Multivariate network meta‐analysis of survival function parameters

Conduct and reporting of multivariate network meta-analyses: a scoping review

OBJECTIVES

Combining multivariate and network meta-analysis methods simultaneously in a multivariate network meta-analysis (MVNMA) provides the methodological framework to analyze the largest amount of evidence relevant to decision-makers (i.e., from indirect evidence and correlated outcomes). The objectives of this scoping review were to summarize the characteristics of MVNMAs published in the health sciences literature and map the methodological guidance available for MVNMA.

STUDY DESIGN AND SETTING

We searched MEDLINE, Embase, and the Cumulative Index to Nursing and Allied Health Literature from inception to 28 August 2023, along with citations of included studies, for quantitative evidence syntheses that applied MVNMA and articles addressing MVNMA methods. Pairs of reviewers independently screened potentially eligible studies. Collected data included bibliographic, methodological, and analytical characteristics of included studies. We reported results as total numbers, frequencies, and percentages for categorical variables and medians and interquartile ranges for continuous variables that were not normally distributed.

RESULTS

After screening 1,075 titles and abstracts, and 112 full texts, we included 38 unique studies, of which, 10 were quantitative evidence syntheses that applied MVNMA and 28 were articles addressing MVNMA methods. Among the 10 MVNMAs, the first was published in 2013, four used studies identified from already published systematic reviews, and eight addressed pharmacological interventions, which were the most common interventions. They evaluated interventions for metastatic melanoma, colorectal cancer, prostate cancer, oral hygiene, disruptive behavior disorders, rheumatoid arthritis, narcolepsy, type 2 diabetes, and overactive bladder syndrome. Five MVNMAs analyzed two outcomes simultaneously, and four MVNMAs analyzed three outcomes simultaneously. Among the articles addressing MVNMA methods, the first was published in 2007 and the majority provided methodological frameworks for conducting MVNMAs (26/28, 93%). One study proposed criteria to standardize reporting of MVNMAs and two proposed items relevant to the quality assessment of MVNMAs. Study authors used data from 18 different illnesses to provide illustrative examples within their methodological guidance.

CONCLUSIONS

The application of MVNMA in the health sciences literature is uncommon. Many methodological frameworks are published; however, standardization and specific criteria to guide reporting and quality assessment are lacking. This overview of the current landscape may help inform future conduct of MVNMAs and research on MVNMA methods.

Multi-state network meta-analysis of progression and survival data

Multiple randomized controlled trials, each comparing a subset of competing interventions, can be synthesized by means of a network meta-analysis to estimate relative treatment effects between all interventions in the evidence base. Here we focus on estimating relative treatment effects for time-to-event outcomes. Cancer treatment effectiveness is frequently quantified by analyzing overall survival (OS) and progression-free survival (PFS). We introduce a method for the joint network meta-analysis of PFS and OS that is based on a time-inhomogeneous tri-state (stable, progression, and death) Markov model where time-varying transition rates and relative treatment effects are modeled with parametric survival functions or fractional polynomials. The data needed to run these analyses can be extracted directly from published survival curves. We demonstrate use by applying the methodology to a network of trials for the treatment of non-small-cell lung cancer. The proposed approach allows the joint synthesis of OS and PFS, relaxes the proportional hazards assumption, extends to a network of more than two treatments, and simplifies the parameterization of decision and cost-effectiveness analyses.

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.

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.

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.

Model-informed drug repurposing: A pharmacometric approach to novel pathogen preparedness, response and retrospection

During a pandemic caused by a novel pathogen (NP), drug repurposing offers the potential of a rapid treatment response via a repurposed drug (RD) while more targeted treatments are developed. Five steps of model‐informed drug repurposing (MIDR) are discussed: (i) utilize RD product label and in vitro NP data to determine initial proof of potential, (ii) optimize potential posology using clinical pharmacokinetics (PK) considering both efficacy and safety, (iii) link events in the viral life cycle to RD PK, (iv) link RD PK to clinical and virologic outcomes, and optimize clinical trial design, and (v) assess RD treatment effects from trials using model‐based meta‐analysis. Activities which fall under these five steps are categorized into three stages: what can be accomplished prior to an NP emergence (preparatory stage), during the NP pandemic (responsive stage) and once the crisis has subsided (retrospective stage). MIDR allows for extraction of a greater amount of information from emerging data and integration of disparate data into actionable insight.