Multilevel network meta-regression for general likelihoods: synthesis of individual and aggregate data with applications to survival analysis

TL;DR

This paper introduces an extended multilevel network meta-regression method that combines individual patient data and aggregate data for various likelihoods, including survival analysis, improving synthesis accuracy in network meta-analyses.

Contribution

It extends ML-NMR to handle any individual-level likelihood, including time-to-event data, by integrating over covariate distributions, broadening its applicability.

Findings

ML-NMR performs comparably to full IPD analysis with less data.

Flexible modeling of baseline hazards using cubic M-splines.

Method implemented in R package multinma.

Abstract

Network meta-analysis combines aggregate data (AgD) from multiple randomised controlled trials, assuming that any effect modifiers are balanced across populations. Individual patient data (IPD) meta-regression is the "gold standard" method to relax this assumption, however IPD are frequently only available in a subset of studies. Multilevel network meta-regression (ML-NMR) extends IPD meta-regression to incorporate AgD studies whilst avoiding aggregation bias, but currently requires the aggregate-level likelihood to have a known closed form. Notably, this prevents application to time-to-event outcomes. We extend ML-NMR to individual-level likelihoods of any form, by integrating the individual-level likelihood function over the AgD covariate distributions to obtain the respective marginal likelihood contributions. We illustrate with two examples of time-to-event outcomes, showing the performance of ML-NMR in a simulated comparison with little loss of precision from a full IPD analysis, and demonstrating flexible modelling of baseline hazards using cubic M-splines with synthetic data on newly diagnosed multiple myeloma. ML-NMR is a general method for synthesising individual and aggregate level data in networks of all sizes. Extension to general likelihoods, including for survival outcomes, greatly increases the applicability of the method. R and Stan code is provided, and the methods are implemented in the multinma R package.