgroups and more. Reviews and simulation studies of the best suited models for estimating possible differential effect of treatment depending on subgroups have been studied mostly within individual participant data meta-analysis. While individual participant data meta-analysis in general is recommended over aggregate data meta-analysis, conducting an aggregate data subgroup meta-analysis could be valuable for exploring treatment effect modifiers before committing to an individual participant data subgroup meta-analysis. Additionally, using solely individual participant data for subgroup meta-analysis requires collecting sufficient individual participant data which may not always be possible. In this article, we compared existing methods with linear mixed models for aggregate data subgroup meta-analysis under a broad selection of scenarios using simulation and two case studies. Both the case studies and simulation studies presented here demonstrate the advantages of the linear mixed model approach in aggregate data subgroup meta-analysis.

Transparent reporting of adaptive clinical trials using concurrently randomised cohorts.

Adaptive clinical trials have designs that evolve over time because of changes to treatments or changes to the chance that participants will receive these treatments. These changes might introduce confounding that biases crude comparisons of the treatment arms and makes the results from standard reporting methods difficult to interpret for adaptive trials. To deal with this shortcoming, a reporting framework for adaptive trials was developed based on concurrently randomised cohort reporting. A concurrently randomised cohort is a subgroup of participants who all had the same treatments available and the same chance of receiving these treatments. The reporting of pre-randomisation characteristics and post-randomisation outcomes for each concurrently randomised cohort in the study is recommended. This approach provides a transparent and unbiased display of the degree of baseline balance and the randomised treatment comparisons for adaptive trials. The key concepts, terminology, and recommendations underlying concurrently randomised cohort reporting are presented, and its routine use in adaptive trial reporting is advocated.

Mediation analysis of the testosterone treatment effect to prevent type 2 diabetes in the Testosterone for Prevention of Type 2 Diabetes Mellitus trial.

OBJECTIVE: To determine if testosterone treatment effect on glycaemia is mediated through changes in total fat mass, abdominal fat mass, skeletal muscle mass, non-dominant hand-grip, oestradiol (E2), and sex hormone-binding globulin (SHBG). DESIGN: Mediation analysis of a randomised placebo-controlled trial of testosterone. METHODS: Six Australian tertiary care centres recruited 1007 males, aged 50-74 years, with waist circumference ≥95 cm, serum total testosterone ≤14 nmol/L (immunoassay), and either impaired glucose tolerance or newly diagnosed type 2 diabetes on an oral glucose tolerance test (OGTT). Participants were enrolled in a lifestyle programme and randomised 1:1 to 3 monthly injections of 1000 mg testosterone undecanoate or placebo for 2 years. Complete data were available for 709 participants (70%). Mediation analyses for the primary outcomes of type 2 diabetes at 2 years (OGTT ≥ 11.1 mmol/L and change in 2-h glucose from baseline), incorporating potential mediators: changes in fat mass, % abdominal fat, skeletal muscle mass, non-dominant hand-grip strength, E2, and SHBG, were performed. RESULTS: For type 2 diabetes at 2 years, the unadjusted OR for treatment was 0.53 (95% CI:.35-.79), which became 0.48 (95% CI:.30-.76) after adjustment for covariates. Including potential mediators attenuated the treatment effect (OR 0.77; 95% CI:.44-1.35; direct effect) with 65% mediated. Only fat mass remained prognostic in the full model (OR: 1.23; 95% CI: 1.09-1.39; P < .001). CONCLUSION: At least part of the testosterone treatment effect was found to be mediated by changes in fat mass, abdominal fat, skeletal muscle mass, grip strength, SHBG, and E2, but predominantly by changes in fat mass.

A Randomized Trial of Nafamostat for Covid-19.

BACKGROUND: Nafamostat mesylate is a potent in vitro antiviral agent that inhibits the host transmembrane protease serine 2 enzyme used by severe acute respiratory syndrome coronavirus 2 for cell entry. METHODS: This open-label, pragmatic, randomized clinical trial in Australia, New Zealand, and Nepal included noncritically ill hospitalized patients with coronavirus disease 2019 (Covid-19). Participants were randomly assigned to usual care or usual care plus nafamostat. The primary end point was death (any cause) or receipt of new invasive or noninvasive ventilation or vasopressor support within 28 days after randomization. Analysis was with a Bayesian logistic model in which an adjusted odds ratio <1.0 indicates improved outcomes with nafamostat. Enrollment was closed due to falling numbers of eligible patients. RESULTS: We screened 647 patients in 21 hospitals (15 in Australia, 4 in New Zealand, and 2 in Nepal) and enrolled 160 participants from May 2021 to August 2022. In the intention-to-treat population, the primary end point occurred in 8 (11%) of 73 patients with usual care and 4 (5%) of 82 with nafamostat. The median adjusted odds ratio for the primary end point for nafamostat was 0.40 (95% credible interval, 0.12 to 1.34) with a posterior probability of effectiveness (adjusted odds ratio <1.0) of 93%. For usual care compared with nafamostat, hyperkalemia occurred in 1 (1%) of 67 and 7 (9%) of 78 participants, respectively, and clinically relevant bleeding occurred in 1 (1%) of 73 and 7 (8%) of 82 participants. CONCLUSIONS: Among hospitalized patients with Covid-19, there was a 93% posterior probability that nafamostat reduced the odds of death or organ support. Prespecified stopping criteria were not met, precluding definitive conclusions. Hyperkalemia and bleeding were more common with nafamostat. (Funded by ASCOT and others; ClinicalTrials.gov number, NCT04483960.)

Estimation of the treatment effect following a clinical trial that stopped early for benefit.

When a clinical trial stops early for benefit, the maximum likelihood estimate (MLE) of the treatment effect may be subject to overestimation bias. Several authors have proposed adjusting for this bias using the conditional MLE, which is obtained by conditioning on early stopping. However, this approach has a fundamental problem in that the adjusted estimate may not be in the direction of benefit, even though the study has stopped early due to benefit. In this paper, we address this problem by embedding both the MLE and the conditional MLE within a broader class of penalised likelihood estimates, and choosing a member of the class that is a favourable compromise between the two. This penalised MLE, and its associated confidence interval, always lie in the direction of benefit when the study stops early for benefit. We study its properties using both simulations and analyses of the ENZAMET trial in metastatic prostate cancer. Conditional on stopping early for benefit, the method is found to have good unbiasedness and coverage properties, along with very favourable efficiency at earlier interim analyses. We recommend the penalised MLE as a supplementary analysis to a conventional primary analysis when a clinical trial stops early for benefit.