A BAYESIAN LONGITUDINAL MULTILEVEL NETWORK META-REGRESSION MODEL FOR REPEATED CONTINUOUS OUTCOMES
Author(s)
Juan Pablo Diaz-Martinez, PhD, Karissa M. Johnston, BSc, MSc, PhD, Greta Lozano-Ortega, MSc, Dieter Ayers, MSc.
Broadstreet HEOR, Vancouver, BC, Canada.
Broadstreet HEOR, Vancouver, BC, Canada.
OBJECTIVES: Multilevel network meta-regression (ML-NMR) enables population-adjusted indirect comparisons when some trials provide individual participant data (IPD) and others only aggregate data, integrating over the covariate distribution rather than inserting aggregate means. We extend ML-NMR to longitudinal, repeatedly measured outcomes, allowing relative treatment effects to vary across follow-up.
METHODS: We developed a Bayesian model jointly synthesizing repeated Gaussian outcomes from IPD and aggregate study-arm summaries. Time is modeled with a spline basis: a common smooth trajectory describes the reference-treatment response, while treatment-specific spline deviations let relative effects vary over time. Studies may contribute at multiple visits without shared timepoints. The linear predictor includes study baselines, treatment effects, prognostic factors, and effect modifiers, with the aggregate likelihood linked to the individual model by integrating over the covariate distribution. Because repeated aggregate summaries from a study arm may be correlated, we compared independent and fixed working covariance structures. Performance was evaluated by simulation and a real evidence network.
RESULTS: The simulation showed that the method accurately estimated the true parameter values for treatment effects, time-related spline coefficients, and prognostic and effect-modifying factors. Mean bias was small and centered near zero for all parameter groups (within ±0.05 for most), and 95% credible interval coverage was close to nominal (≈90-100%). Results were similar across independent and correlated working covariance structures (ρ=0.25-0.75), indicating robustness to the assumed within-arm covariance.
CONCLUSIONS: Longitudinal ML-NMR enables coherent population-adjusted synthesis of repeated continuous outcomes from mixed IPD and aggregate evidence, supporting time-varying relative effects without aligned visit schedules. We will discuss how the same multilevel structure could be extended to other likelihoods and non-linear links. Future work will examine non-Gaussian outcomes and limits under sparse networks, and model code will be released in a public repository.
METHODS: We developed a Bayesian model jointly synthesizing repeated Gaussian outcomes from IPD and aggregate study-arm summaries. Time is modeled with a spline basis: a common smooth trajectory describes the reference-treatment response, while treatment-specific spline deviations let relative effects vary over time. Studies may contribute at multiple visits without shared timepoints. The linear predictor includes study baselines, treatment effects, prognostic factors, and effect modifiers, with the aggregate likelihood linked to the individual model by integrating over the covariate distribution. Because repeated aggregate summaries from a study arm may be correlated, we compared independent and fixed working covariance structures. Performance was evaluated by simulation and a real evidence network.
RESULTS: The simulation showed that the method accurately estimated the true parameter values for treatment effects, time-related spline coefficients, and prognostic and effect-modifying factors. Mean bias was small and centered near zero for all parameter groups (within ±0.05 for most), and 95% credible interval coverage was close to nominal (≈90-100%). Results were similar across independent and correlated working covariance structures (ρ=0.25-0.75), indicating robustness to the assumed within-arm covariance.
CONCLUSIONS: Longitudinal ML-NMR enables coherent population-adjusted synthesis of repeated continuous outcomes from mixed IPD and aggregate evidence, supporting time-varying relative effects without aligned visit schedules. We will discuss how the same multilevel structure could be extended to other likelihoods and non-linear links. Future work will examine non-Gaussian outcomes and limits under sparse networks, and model code will be released in a public repository.
Conference/Value in Health Info
2026-11, ISPOR Europe 2026, Vienna, Austria
Value in Health, Volume 29, Issue 12S
Code
MSR169
Topic
Methodological & Statistical Research
Disease
No Additional Disease & Conditions/Specialized Treatment Areas