Bayesian one-step IPD network meta-analysis of time-to-event data using Royston-Parmar models

Bayesian pairwise meta-analysis of time-to-event outcomes in the presence of non-proportional hazards: A simulation study of flexible parametric, piecewise exponential and fractional polynomial models

BACKGROUND

Traditionally, meta-analysis of time-to-event outcomes reports a single pooled hazard ratio assuming proportional hazards (PH). For health technology assessment evaluations, hazard ratios are frequently extrapolated across a lifetime horizon. However, when treatment effects vary over time, an assumption of PH is not always valid. The Royston-Parmar (RP), piecewise exponential (PE), and fractional polynomial (FP) models can accommodate non-PH and provide plausible extrapolations of survival curves beyond observed data.

METHODS

Simulation study to assess and compare the performance of RP, PE, and FP models in a Bayesian framework estimating restricted mean survival time difference (RMSTD) at 50 years from a pairwise meta-analysis with evidence of non-PH. Individual patient data were generated from a mixture Weibull distribution. Twelve scenarios were considered varying the amount of follow-up data, number of trials in a meta-analysis, non-PH interaction coefficient, and prior distributions. Performance was assessed through bias and mean squared error. Models were applied to a metastatic breast cancer example.

RESULTS

FP models performed best when the non-PH interaction coefficient was 0.2. RP models performed best in scenarios with complete follow-up data. PE models performed well on average across all scenarios. In the metastatic breast cancer example, RMSTD at 50-years ranged from -14.6 to 8.48 months.

CONCLUSIONS

Synthesis of time-to-event outcomes and estimation of RMSTD in the presence of non-PH can be challenging and computationally intensive. Different approaches make different assumptions regarding extrapolation and sensitivity analyses varying key assumptions are essential to check the robustness of conclusions to different assumptions for the underlying survival function.

Implementing Multilevel Network Meta-Regression for Time-To-Event Outcomes: A Case Study in Relapsed Refractory Multiple Myeloma

OBJECTIVES

Multilevel network meta-regression (ML-NMR) leverages individual patient data (IPD) and aggregate data from a network of randomized controlled trials (RCTs) to assess the comparative efficacy of multiple treatments, while adjusting for between-study differences. We provide an overview of ML-NMR for time-to-event outcomes and apply it to an illustrative case study, including example R code.

METHODS

The case study evaluated the comparative efficacy of idecabtagene vicleucel (ide-cel), selinexor+dexamethasone (Sd), belantamab mafodotin (BM), and conventional care (CC) for patients with triple-class exposed relapsed/refractory multiple myeloma in terms of overall survival. Single-arm clinical trials and real-world data were naively combined to create an aggregate data artificial RCT (aRCT) (MAMMOTH-CC versus DREAMM-2-BM versus STORM-2-Sd) and an IPD aRCT (KarMMa-ide-cel versus KarMMa-RW-CC). With some assumptions, we incorporated continuous covariates with skewed distributions, reported as median and range. The ML-NMR models adjusted for number of prior lines, triple-class refractory status, and age and were compared using the leave-one-out information criterion. We summarized predicted hazard ratios and survival (95% credible intervals) in the IPD aRCT population.

RESULTS

The Weibull ML-NMR model had the lowest leave-one-out information criterion. Ide-cel was more efficacious than Sd, BM, and CC in terms of overall survival. Effect modifiers had minimal impact on the model, and only triple-class refractory was a prognostic factor.

CONCLUSIONS

We demonstrate an application of ML-NMR for time-to-event outcomes and introduce code that can be used to aid implementation. Given its benefits, we encourage practitioners to utilize ML-NMR when population adjustment is necessary for comparisons of multiple treatments.

Balancing Efficacy and Tolerability of First-Line Systemic Therapies for Advanced Hepatocellular Carcinoma: A Network Meta-Analysis

Background

Atezolizumab + bevacizumab represent the current standard of care for first-line treatment of advanced hepatocellular carcinoma (HCC). However, direct comparison with other combination treatments including immune checkpoint inhibitors (ICI) + tyrosine kinase inhibitors (TKIs) are lacking.

Objectives

This network meta-analysis (NMA) aims to indirectly compare the efficacy and the safety of first-line systemic therapies for unresectable advanced HCC.

Method

A literature search of MEDLINE, Embase, and SCOPUS databases was conducted up to October 31, 2022. Phase 3 randomized controlled trials (RCTs) testing TKIs, including sorafenib and lenvatinib, or ICIs reporting overall survival (OS) and progression-free survival (PFS) were included. Individual survival data were extracted from OS and PFS curves to calculate restricted mean survival time. A Bayesian NMA was performed to compare treatments in terms of efficacy (15- and 30-month OS, 6-month PFS) and safety, represented by grade ≥3 (severe) adverse events (SAEs). The incremental safety-effectiveness ratio as measure of net health benefit was calculated as the difference in SAE probability divided by survival difference between the 2 most effective treatments.

Results

Nine RCTs enrolling 6,600 patients were included. Atezolizumab plus bevacizumab showed the highest probability (88%) of achieving the 30-month OS landmark. Lenvatinib showed a probability of 86% of achieving best PFS outcomes. ICI monotherapies ranked as most tolerable. Atezolizumab plus bevacizumab showed the best net health benefit for OS, compared to durvalumab plus tremelimumab. When evaluating the net health benefit for PFS, at a willingness-to-risk threshold of 10% of SAEs for life-month gained, atezolizumab plus bevacizumab was favoured in 78% of cases, while at threshold of 30% of SAEs for life-month gained, lenvatinib was favoured in 76% of cases.

Conclusions

Atezolizumab plus bevacizumab is the best treatment in terms of net benefit and therefore it should be recommended as standard of care. Compared to atezolizumab plus bevacizumab, lenvatinib monotherapy had the best net benefit for PFS when physicians and patients are available to accept a higher risk of toxicity.

Twenty years of network meta-analysis: Continuing controversies and recent developments

Network meta-analysis (NMA) is an extension of pairwise meta-analysis (PMA) which combines evidence from trials on multiple treatments in connected networks. NMA delivers internally consistent estimates of relative treatment efficacy, needed for rational decision making. Over its first 20 years NMA's use has grown exponentially, with applications in both health technology assessment (HTA), primarily re-imbursement decisions and clinical guideline development, and clinical research publications. This has been a period of transition in meta-analysis, first from its roots in educational and social psychology, where large heterogeneous datasets could be explored to find effect modifiers, to smaller pairwise meta-analyses in clinical medicine on average with less than six studies. This has been followed by narrowly-focused estimation of the effects of specific treatments at specific doses in specific populations in sparse networks, where direct comparisons are unavailable or informed by only one or two studies. NMA is a powerful and well-established technique but, in spite of the exponential increase in applications, doubts about the reliability and validity of NMA persist. Here we outline the continuing controversies, and review some recent developments. We suggest that heterogeneity should be minimized, as it poses a threat to the reliability of NMA which has not been fully appreciated, perhaps because it has not been seen as a problem in PMA. More research is needed on the extent of heterogeneity and inconsistency in datasets used for decision making, on formal methods for making recommendations based on NMA, and on the further development of multi-level network meta-regression.

A Comparison of Alternative Network Meta-Analysis Methods in the Presence of Nonproportional Hazards: A Case Study in First-Line Advanced or Metastatic Renal Cell Carcinoma

OBJECTIVES

Network meta-analysis (NMA) of time-to-event outcomes based on constant hazard ratios can result in biased findings when the proportional hazards (PHs) assumption does not hold in a subset of trials. We aimed to summarize the published non-PH NMA methods for time-to-event outcomes, demonstrate their application, and compare their results.

METHODS

The following non-PH NMA methods were compared through an illustrative case study in oncology of 4 randomized controlled trials in terms of progression-free survival and overall survival: (1) 1-step or (2) 2-step multivariate NMAs based on traditional survival distributions or fractional polynomials, (3) NMAs with restricted cubic splines for baseline hazard, and (4) restricted mean survival NMA.

RESULTS

For progression-free survival, the PH assumption did not hold across trials and non-PH NMA methods better reflected the relative treatment effects over time. The most flexible models (fractional polynomials and restricted cubic splines) fit better to the data than the other approaches. Estimated hazard ratios obtained with different non-PH NMA methods were similar at 5 years of follow-up but differed thereafter in the extrapolations. Although there was no strong evidence of PH violation for overall survival, non-PH NMA methods captured this uncertainty in the relative treatment effects over time.

CONCLUSIONS

When the PH assumption is questionable in a subset of the randomized controlled trials, we recommend assessing alternative non-PH NMA methods to estimate relative treatment effects for time-to-event outcomes. We propose a transparent and explicit stepwise model selection process considering model fit, external constraints, and clinical validity. Given inherent uncertainty, sensitivity analyses are suggested.

Bayesian hierarchical model-based network meta-analysis to overcome survival extrapolation challenges caused by data immaturity

Aim: This research evaluated standard Weibull mixture cure (WMC) network meta-analysis (NMA) with Bayesian hierarchical (BH) WMC NMA to inform long-term survival of therapies. Materials & methods: Four trials in previously treated metastatic non-small-cell lung cancer with PD-L1 >1% were used comparing docetaxel with nivolumab, pembrolizumab and atezolizumab. Cure parameters related to a certain treatment class were assumed to share a common distribution. Results: Standard WMC NMA predicted cure rates were 0.03 (0.01; 0.07), 0.18 (0.12; 0.24), 0.07 (0.02; 0.15) and 0.03 (0.00; 0.09) for docetaxel, nivolumab, pembrolizumab and atezolizumab, respectively, with corresponding incremental life years (LY) of 3.11 (1.65; 4.66), 1.06 (0.41; 2.37) and 0.42 (-0.57; 1.68). The Bayesian hierarchical-WMC-NMA rates were 0.06 (0.03; 0.10), 0.17 (0.11; 0.23), 0.12 (0.05; 0.20) and 0.12 (0.03; 0.23), respectively, with incremental LY of 2.35 (1.04; 3.93), 1.67 (0.68; 2.96) and 1.36 (-0.05; 3.64). Conclusion: BH-WMC-NMA impacts incremental mean LYs and cost-effectiveness ratios, potentially affecting reimbursement decisions.

A Guide to Selecting Flexible Survival Models to Inform Economic Evaluations of Cancer Immunotherapies

OBJECTIVES

Parametric models are routinely used to estimate the benefit of cancer drugs beyond trial follow-up. The advent of immune checkpoint inhibitors has challenged this paradigm, and emerging evidence suggests that more flexible survival models, which can better capture the shapes of complex hazard functions, might be needed for these interventions. Nevertheless, there is a need for an algorithm to help analysts decide whether flexible models are required and, if so, which should be chosen for testing. This position article has been produced to bridge this gap.

METHODS

A virtual advisory board comprising 7 international experts with in-depth knowledge of survival analysis and health technology assessment was held in summer 2021. The experts discussed 24 questions across 6 topics: the current survival model selection procedure, data maturity, heterogeneity of treatment effect, cure and mortality, external evidence, and additions to existing guidelines. Their responses culminated in an algorithm to inform selection of flexible survival models.

RESULTS

The algorithm consists of 8 steps and 4 questions. Key elements include the systematic identification of relevant external data, using clinical expert input at multiple points in the selection process, considering the future and the observed hazard functions, assessing the potential for long-term survivorship, and presenting results from all plausible models.

CONCLUSIONS

This algorithm provides a systematic, evidence-based approach to justify the selection of survival extrapolation models for cancer immunotherapies. If followed, it should reduce the risk of selecting inappropriate models, partially addressing a key area of uncertainty in the economic evaluation of these agents.

A network meta-analysis of immunotherapy-based treatments for advanced nonsquamous non-small cell lung cancer

Introduction: In the absence of head-to-head trials comparing immunotherapies for advanced nonsquamous non-small-cell lung cancer (NsqNSCLC), a network meta-analysis (NMA) was conducted to compare the relative efficacy of these treatments. Materials & methods: A systematic literature review of randomized controlled trials evaluating first-line-to-progression and second-line treatments for advanced NsqNSCLC informed Bayesian NMAs for overall survival (OS) and progression-free survival (PFS) end points. Results: Among first-line-to-progression treatments, pembrolizumab + pemetrexed + platinum showed the greatest OS benefit versus other regimens and a PFS benefit versus all but three regimens. Among second-line treatments, an OS benefit was seen for atezolizumab, nivolumab and pembrolizumab versus docetaxel. Conclusion: Pembrolizumab + pemetrexed + platinum showed the maximum OS benefit in the first-line setting. In the second-line setting, anti-PD-1/anti-PD-L1 monotherapies were better than docetaxel.

A systematic review and network meta-analysis of first-line immune checkpoint inhibitor combination therapies in patients with advanced non-squamous non-small cell lung cancer

INTRODUCTION

Clinical evidence suggests that first-line immune checkpoint inhibitor (ICI) combination therapies can improve survival in patients with advanced non-squamous non-small cell lung cancer (nsq-NSCLC). However, the optimal strategy remains unknown without a systematic comparison of their long-term effects.

METHODS

We performed a systematic review and network meta-analysis by retrieving up-to-date literature from PubMed® (National Library of Medicine, Bethesda, MD, USA), Embase® (Elsevier, Amsterdam, Netherlands), MEDLINE® (National Library of Medicine), ClinicalTrials.gov (National Library of Medicine), and major international conference publications. Published studies and abstracts comparing first-line ICI combination therapies with other treatments for patients with advanced nsq-NSCLC were included. Restricted mean survival time (RMST) was measured over 12 months for progression-free survival (PFS) and 18 months for overall survival (OS), and the Royston-Parmar model was used to extrapolate and compare data for the long-term outcomes.

RESULTS

We included a total of 11 trials involving 12 therapies and 6,130 patients. Pembrolizumab plus chemotherapy exhibited the best overall survival (OS) benefit at both 18 and 60 months [RMST = 2.95, 95% confidence interval (CI) 1.96 to 3.97; life-years gained over a 5-year period = 2.18 years]. Nivolumab plus bevacizumab plus chemotherapy was found to present the best progression-free survival (PFS) benefit at 12 months (RMST 3.02, 95% CI 2.11 to 3.91), whereas atezolizumab plus bevacizumab plus chemotherapy showed the best PFS benefit at 36 months (life-years gained over 3 years = 1.22 years). Subgroup analyses showed that among patients with programmed death-ligand 1 (PD-L1) expression ≥ 50%, atezolizumab plus chemotherapy and nivolumab plus ipilimumab resulted in superior OS benefits at 18 and 60 months, respectively. Among patients with PD-L1 expression< 1%, pembrolizumab plus chemotherapy was associated with OS benefits at both 18 and 60 months. Sintilimab plus chemotherapy was associated with relatively fewer grade ≥ 3 adverse events than other ICI combination therapies.

CONCLUSION

Our results show that ICI combination therapies showed better survival benefits than chemotherapy. Pembrolizumab plus chemotherapy could provide the best OS benefits to patients with advanced nsq-NSCLC, whereas atezolizumab plus bevacizumab plus chemotherapy could bring the best PFS benefits. The optimal ICI combination therapy varies depending on PD-L1 expression level.

SYSTEMATIC REVIEW REGISTRATION

https://www.crd.york.ac.uk/PROSPERO/display_record.php?RecordID=325005, identifier CRD42022325005.

Novel and existing flexible survival methods for network meta-analyses

Aim: Technical Support Document 21 discusses trial-based, flexible relative survival models. The authors generalized flexible relative survival models to the network meta-analysis (NMA) setting while accounting for different treatment-effect specifications. Methods: The authors compared the standard parametric model with mixture, mixture cure and nonmixture cure, piecewise, splines and fractional polynomial models. The optimal treatment-effect parametrization was defined in two steps. First, all models were run with treatment effects on all parameters and subsequently the optimal model was defined by removing uncertain treatment effects, for which the parameter was smaller than its standard deviation. The authors used a network in previously treated advanced non-small-cell lung cancer. Results: Flexible model-based NMAs impact fit and incremental mean survival and they increase corresponding uncertainty. Treatment-effect specification impacts incremental survival, reduces uncertainty and improves the fit statistic. Conclusion: Extrapolation techniques already available for individual trials can now be used for NMAs to ensure that the most plausible extrapolations are being used for health technology assessment submissions.

Using individual participant data to improve network meta-analysis projects

A network meta-analysis combines the evidence from existing randomised trials about the comparative efficacy of multiple treatments. It allows direct and indirect evidence about each comparison to be included in the same analysis, and provides a coherent framework to compare and rank treatments. A traditional network meta-analysis uses aggregate data (eg, treatment effect estimates and standard errors) obtained from publications or trial investigators. An alternative approach is to obtain, check, harmonise and meta-analyse the individual participant data (IPD) from each trial. In this article, we describe potential advantages of IPD for network meta-analysis projects, emphasising five key benefits: (1) improving the quality and scope of information available for inclusion in the meta-analysis, (2) examining and plotting distributions of covariates across trials (eg, for potential effect modifiers), (3) standardising and improving the analysis of each trial, (4) adjusting for prognostic factors to allow a network meta-analysis of conditional treatment effects and (5) including treatment-covariate interactions (effect modifiers) to allow relative treatment effects to vary by participant-level covariate values (eg, age, baseline depression score). A running theme of all these benefits is that they help examine and reduce heterogeneity (differences in the true treatment effect between trials) and inconsistency (differences in the true treatment effect between direct and indirect evidence) in the network. As a consequence, an IPD network meta-analysis has the potential for more precise, reliable and informative results for clinical practice and even allows treatment comparisons to be made for individual patients and targeted populations conditional on their particular characteristics.

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.

Bayesian multivariate network meta-analysis model for the difference in restricted mean survival times

Network meta-analysis (NMA) is essential for clinical decision-making. NMA enables inference for all pair-wise comparisons between interventions available for the same indication, by using both direct evidence and indirect evidence. In randomized trials with time-to event outcome data, such as lung cancer data, conventional NMA methods rely on the hazard ratio and the proportional hazards assumption, and ignore the varying follow-up durations across trials. We introduce a novel multivariate NMA model for the difference in restricted mean survival times (RMST). Our model synthesizes all the available evidence from multiple time points simultaneously and borrows information across time points through within-study covariance and between-study covariance for the differences in RMST. We propose an estimator of the within-study covariance and we then assume it to be known. We estimate the model under the Bayesian framework. We evaluated our model by conducting a simulation study. Our multiple-time-point model yields lower mean squared error over the conventional single-time-point model at all time points, especially when the availability of evidence decreases. We illustrated the model on a network of randomized trials of second-line treatments of advanced non-small-cell lung cancer. Our multiple-time-point model yielded increased precision and detected evidence of benefit at earlier time points as compared to the single-time-point model. Our model has the advantage of providing clinically interpretable measures of treatment effects.

A frequentist one-step model for a simple network meta-analysis of time-to-event data in presence of an effect modifier

Introduction

Individual patient data (IPD) present particular advantages in network meta-analysis (NMA) because interactions may lead an aggregated data (AD)-based model to wrong a treatment effect (TE) estimation. However, fewer works have been conducted for IPD with time-to-event contrary to binary outcomes. We aimed to develop a general frequentist one-step model for evaluating TE in the presence of interaction in a three-node NMA for time-to-event data.

Methods

One-step, frequentist, IPD-based Cox and Poisson generalized linear mixed models were proposed. We simulated a three-node network with or without a closed loop with (1) no interaction, (2) covariate-treatment interaction, and (3) covariate distribution heterogeneity and covariate-treatment interaction. These models were applied to the NMA (Meta-analyses of Chemotherapy in Head and Neck Cancer [MACH-NC] and Radiotherapy in Carcinomas of Head and Neck [MARCH]), which compared the addition of chemotherapy or modified radiotherapy (mRT) to loco-regional treatment with two direct comparisons. AD-based (contrast and meta-regression) models were used as reference.

Results

In the simulated study, no IPD models failed to converge. IPD-based models performed well in all scenarios and configurations with small bias. There were few variations across different scenarios. In contrast, AD-based models performed well when there were no interactions, but demonstrated some bias when interaction existed and a larger one when the modifier was not distributed evenly. While meta-regression performed better than contrast-based only, it demonstrated a large variability in estimated TE. In the real data example, Cox and Poisson IPD-based models gave similar estimations of the model parameters. Interaction decomposition permitted by IPD explained the ecological bias observed in the meta-regression.

Conclusion

The proposed general one-step frequentist Cox and Poisson models had small bias in the evaluation of a three-node network with interactions. They performed as well or better than AD-based models and should also be undertaken whenever possible.

Penalized Poisson model for network meta-analysis of individual patient time-to-event data

Network meta-analysis (NMA) allows the combination of direct and indirect evidence from a set of randomized clinical trials. Performing NMA using individual patient data (IPD) is considered as a "gold standard" approach as it provides several advantages over NMA based on aggregate data. For example, it allows to perform advanced modeling of covariates or covariate-treatment interactions. An important issue in IPD NMA is the selection of influential parameters among terms that account for inconsistency, covariates, covariate-by-treatment interactions or nonproportionality of treatments effect for time to event data. This issue has not been deeply studied in the literature yet and in particular not for time-to-event data. A major difficulty is to jointly account for between-trial heterogeneity which could have a major influence on the selection process. The use of penalized generalized mixed effect model is a solution, but existing implementations have several shortcomings and an important computational cost that precludes their use for complex IPD NMA. In this article, we propose a penalized Poisson regression model to perform IPD NMA of time-to-event data. It is based only on fixed effect parameters which improve its computational cost over the use of random effects. It could be easily implemented using existing penalized regression package. Computer code is shared for implementation. The methods were applied on simulated data to illustrate the importance to take into account between trial heterogeneity during the selection procedure. Finally, it was applied to an IPD NMA of overall survival of chemotherapy and radiotherapy in nasopharyngeal carcinoma.

Individual Patient Data Meta-Analysis and Network Meta-Analysis

Meta-analyses are often conducted using trial-level summary data. However, when individual patient data (IPD ) is available, there is greater flexibility in the analysis and a wider range of statistical models that can be fitted. There are two approaches to fitting IPD models. The traditional two-stage approach involves analyzing each trial individually in the first stage and then combining trial estimates of treatment effectiveness in the second stage using methods developed for aggregate data meta-analysis. Growing in popularity is the one-stage approach in which trials are analyzed and synthesized within one statistical model whilst the clustering of patients within trials is accounted for. This chapter outlines both fixed effect and random effects one- and two-stage meta-analysis models for continuous, binary, and time-to-event outcomes. The meta-analysis framework is then extended to the scenario where there are more than two treatments and network meta-analysis models are described.The availability of IPD provides greater statistical power for investigating interactions between treatments and covariates. Treatment-covariate interactions contain both within- and across-trial information where the across-trial information may be subject to ecological bias. This chapter presents network meta-analysis models separating out the within- and across-trial information and finishes by considering practical solutions for dealing with missing covariate data, assessing the consistency assumption, combining IPD and aggregate data and specific considerations for time-to-event outcomes.

Progress and challenges of network meta-analysis

In the past years, network meta-analysis (NMA) has been widely used among clinicians, guideline makers, and health technology assessment agencies and has played an important role in clinical decision-making and guideline development. To inform further development of NMAs, we conducted a bibliometric analysis to assess the current status of published NMA methodological studies, summarized the methodological progress of seven types of NMAs, and discussed the current challenges of NMAs.

Chemotherapy and radiotherapy in locally advanced head and neck cancer: an individual patient data network meta-analysis

BACKGROUND

Randomised, controlled trials and meta-analyses have shown the survival benefit of concomitant chemoradiotherapy or hyperfractionated radiotherapy in the treatment of locally advanced head and neck cancer. However, the relative efficacy of these treatments is unknown. We aimed to determine whether one treatment was superior to the other.

METHODS

We did a frequentist network meta-analysis based on individual patient data of meta-analyses evaluating the role of chemotherapy (Meta-Analysis of Chemotherapy in Head and Neck Cancer [MACH-NC]) and of altered fractionation radiotherapy (Meta-Analysis of Radiotherapy in Carcinomas of Head and Neck [MARCH]). Randomised, controlled trials that enrolled patients with non-metastatic head and neck squamous cell cancer between Jan 1, 1980, and Dec 31, 2016, were included. We used a two-step random-effects approach, and the log-rank test, stratified by trial to compare treatments, with locoregional therapy as the reference. Overall survival was the primary endpoint. The global Cochran Q statistic was used to assess homogeneity and consistency and P score to rank treatments (higher scores indicate more effective therapies).

FINDINGS

115 randomised, controlled trials, which enrolled patients between Jan 1, 1980, and April 30, 2012, yielded 154 comparisons (28 978 patients with 19 253 deaths and 20 579 progression events). Treatments were grouped into 16 modalities, for which 35 types of direct comparisons were available. Median follow-up based on all trials was 6·6 years (IQR 5·0-9·4). Hyperfractionated radiotherapy with concomitant chemotherapy (HFCRT) was ranked as the best treatment for overall survival (P score 97%; hazard ratio 0·63 [95% CI 0·51-0·77] compared with locoregional therapy). The hazard ratio of HFCRT compared with locoregional therapy with concomitant chemoradiotherapy with platinum-based chemotherapy (CLRT_P) was 0·82 (95% CI 0·66-1·01) for overall survival. The superiority of HFCRT was robust to sensitivity analyses. Three other modalities of treatment had a better P score, but not a significantly better HR, for overall survival than CLRT_P (P score 78%): induction chemotherapy with taxane, cisplatin, and fluorouracil followed by locoregional therapy (IC_TaxPF-LRT; 89%), accelerated radiotherapy with concomitant chemotherapy (82%), and IC_TaxPF followed by CLRT (80%).

INTERPRETATION

The results of this network meta-analysis suggest that further intensifying chemoradiotherapy, using HFCRT or IC_TaxPF-CLRT, could improve outcomes over chemoradiotherapy for the treatment of locally advanced head and neck cancer.

FUNDINGS

French Institut National du Cancer, French Ligue Nationale Contre le Cancer, and Fondation ARC.

Antihypertensive treatment and risk of cancer: an individual participant data meta-analysis

BACKGROUND

Some studies have suggested a link between antihypertensive medication and cancer, but the evidence is so far inconclusive. Thus, we aimed to investigate this association in a large individual patient data meta-analysis of randomised clinical trials.

METHODS

We searched PubMed, MEDLINE, The Cochrane Central Register of Controlled Trials, and ClinicalTrials.gov from Jan 1, 1966, to Sept 1, 2019, to identify potentially eligible randomised controlled trials. Eligible studies were randomised controlled trials comparing one blood pressure lowering drug class with a placebo, inactive control, or other blood pressure lowering drug. We also required that trials had at least 1000 participant years of follow-up in each treatment group. Trials without cancer event information were excluded. We requested individual participant data from the authors of eligible trials. We pooled individual participant-level data from eligible trials and assessed the effects of angiotensin-converting enzyme inhibitors (ACEIs), angiotensin II receptor blockers (ARBs), β blockers, calcium channel blockers, and thiazide diuretics on cancer risk in one-stage individual participant data and network meta-analyses. Cause-specific fixed-effects Cox regression models, stratified by trial, were used to calculate hazard ratios (HRs). The primary outcome was any cancer event, defined as the first occurrence of any cancer diagnosed after randomisation. This study is registered with PROSPERO (CRD42018099283).

FINDINGS

33 trials met the inclusion criteria, and included 260 447 participants with 15 012 cancer events. Median follow-up of included participants was 4·2 years (IQR 3·0-5·0). In the individual participant data meta-analysis comparing each drug class with all other comparators, no associations were identified between any antihypertensive drug class and risk of any cancer (HR 0·99 [95% CI 0·95-1·04] for ACEIs; 0·96 [0·92-1·01] for ARBs; 0·98 [0·89-1·07] for β blockers; 1·01 [0·95-1·07] for thiazides), with the exception of calcium channel blockers (1·06 [1·01-1·11]). In the network meta-analysis comparing drug classes against placebo, we found no excess cancer risk with any drug class (HR 1·00 [95% CI 0·93-1·09] for ACEIs; 0·99 [0·92-1·06] for ARBs; 0·99 [0·89-1·11] for β blockers; 1·04 [0·96-1·13] for calcium channel blockers; 1·00 [0·90-1·10] for thiazides).

INTERPRETATION

We found no consistent evidence that antihypertensive medication use had any effect on cancer risk. Although such findings are reassuring, evidence for some comparisons was insufficient to entirely rule out excess risk, in particular for calcium channel blockers.

FUNDING

British Heart Foundation, National Institute for Health Research, Oxford Martin School.

A review of the quantitative effectiveness evidence synthesis methods used in public health intervention guidelines

BACKGROUND

The complexity of public health interventions create challenges in evaluating their effectiveness. There have been huge advancements in quantitative evidence synthesis methods development (including meta-analysis) for dealing with heterogeneity of intervention effects, inappropriate 'lumping' of interventions, adjusting for different populations and outcomes and the inclusion of various study types. Growing awareness of the importance of using all available evidence has led to the publication of guidance documents for implementing methods to improve decision making by answering policy relevant questions.

METHODS

The first part of this paper reviews the methods used to synthesise quantitative effectiveness evidence in public health guidelines by the National Institute for Health and Care Excellence (NICE) that had been published or updated since the previous review in 2012 until the 19th August 2019.The second part of this paper provides an update of the statistical methods and explains how they address issues related to evaluating effectiveness evidence of public health interventions.

RESULTS

The proportion of NICE public health guidelines that used a meta-analysis as part of the synthesis of effectiveness evidence has increased since the previous review in 2012 from 23% (9 out of 39) to 31% (14 out of 45). The proportion of NICE guidelines that synthesised the evidence using only a narrative review decreased from 74% (29 out of 39) to 60% (27 out of 45).An application in the prevention of accidents in children at home illustrated how the choice of synthesis methods can enable more informed decision making by defining and estimating the effectiveness of more distinct interventions, including combinations of intervention components, and identifying subgroups in which interventions are most effective.

CONCLUSIONS

Despite methodology development and the publication of guidance documents to address issues in public health intervention evaluation since the original review, NICE public health guidelines are not making full use of meta-analysis and other tools that would provide decision makers with fuller information with which to develop policy. There is an evident need to facilitate the translation of the synthesis methods into a public health context and encourage the use of methods to improve decision making.

Nonproportional Hazards in Network Meta-Analysis: Efficient Strategies for Model Building and Analysis

OBJECTIVES

To develop efficient approaches for fitting network meta-analysis (NMA) models with time-varying hazard ratios (such as fractional polynomials and piecewise constant models) to allow practitioners to investigate a broad range of models rapidly and to achieve a more robust and comprehensive model selection strategy.

METHODS

We reformulated the fractional polynomial and piecewise constant NMA models using analysis of variance-like parameterization. With this approach, both models are expressed as generalized linear models (GLMs) with time-varying covariates. Such models can be fitted efficiently with standard frequentist techniques. We applied our approach to the example data from the study by Jansen et al, in which fractional polynomial NMA models were introduced.

RESULTS

Fitting frequentist fixed-effect NMAs for a large initial set of candidate models took less than 1 second with standard GLM routines. This allowed for model selection from a large range of hazard ratio structures by comparing a set of criteria including Akaike information criterion/Bayesian information criterion, visual inspection of goodness-of-fit, and long-term extrapolations. The "best" models were then refitted in a Bayesian framework. Estimates agreed very closely.

CONCLUSIONS

NMA models with time-varying hazard ratios can be explored efficiently with a stepwise approach. A frequentist fixed-effect framework enables rapid exploration of different models. The best model can then be assessed further in a Bayesian framework to capture and propagate uncertainty for decision-making.

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.

Healthcare Costs of Treating Privately Insured Patients with Acute Myeloid Leukemia in the United States from 2004 to 2014: A Generalized Additive Modeling Approach

OBJECTIVES

The primary objective of this study was to predict healthcare cost trajectories for patients with newly diagnosed acute myeloid leukemia (AML) receiving allogeneic hematopoietic cell transplantation (alloHCT), as a function of days since chemotherapy initiation, days relative to alloHCT, and days before death or last date of insurance eligibility (LDE). An exploratory objective examined patients with AML receiving chemotherapy only.

METHODS

We used Optum's de-identified Clinformatics^® Data Mart Database to construct cumulative cost trajectories from chemotherapy initiation to death or LDE (through 31 December 2014) for US patients aged 20-74 years diagnosed between 1 March 2004 and 31 December 2013 (n = 187 alloHCT; n = 253 chemotherapy only). We used generalized additive modeling (GAM) to predict expected trajectories and bootstrapped confidence intervals (CIs) at user-specified intervals conditional on dates of alloHCT and death or LDE relative to chemotherapy initiation.

RESULTS

Expected costs (in 2017 values) for a hypothetical patient receiving alloHCT 60 days after chemotherapy initiation and followed for 5 years were $US572,000 (95% CI 517,000-633,000); $US119,000 (95% CI 51,000-192,000); $US102,000 (95% CI 0-285,000); $US79,000 (95% CI 0-233,000), for years 1-4, respectively, and either $US494,000 (95% CI 212,000-799,000) or $US108,000 (95% CI 0-230,000) in year 5, whether the patient died or was lost to follow-up on day 1825, respectively.

CONCLUSIONS

Rates of cost accrual varied over time since chemotherapy initiation, with accelerations around the time of alloHCT and death. GAM is a potentially useful approach for imputing longitudinal costs relative to treatment initiation and one or more intercurrent, clinical, or terminal events in randomized controlled trials or registries with unrecorded costs or for dynamic decision-analytic models.

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.

Identifying inconsistency in network meta-analysis: Is the net heat plot a reliable method?

One of the biggest challenges for network meta‐analysis is inconsistency, which occurs when the direct and indirect evidence conflict. Inconsistency causes problems for the estimation and interpretation of treatment effects and treatment contrasts. Krahn and colleagues proposed the net heat approach as a graphical tool for identifying and locating inconsistency within a network of randomized controlled trials. For networks with a treatment loop, the net heat plot displays statistics calculated by temporarily removing each design one at a time, in turn, and assessing the contribution of each remaining design to the inconsistency. The net heat plot takes the form of a matrix which is displayed graphically with coloring indicating the degree of inconsistency in the network. Applied to a network of individual participant data assessing overall survival in 7531 patients with lung cancer, we were surprised to find no evidence of important inconsistency from the net heat approach; this contradicted other approaches for assessing inconsistency such as the Bucher approach, Cochran's Q statistic, node‐splitting, and the inconsistency parameter approach, which all suggested evidence of inconsistency within the network at the 5% level. Further theoretical work shows that the calculations underlying the net heat plot constitute an arbitrary weighting of the direct and indirect evidence which may be misleading. We illustrate this further using a simulation study and a network meta‐analysis of 10 treatments for diabetes. We conclude that the net heat plot does not reliably signal inconsistency or identify designs that cause inconsistency.

Individual patient data network meta-analysis using either restricted mean survival time difference or hazard ratios: is there a difference? A case study on locoregionally advanced nasopharyngeal carcinomas

BACKGROUND

This study aimed at applying the restricted mean survival time difference (rmstD) as an absolute outcome measure in a network meta-analysis and comparing the results with those obtained using hazard ratios (HR) from the individual patient data (IPD) network meta-analysis (NMA) on the role of chemotherapy for nasopharyngeal carcinoma (NPC) recently published by the MAC-NPC collaborative group (Meta-Analysis of Chemotherapy [CT] in NPC).

PATIENTS AND METHODS

Twenty trials (5144 patients) comparing radiotherapy (RT) with or without CT in non-metastatic NPC were included. Treatments were grouped in seven categories: RT alone (RT), induction CT followed by RT (IC-RT), RT followed by adjuvant CT (RT-AC), IC followed by RT followed by AC (IC-RT-AC), concomitant chemoradiotherapy (CRT), IC followed by CRT (IC-CRT), and CRT followed by AC (CRT-AC). The primary endpoint was overall survival (OS); secondary endpoints were progression-free survival and locoregional control. The rmstD was estimated at t* = 10 years in each trial. Random-effect frequentist NMA models were applied. P score was used to rank treatments. Heterogeneity and inconsistency were evaluated.

RESULTS

The three treatments that had the highest effect on OS with rmstD were CRT-AC, IC-CRT, and CRT (respective P scores of 92%, 72%, and 64%) compared to CRT-AC, CRT, and IC-CRT when using HR (respective P scores of 96%, 71%, and 63%). Of the 32 HR and rmstD analyzed, 5 had a different interpretation, 3 with a direction change (different direction of treatment effect) and 2 with a change in significance (same direction but a change in statistical significance). Results for secondary endpoints were overall in agreement.

CONCLUSION

The use of either HR or rmstD impacts the results of NMA. Given the sensitivity of HR to non-proportional hazards, this finding could have implications in terms of meta-analysis methodology.

A framework for identifying treatment-covariate interactions in individual participant data network meta-analysis

Background: Stratified medicine seeks to identify patients most likely to respond to treatment. Individual participant data (IPD) network meta‐analysis (NMA) models have greater power than individual trials to identify treatment‐covariate interactions (TCIs). Treatment‐covariate interactions contain “within” and “across” trial interactions, where the across‐trial interaction is more susceptible to confounding and ecological bias.

Methods: We considered a network of IPD from 37 trials (5922 patients) for cervical cancer (2394 events), where previous research identified disease stage as a potential interaction covariate. We compare 2 models for NMA with TCIs: (1) 2 effects separating within‐ and across‐trial interactions and (2) a single effect combining within‐ and across‐trial interactions. We argue for a visual assessment of consistency of within‐ and across‐trial interactions and consider more detailed aspects of interaction modelling, eg, common vs trial‐specific effects of the covariate. This leads us to propose a practical framework for IPD NMA with TCIs.

Results: Following our framework, we found no evidence in the cervical cancer network for a treatment‐stage interaction on the basis of the within‐trial interaction. The NMA provided additional power for an across‐trial interaction over and above the pairwise evidence. Following our proposed framework, we found that the within‐ and across‐trial interactions should not be combined.

Conclusion: Across‐trial interactions are susceptible to confounding and ecological bias. It is important to separate the sources of evidence to check their consistency and identify which sources of evidence are driving the conclusion. Our framework provides practical guidance for researchers, reducing the risk of unduly optimistic interpretation of TCIs.

Bayesian one-step IPD network meta-analysis of time-to-event data using Royston-Parmar models

Network meta‐analysis (NMA) combines direct and indirect evidence from trials to calculate and rank treatment estimates. While modelling approaches for continuous and binary outcomes are relatively well developed, less work has been done with time‐to‐event outcomes. Such outcomes are usually analysed using Cox proportional hazard (PH) models. However, in oncology with longer follow‐up time, and time‐dependent effects of targeted treatments, this may no longer be appropriate. Network meta‐analysis conducted in the Bayesian setting has been increasing in popularity. However, fitting the Cox model is computationally intensive, making it unsuitable for many datasets. Royston‐Parmar models are a flexible alternative that can accommodate time‐dependent effects. Motivated by individual participant data (IPD) from 37 cervical cancer trials (5922 women) comparing surgery, radiotherapy, and chemotherapy, this paper develops an IPD Royston‐Parmar Bayesian NMA model for overall survival. We give WinBUGS code for the model. We show how including a treatment‐ln(time) interaction can be used to conduct a global test for PH, illustrate how to test for consistency of direct and indirect evidence, and assess within‐design heterogeneity. Our approach provides a computationally practical, flexible Bayesian approach to NMA of IPD survival data, which readily extends to include additional complexities, such as non‐PH, increasingly found in oncology trials.