Two-stage meta-analysis of survival data from individual participants using percentile ratios

Heterogeneity in meta-analysis: a comprehensive overview

In recent years, meta-analysis has evolved to a critically important field of Statistics, and has significant applications in Medicine and Health Sciences. In this work we briefly present existing methodologies to conduct meta-analysis along with any discussion and recent developments accompanying them. Undoubtedly, studies brought together in a systematic review will differ in one way or another. This yields a considerable amount of variability, any kind of which may be termed heterogeneity. To this end, reports of meta-analyses commonly present a statistical test of heterogeneity when attempting to establish whether the included studies are indeed similar in terms of the reported output or not. We intend to provide an overview of the topic, discuss the potential sources of heterogeneity commonly met in the literature and provide useful guidelines on how to address this issue and to detect heterogeneity. Moreover, we review the recent developments in the Bayesian approach along with the various graphical tools and statistical software that are currently available to the analyst. In addition, we discuss sensitivity analysis issues and other approaches of understanding the causes of heterogeneity. Finally, we explore heterogeneity in meta-analysis for time to event data in a nutshell, pointing out its unique characteristics.

MetaBayesDTA: codeless Bayesian meta-analysis of test accuracy, with or without a gold standard

BACKGROUND

The statistical models developed for meta-analysis of diagnostic test accuracy studies require specialised knowledge to implement. This is especially true since recent guidelines, such as those in Version 2 of the Cochrane Handbook of Systematic Reviews of Diagnostic Test Accuracy, advocate more sophisticated methods than previously. This paper describes a web-based application - MetaBayesDTA - that makes many advanced analysis methods in this area more accessible.

RESULTS

We created the app using R, the Shiny package and Stan. It allows for a broad array of analyses based on the bivariate model including extensions for subgroup analysis, meta-regression and comparative test accuracy evaluation. It also conducts analyses not assuming a perfect reference standard, including allowing for the use of different reference tests.

CONCLUSIONS

Due to its user-friendliness and broad array of features, MetaBayesDTA should appeal to researchers with varying levels of expertise. We anticipate that the application will encourage higher levels of uptake of more advanced methods, which ultimately should improve the quality of test accuracy reviews.

Challenges of modelling approaches for network meta-analysis of time-to-event outcomes in the presence of non-proportional hazards to aid decision making: Application to a melanoma network

BACKGROUND

Synthesis of clinical effectiveness from multiple trials is a well-established component of decision-making. Time-to-event outcomes are often synthesised using the Cox proportional hazards model assuming a constant hazard ratio over time. However, with an increasing proportion of trials reporting treatment effects where hazard ratios vary over time and with differing lengths of follow-up across trials, alternative synthesis methods are needed.

OBJECTIVES

To compare and contrast five modelling approaches for synthesis of time-to-event outcomes and provide guidance on key considerations for choosing between the modelling approaches.

METHODS

The Cox proportional hazards model and five other methods of estimating treatment effects from time-to-event outcomes, which relax the proportional hazards assumption, were applied to a network of melanoma trials reporting overall survival: restricted mean survival time, generalised gamma, piecewise exponential, fractional polynomial and Royston-Parmar models.

RESULTS

All models fitted the melanoma network acceptably well. However, there were important differences in extrapolations of the survival curve and interpretability of the modelling constraints demonstrating the potential for different conclusions from different modelling approaches.

CONCLUSION

The restricted mean survival time, generalised gamma, piecewise exponential, fractional polynomial and Royston-Parmar models can accommodate non-proportional hazards and differing lengths of trial follow-up within a network meta-analysis of time-to-event outcomes. We recommend that model choice is informed using available and relevant prior knowledge, model transparency, graphically comparing survival curves alongside observed data to aid consideration of the reliability of the survival estimates, and consideration of how the treatment effect estimates can be incorporated within a decision model.

A non-parametric approach for jointly combining evidence on progression free and overall survival time in network meta-analysis

Randomised controlled trials of cancer treatments typically report progression free survival (PFS) and overall survival (OS) outcomes. Existing methods to synthesise evidence on PFS and OS either rely on the proportional hazards assumption or make parametric assumptions which may not capture the diverse survival curve shapes across studies and treatments. Furthermore, PFS and OS are not independent: OS is the sum of PFS and post-progression survival (PPS). Our aim was to develop a non-parametric approach for jointly synthesising evidence from published Kaplan-Meier survival curves of PFS and OS without assuming proportional hazards. Restricted mean survival times (RMST) are estimated by the area under the survival curves (AUCs) up to a restricted follow-up time. The correlation between AUCs due to the constraint that OS>PFS is estimated using bootstrap re-sampling. Network meta-analysis models are given for RMST for PFS and PPS and ensure that OS=PFS + PPS. Both additive and multiplicative network meta-analysis models are presented to obtain relative treatment effects as either differences or ratios of RMST. The methods are illustrated with a network meta-analysis of treatments for Stage IIIA-N2 Non-Small Cell Lung Cancer. The approach has implications for health economic models of cancer treatments which require estimates of the mean time spent in the PFS and PPS health-states. The methods can be applied to a single time-to-event outcome, and so have wide applicability in any field where time-to-event outcomes are reported, the proportional hazards assumption is in doubt, and survival curve shapes differ across studies and interventions. This article is protected by copyright. All rights reserved.

Uptake of methodological advances for synthesis of continuous and time-to-event outcomes would maximize use of the evidence base

Objective

The objective of the study is to establish how often continuous and time-to-event outcomes are synthesized in health technology assessment (HTA), the statistical methods and software used in their analysis and how often evidence synthesis informs decision models.

Study Design and Setting

This is a review of National Institute of Health Research HTA reports, National Institute for Health and Care Excellence (NICE) technology appraisals, and NICE guidelines reporting quantitative meta-analysis or network meta-analysis of at least one continuous or time-to-event outcome published from April 01, 2018 to March 31, 2019.

Results

We identified 47 eligible articles. At least one continuous or time-to-event outcome was synthesized in 51% and 55% of articles, respectively. Evidence synthesis results informed decision models in two-thirds of articles. The review and expert knowledge identified five areas where methodology is available for improving the synthesis of continuous and time-to-event outcomes: i) outcomes reported on multiple scales, ii) reporting of multiple related outcomes, iii) appropriateness of the additive scale, iv) reporting of multiple time points, and v) nonproportional hazards. We identified three anticipated barriers to the uptake and implementation of these methods: i) statistical expertise, ii) software, and iii) reporting of trials.

Conclusion

Continuous and time-to-event outcomes are routinely reported in HTA. However, increased uptake of methodological advances could maximize the evidence base used to inform the decision making process.

Multivariate network meta-analysis of survival function parameters

BACKGROUND

Network meta-analysis (NMA) of survival data with a multidimensional treatment effect has been introduced as an alternative to NMA based on the proportional hazards assumption. However, these flexible models have some limitations, such as the use of an approximate likelihood based on discrete hazards, rather than a likelihood for individual event times. The aim of this article is to overcome the limitations and present an alternative implementation of these flexible NMA models for time-to-event outcomes with a two-step approach.

METHODS

First, for each arm of every randomised controlled trial (RCT) connected in the network of evidence, reconstructed patient data are fit to alternative survival distributions, including the exponential, Weibull, Gompertz, log-normal, and log-logistic. Next, for each distribution, its scale and shape parameters are included in a multivariate NMA to obtain time-varying estimates of relative treatment effects between competing interventions.

RESULTS

An illustrative analysis is presented for a network of RCTs evaluating multiple interventions for advanced melanoma regarding overall survival. Alternative survival distributions were compared based on model fit criteria. Based on the log-logistic distribution, the difference in shape and scale parameters for each treatment versus dacarbazine (DTIC) was identified and the corresponding log hazard and survival curves were presented.

CONCLUSIONS

The presented two-step NMA approach provides an evidence synthesis framework for time-to-event outcomes grounded in standard practice of parametric survival analysis. The method allows for a more transparent and efficient model selection process.

Individual participant data meta-analysis of intervention studies with time-to-event outcomes: A review of the methodology and an applied example

Many randomized trials evaluate an intervention effect on time-to-event outcomes. Individual participant data (IPD) from such trials can be obtained and combined in a so-called IPD meta-analysis (IPD-MA), to summarize the overall intervention effect. We performed a narrative literature review to provide an overview of methods for conducting an IPD-MA of randomized intervention studies with a time-to-event outcome. We focused on identifying good methodological practice for modeling frailty of trial participants across trials, modeling heterogeneity of intervention effects, choosing appropriate association measures, dealing with (trial differences in) censoring and follow-up times, and addressing time-varying intervention effects and effect modification (interactions).We discuss how to achieve this using parametric and semi-parametric methods, and describe how to implement these in a one-stage or two-stage IPD-MA framework. We recommend exploring heterogeneity of the effect(s) through interaction and non-linear effects. Random effects should be applied to account for residual heterogeneity of the intervention effect. We provide further recommendations, many of which specific to IPD-MA of time-to-event data from randomized trials examining an intervention effect.We illustrate several key methods in a real IPD-MA, where IPD of 1225 participants from 5 randomized clinical trials were combined to compare the effects of Carbamazepine and Valproate on the incidence of epileptic seizures.

Development of an interactive web-based tool to conduct and interrogate meta-analysis of diagnostic test accuracy studies: MetaDTA

Background

Recommended statistical methods for meta-analysis of diagnostic test accuracy studies require relatively complex bivariate statistical models which can be a barrier for non-statisticians. A further barrier exists in the software options available for fitting such models. Software accessible to non-statisticians, such as RevMan, does not support the fitting of bivariate models thus users must seek statistical support to use R, Stata or SAS. Recent advances in web technologies make analysis tool creation much simpler than previously. As well as accessibility, online tools can allow tailored interactivity not found in other packages allowing multiple perspectives of data to be displayed and information to be tailored to the user’s preference from a simple interface. We set out to: (i) Develop a freely available web-based “point and click” interactive tool which allows users to input their DTA study data and conduct meta-analyses for DTA reviews, including sensitivity analyses. (ii) Illustrate the features and benefits of the interactive application using an existing DTA meta-analysis for detecting dementia.

Methods

To create our online freely available interactive application we used the existing R packages lme4 and Shiny to analyse the data and create an interactive user interface respectively.

Results

MetaDTA, an interactive online application was created for conducting meta-analysis of DTA studies. The user interface was designed to be easy to navigate having different tabs for different functions. Features include the ability for users to enter their own data, customise plots, incorporate quality assessment results and quickly conduct sensitivity analyses. All plots produced can be exported as either .png or .pdf files to be included in report documents. All tables can be exported as .csv files.

Conclusions

MetaDTA, is a freely available interactive online application which meta-analyses DTA studies, plots the summary ROC curve, incorporates quality assessment results and allows for sensitivity analyses to be conducted in a timely manner. Due to the rich feature-set and user-friendliness of the software it should appeal to a wide audience including those without specialist statistical knowledge. We encourage others to create similar applications for specialist analysis methods to encourage broader uptake which in-turn could improve research quality.

One-stage individual participant data meta-analysis models: estimation of treatment-covariate interactions must avoid ecological bias by separating out within-trial and across-trial information

Stratified medicine utilizes individual‐level covariates that are associated with a differential treatment effect, also known as treatment‐covariate interactions. When multiple trials are available, meta‐analysis is used to help detect true treatment‐covariate interactions by combining their data. Meta‐regression of trial‐level information is prone to low power and ecological bias, and therefore, individual participant data (IPD) meta‐analyses are preferable to examine interactions utilizing individual‐level information. However, one‐stage IPD models are often wrongly specified, such that interactions are based on amalgamating within‐ and across‐trial information. We compare, through simulations and an applied example, fixed‐effect and random‐effects models for a one‐stage IPD meta‐analysis of time‐to‐event data where the goal is to estimate a treatment‐covariate interaction. We show that it is crucial to centre patient‐level covariates by their mean value in each trial, in order to separate out within‐trial and across‐trial information. Otherwise, bias and coverage of interaction estimates may be adversely affected, leading to potentially erroneous conclusions driven by ecological bias. We revisit an IPD meta‐analysis of five epilepsy trials and examine age as a treatment effect modifier. The interaction is −0.011 (95% CI: −0.019 to −0.003; p = 0.004), and thus highly significant, when amalgamating within‐trial and across‐trial information. However, when separating within‐trial from across‐trial information, the interaction is −0.007 (95% CI: −0.019 to 0.005; p = 0.22), and thus its magnitude and statistical significance are greatly reduced. We recommend that meta‐analysts should only use within‐trial information to examine individual predictors of treatment effect and that one‐stage IPD models should separate within‐trial from across‐trial information to avoid ecological bias. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Discontinuation of oral antivirals in chronic hepatitis B: A systematic review

The possibility of safe discontinuation of therapy with nucleos(t)ide analogues (NAs) remains one of the most controversial topics in the management of chronic hepatitis B. Therefore, we systematically reviewed the existing data on NA discontinuation in this setting and tried to identify factors affecting the probability of posttherapy remission. A literature search was performed in order to identify all published studies including patients who discontinued NAs in virological remission (VR) and were followed for ≥12 months thereafter. Twenty-five studies with 1716 patients were included. The pooled rates of durable VR remission were 51.4%, 39.3%, and 38.2% at 12, 24, and 36 months, respectively, after NA discontinuation, being relatively higher in initially hepatitis B e antigen (HBeAg)-positive patients (62.5%, 53.4%, 51.5%) than HBeAg-negative patients (43.7%, 31.3%, 30.1%) (P = 0.064). The weighted probability of durable biochemical remission was 65.4%, being numerically higher in HBeAg-positive than HBeAg-negative patients (76.2% versus 56.7%, P = 0.130). The weighted probability of hepatitis B surface antigen loss was 2.0%. The rates of durable VR did not significantly differ according to the VR definition (hepatitis B virus DNA <200, < 2000, < 20,000 IU/mL) or duration of on-therapy VR in HBeAg-positive patients, but they were significantly higher in studies with HBeAg-negative patients and on-therapy VR > 24 than ≤ 24 months (VR at 12 months off-NAs: 75.0% versus 35.6%, P = 0.005). The weighted probability of durable HBeAg seroconversion was 91.9% and 88.0% at 12 and 24 months, respectively, after NA discontinuation without being affected by the duration of on-therapy VR or consolidation therapy (>6 months in all studies).

CONCLUSION

Durable VR seems to be feasible in a substantial proportion of patients who discontinue long-term NA therapy; on-therapy VR > 24 months offers higher chances of off-NA VR in patients with HBeAg-negative chronic hepatitis B.

Bias and precision of methods for estimating the difference in restricted mean survival time from an individual patient data meta-analysis

Background

The difference in restricted mean survival time (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ rmstD\left({t}^{\ast}\right) $$\end{document}rmstDt∗), the area between two survival curves up to time horizon \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {t}^{\ast } $$\end{document}t∗, is often used in cost-effectiveness analyses to estimate the treatment effect in randomized controlled trials. A challenge in individual patient data (IPD) meta-analyses is to account for the trial effect. We aimed at comparing different methods to estimate the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ rmstD\left({t}^{\ast}\right) $$\end{document}rmstDt∗ from an IPD meta-analysis.

Methods

We compared four methods: the area between Kaplan-Meier curves (experimental vs. control arm) ignoring the trial effect (Naïve Kaplan-Meier); the area between Peto curves computed at quintiles of event times (Peto-quintile); the weighted average of the areas between either trial-specific Kaplan-Meier curves (Pooled Kaplan-Meier) or trial-specific exponential curves (Pooled Exponential). In a simulation study, we varied the between-trial heterogeneity for the baseline hazard and for the treatment effect (possibly correlated), the overall treatment effect, the time horizon \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {t}^{\ast } $$\end{document}t∗, the number of trials and of patients, the use of fixed or DerSimonian-Laird random effects model, and the proportionality of hazards. We compared the methods in terms of bias, empirical and average standard errors. We used IPD from the Meta-Analysis of Chemotherapy in Nasopharynx Carcinoma (MAC-NPC) and its updated version MAC-NPC2 for illustration that included respectively 1,975 and 5,028 patients in 11 and 23 comparisons.

Results

The Naïve Kaplan-Meier method was unbiased, whereas the Pooled Exponential and, to a much lesser extent, the Pooled Kaplan-Meier methods showed a bias with non-proportional hazards. The Peto-quintile method underestimated the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ rmstD\left({t}^{\ast}\right) $$\end{document}rmstDt∗, except with non-proportional hazards at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {t}^{\ast } $$\end{document}t∗= 5 years. In the presence of treatment effect heterogeneity, all methods except the Pooled Kaplan-Meier and the Pooled Exponential with DerSimonian-Laird random effects underestimated the standard error of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ rmstD\left({t}^{\ast}\right) $$\end{document}rmstDt∗. Overall, the Pooled Kaplan-Meier method with DerSimonian-Laird random effects formed the best compromise in terms of bias and variance. The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ rmstD\left({t}^{\ast },=,10,\kern0.5em ,\mathrm{years}\right) $$\end{document}rmstDt∗=10years estimated with the Pooled Kaplan-Meier method was 0.49 years (95 % CI: [−0.06;1.03], p = 0.08) when comparing radiotherapy plus chemotherapy vs. radiotherapy alone in the MAC-NPC and 0.59 years (95 % CI: [0.34;0.84], p < 0.0001) in the MAC-NPC2.

Conclusions

We recommend the Pooled Kaplan-Meier method with DerSimonian-Laird random effects to estimate the difference in restricted mean survival time from an individual-patient data meta-analysis.

Electronic supplementary material

The online version of this article (doi:10.1186/s12874-016-0137-z) contains supplementary material, which is available to authorized users.

Get real in individual participant data (IPD) meta-analysis: a review of the methodology

Individual participant data (IPD) meta-analysis is an increasingly used approach for synthesizing and investigating treatment effect estimates. Over the past few years, numerous methods for conducting an IPD meta-analysis (IPD-MA) have been proposed, often making different assumptions and modeling choices while addressing a similar research question. We conducted a literature review to provide an overview of methods for performing an IPD-MA using evidence from clinical trials or non-randomized studies when investigating treatment efficacy. With this review, we aim to assist researchers in choosing the appropriate methods and provide recommendations on their implementation when planning and conducting an IPD-MA.

Meta-analysis of time-to-event outcomes from randomized trials using restricted mean survival time: application to individual participant data

Meta-analysis of time-to-event outcomes using the hazard ratio as a treatment effect measure has an underlying assumption that hazards are proportional. The between-arm difference in the restricted mean survival time is a measure that avoids this assumption and allows the treatment effect to vary with time. We describe and evaluate meta-analysis based on the restricted mean survival time for dealing with non-proportional hazards and present a diagnostic method for the overall proportional hazards assumption. The methods are illustrated with the application to two individual participant meta-analyses in cancer. The examples were chosen because they differ in disease severity and the patterns of follow-up, in order to understand the potential impacts on the hazards and the overall effect estimates. We further investigate the estimation methods for restricted mean survival time by a simulation study.