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.

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.

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.

A Randomized Trial of Nafamostat for Covid-19.

A Randomized Trial of Nafamostat for Covid-19Nafamostat mesylate is a potent in vitro antiviral that inhibits the host transmembrane protease serine 2 enzyme used by SARS-CoV-2 for cell entry. Morpeth et al report the results of an open-label randomized clinical trial of nafamostat for noncritically ill patients with Covid-19.

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.

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.

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 .

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.

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.

Unpacking the behavioural components and delivery features of early childhood obesity prevention interventions in the TOPCHILD Collaboration: a systematic review and intervention coding protocol.

INTRODUCTION: Little is known about how early (eg, commencing antenatally or in the first 12 months after birth) obesity prevention interventions seek to change behaviour and which components are or are not effective. This study aims to (1) characterise early obesity prevention interventions in terms of target behaviours, delivery features and behaviour change techniques (BCTs), (2) explore similarities and differences in BCTs used to target behaviours and (3) explore effectiveness of intervention components in preventing childhood obesity. METHODS AND ANALYSIS: Annual comprehensive systematic searches will be performed in Epub Ahead of Print/MEDLINE, Embase, Cochrane (CENTRAL), CINAHL, PsycINFO, as well as clinical trial registries. Eligible randomised controlled trials of behavioural interventions to prevent childhood obesity commencing antenatally or in the first year after birth will be invited to join the Transforming Obesity in CHILDren Collaboration. Standard ontologies will be used to code target behaviours, delivery features and BCTs in both published and unpublished intervention materials provided by trialists. Narrative syntheses will be performed to summarise intervention components and compare applied BCTs by types of target behaviours. Exploratory analyses will be undertaken to assess effectiveness of intervention components. ETHICS AND DISSEMINATION: The study has been approved by The University of Sydney Human Research Ethics Committee (project no. 2020/273) and Flinders University Social and Behavioural Research Ethics Committee (project no. HREC CIA2133-1). The study's findings will be disseminated through peer-reviewed publications, conference presentations and targeted communication with key stakeholders. PROSPERO REGISTRATION NUMBER: CRD42020177408.

Transforming Obesity Prevention for CHILDren (TOPCHILD) Collaboration: protocol for a systematic review with individual participant data meta-analysis of behavioural interventions for the prevention of early childhood obesity.

INTRODUCTION: Behavioural interventions in early life appear to show some effect in reducing childhood overweight and obesity. However, uncertainty remains regarding their overall effectiveness, and whether effectiveness differs among key subgroups. These evidence gaps have prompted an increase in very early childhood obesity prevention trials worldwide. Combining the individual participant data (IPD) from these trials will enhance statistical power to determine overall effectiveness and enable examination of individual and trial-level subgroups. We present a protocol for a systematic review with IPD meta-analysis to evaluate the effectiveness of obesity prevention interventions commencing antenatally or in the first year after birth, and to explore whether there are differential effects among key subgroups. METHODS AND ANALYSIS: Systematic searches of Medline, Embase, Cochrane Central Register of Controlled Trials, Cumulative Index to Nursing and Allied Health Literature (CINAHL), PsycInfo and trial registries for all ongoing and completed randomised controlled trials evaluating behavioural interventions for the prevention of early childhood obesity have been completed up to March 2021 and will be updated annually to include additional trials. Eligible trialists will be asked to share their IPD; if unavailable, aggregate data will be used where possible. An IPD meta-analysis and a nested prospective meta-analysis will be performed using methodologies recommended by the Cochrane Collaboration. The primary outcome will be body mass index z-score at age 24±6 months using WHO Growth Standards, and effect differences will be explored among prespecified individual and trial-level subgroups. Secondary outcomes include other child weight-related measures, infant feeding, dietary intake, physical activity, sedentary behaviours, sleep, parenting measures and adverse events. ETHICS AND DISSEMINATION: Approved by The University of Sydney Human Research Ethics Committee (2020/273) and Flinders University Social and Behavioural Research Ethics Committee (HREC CIA2133-1). Results will be relevant to clinicians, child health services, researchers, policy-makers and families, and will be disseminated via publications, presentations and media releases. PROSPERO REGISTRATION NUMBER: CRD42020177408.

Penalized likelihood estimation of the proportional hazards model for survival data with interval censoring.

This paper considers the problem of semi-parametric proportional hazards model fitting where observed survival times contain event times and also interval, left and right censoring times. Although this is not a new topic, many existing methods suffer from poor computational performance. In this paper, we adopt a more versatile penalized likelihood method to estimate the baseline hazard and the regression coefficients simultaneously. The baseline hazard is approximated using basis functions such as M-splines. A penalty is introduced to regularize the baseline hazard estimate and also to ease dependence of the estimates on the knots of the basis functions. We propose a Newton-MI (multiplicative iterative) algorithm to fit this model. We also present novel asymptotic properties of our estimates, allowing for the possibility that some parameters of the approximate baseline hazard may lie on the parameter space boundary. Comparisons of our method against other similar approaches are made through an intensive simulation study. Results demonstrate that our method is very stable and encounters virtually no numerical issues. A real data application involving melanoma recurrence is presented and an R package 'survivalMPL' implementing the method is available on R CRAN.

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.

Sensitivity analyses assessing the impact of early stopping on systematic reviews: Recommendations for interpreting guidelines.

The CONSORT Statement says that data-driven early stopping of a clinical trial is likely to weaken the inferences that can be drawn from the trial. The GRADE guidelines go further, saying that early stopping is a study limitation that carries the risk of bias, and recommending sensitivity analyses in which trials stopped early are omitted from evidence synthesis. Despite extensive debate in the literature over these issues, the existence of clear recommendations in high profile guidelines makes it inevitable that systematic reviewers will consider sensitivity analyses investigating the impact of early stopping. The purpose of this article is to assess methodologies for conducting such sensitivity analyses, and to make recommendations about how the guidelines should be interpreted. We begin with a clarifying overview of the impacts of early stopping on treatment effect estimation in single studies and meta-analyses. We then warn against naive approaches for conducting sensitivity analyses, including simply omitting trials stopped early from meta-analyses. This approach underestimates treatment effects, which may have serious implications if cost-effectiveness analyses determine whether treatments are made widely available. Instead, we discuss two unbiased approaches to sensitivity analysis, one of which is straightforward but statistically inefficient, and the other of which achieves greater statistical efficiency by making use of recent methodological developments in the analysis of clinical trials. We end with recommendations for interpreting: (a) the CONSORT Statement on reporting of reasons for early stopping, and (b) the GRADE guidelines on sensitivity analyses assessing the impact of early stopping.

Changes in plasma lipids predict pravastatin efficacy in secondary prevention.

BACKGROUNDStatins have pleiotropic effects on lipid metabolism. The relationship between these effects and future cardiovascular events is unknown. We characterized the changes in lipids upon pravastatin treatment and defined the relationship with risk reduction for future cardiovascular events.METHODSPlasma lipids (n = 342) were measured in baseline and 1-year follow-up samples from a Long-Term Intervention with Pravastatin in Ischaemic Disease (LIPID) study subcohort (n = 4991). The associations of changes in lipids with treatment and cardiovascular outcomes were investigated using linear and Cox regression. The effect of treatment on future cardiovascular outcomes was examined by the relative risk reduction (RRR).RESULTSPravastatin treatment was associated with changes in 206 lipids. Species containing arachidonic acid were positively associated while phosphatidylinositol species were negatively associated with pravastatin treatment. The RRR from pravastatin treatment for cardiovascular events decreased from 23.5% to 16.6% after adjustment for clinical risk factors and change in LDL-cholesterol (LDL-C) and to 3.0% after further adjustment for the change in the lipid ratio PI(36:2)/PC(38:4). Change in PI(36:2)/PC(38:4) mediated 58% of the treatment effect. Stratification of patients into quartiles of change in PI(36:2)/PC(38:4) indicated no benefit of pravastatin in the fourth quartile.CONCLUSIONThe change in PI(36:2)/PC(38:4) predicted benefit from pravastatin, independent of change in LDL-C, demonstrating its potential as a biomarker for monitoring the clinical benefit of statin treatment in secondary prevention.TRIAL REGISTRATIONAustralian New Zealand Clinical Trials Registry identifier ACTRN12616000535471.FUNDINGBristol-Myers Squibb; NHMRC grants 211086, 358395, and 1029754; NHMRC program grant 1149987; NHMRC fellowship 108026; and the Operational Infrastructure Support Program of the Victorian government of Australia.

Underestimation of treatment effects in sequentially monitored clinical trials that did not stop early for benefit.

In recent years, there has been a prominent discussion in the literature about the potential for overestimation of the treatment effect when a clinical trial stops at an interim analysis due to the experimental treatment showing a benefit over the control. However, there has been much less attention paid to the converse issue, namely, that sequentially monitored clinical trials which did not stop early for benefit tend to underestimate the treatment effect. In meta-analyses of many studies, these two sources of bias will tend to balance each other to produce an unbiased estimate of the treatment effect. However, for the interpretation of a single study in isolation, underestimation due to interim analysis may be an important consideration. In this paper, we discuss the nature of this underestimation, including theoretical and simulation results demonstrating that it can be substantial in some contexts. Furthermore, we show how a conditional approach to estimation, in which we condition on the study reaching its final analysis, may be used to validly inflate the observed treatment difference from a sequentially monitored clinical trial. Expressions for the conditional bias and information are derived, and these are used in supplied R code that computes the bias-adjusted estimate and an associated confidence interval. As well as simulation results demonstrating the validity of the methods, we present a data analysis example from a pivotal clinical trial in cardiovascular disease. The methods will be most useful when an unbiased treatment effect estimate is critical, such as in cost-effectiveness analysis or risk prediction.

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.

Progression-free survival as a surrogate endpoint for overall survival in modern ovarian cancer trials: a meta-analysis.

BACKGROUND: Progression-free survival (PFS) has been adopted as the primary endpoint in many randomized controlled trials, and can be determined much earlier than overall survival (OS). We investigated whether PFS is a good surrogate endpoint for OS in trials of first-line treatment for epithelial ovarian cancer (EOC), and whether this relationship has changed with the introduction of new treatment types. METHODS: In a meta-analysis, we identified summary data [hazard ratio (HR) and median time] from published randomized controlled trials. Linear regression was used to assess the association between treatment effects on PFS and OS overall, and for subgroups defined by treatment type, postprogression survival (PPS) and established prognostic factors. RESULTS: Correlation between HRs for PFS and OS, in 26 trials with 30 treatment comparisons comprising 24,870 patients, was modest (r2 = 0.52, weighted by trial sample size). The correlation diminished with recency: preplatinum/paclitaxel era, r2= 0.66; platinum/paclitaxel, r2= 0.44; triplet combinations, r2= 0.22; biologicals, r2= 0.30. The median PPS increased over time for the experimental (Ptrend = 0.03) and control arms (Ptrend = 0.003). The difference in median PPS between treatment arms strongly correlated with the difference in median OS (r2 = 0.83). In trials where the control therapy had median PPS of less than 18 months, correlation between PFS and OS was stronger (r2 = 0.64) than where the median PPS was longer (r2 = 0.48). CONCLUSIONS: In EOC, correlation in the relative treatment effect between PFS and OS in first-line platinum-based chemotherapy randomized controlled trials is moderate and has weakened with increasing availability of effective salvage therapies.