Monica Simeoni, Matt Zierhut
This tutorial aims to expound on methodological aspects typically encountered when performing model-based meta-analyses (MBMA). This includes how to handle placebo response and relative treatment effects, data weighting, and covariate influences, with emphasis on concepts, applications, practical implementation, and case studies.
Comparisons of relative treatment effects in MBMA are commonly anchored around placebo as a global reference treatment, even for trials not including a placebo arm. When relative treatment effects (i.e., difference relative to reference) are the primary interest, the placebo response can be described with a non-parametric (or unstructured) component [1, 2]. This is contrasted to an alternative approach where a parametric placebo function uses prognostic (non-treatment-related) covariates and random effects to describe between-study heterogeneity in the placebo effects. This tutorial will elaborate on why and in which settings the unstructured placebo approach is generally recommended. Covariate exploration will also be discussed, highlighting the critical differences between prognostic covariates (which are treatment-independent) and predictive covariates (which influence relative treatment effects).
Unlike models that use individual patient data (IPD), when using MBMA with aggregate data (AD), each data point is not equally weighted. A typical aggregate-level continuous outcome “data point” is depicted by two pieces of information; the outcome (e.g., a mean value) and the associated measure of precision (e.g., a standard error). Focusing on MBMA with AD, each data point represents a population of patients, with larger populations (or more precise measurements) more heavily weighted than smaller populations. Specifically, variance functions are used to model the variance structure of the within-group errors [3], i.e., within-study arm errors. The type of outcome being analyzed, e.g., mean value across subjects or proportion of responders in a study arm, dictates the variance structure and inherently the weighting of the data.
This tutorial delves into the importance of using appropriate measures of precision as weights, when reported. When measures of precision are not reported, or when covariates are not reported, several remedial approaches are available, often guided by the extent of missingness. The impact, e.g., on precision of key model parameters of using either reported measures of precision, reported and imputed measures of precision, or simply weighting by sample size, will be reviewed. The analysis of transformed outcomes, e.g., log-transformed values and their appropriate variance structure (weights) will be also discussed.
Finally, model evaluation diagnostics (e.g., residual-based and partial residual plots [4]) will be illustrated and discussed.
References:
1. Hennessy, B., Zierhut, M. L., Kracker, H., Keenan, A. & Sidorenko, T. Comparative Efficacy of Relapsing Multiple Sclerosis Therapies: Model-Based Meta-Analyses for Confirmed Disability Accumulation and Annualized Relapse Rate. Multiple Sclerosis and Related Disorders 64, 103908 (2022).
2. Boyd, R., DiCarlo, L. & Mandema, J. Direct Oral Anticoagulants Vs. Enoxaparin for Prevention of Venous Thromboembolism Following Orthopedic Surgery: A Dose–Response Meta‐analysis. Clinical Translational Sci 10, 260–270 (2017).
3. Pinheiro, J., & Bates, D. (2000). Mixed-Effects Models in S and S-PLUS. Statistics and Computing (528 p.). Springer-Verlag.
4. Maringwa J, Diderichsen PM, Valiathan C. Partial Residual Plots as an Integrated Model Diagnostic Tool in Model‐Based Meta‐Analysis.
Reference: PAGE 34 (2026) Abstr 12224 [www.page-meeting.org/?abstract=12224]