Mixed-effects two-stage residual inclusion methods for individual patient data meta-analysis: A methodological framework for causal inference in survival analysis
- 1Heidelberg Institute for Global Health, UniversitätsKlinikum Heidelberg, Germany
- 2Volkswirtschaftslehre, Katholische Universität Eichstätt-Ingolstadt, Germany
- 3Julius Center for Health Sciences and Primary Care, Utrecht University, Netherlands
Abstract
Individual patient data meta-analyses (IPDMAs) provide powerful tools for synthesizing evidence across studies, yet methods for addressing unmeasured confounding in observational IPDMAs with survival outcomes are rarely implemented. Instrumental variable (IV) approaches offer causal inference capabilities but face practical challenges in hierarchical data structures, particularly the lack of standard diagnostics for instrument strength in nonlinear mixed-effects models. We adapt and evaluate a frequentist mixed-effects two-stage residual inclusion (2SRI) framework for survival IPDMAs, extending traditional IV methods to accommodate study-level and temporal clustering while handling time-to-event outcomes through Cox proportional hazards models. Because classical F-statistics are unavailable for logistic mixed-effects first-stage models, we propose the Wald χ2chi squared statistic as a practical instrument-strength diagnostic and empirically characterize its relationship to estimator performance. Through a comprehensive simulation study with 48 scenarios—varying unmeasured confounding (weak to very strong), instrument–treatment association strength (0.3–1.0), and cross-study IV allocation patterns—we evaluated 2SRI against naive mixed-effects Cox models using bias, coverage, variance, and mean squared error. The design was anchored to realistic IPDMA structure (10 studies, N≈4,357upper N almost equals 4 comma 357 ) from pooled Ebola data, with 1,000 replications per scenario. Results show that under weak confounding, naive models dominate on all metrics. With moderate-to-strong confounding and realized Wald χ2chi squared exceeding 150–200, mixed-effects 2SRI substantially reduces bias and achieves near-nominal coverage, though with inflated variance. We provide empirical guideposts linking realized first-stage strength to expected performance, enabling analysts to judge when 2SRI will outperform conventional approaches in hierarchical survival IPDMAs. All simulations assume a common treatment effect across studies. Performance under heterogeneous effects remains to be established.
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BibTeX
@article{hufstedler2026mixedeffects,
title = {{Mixed-effects two-stage residual inclusion methods for individual patient data meta-analysis: A methodological framework for causal inference in survival analysis}},
author = {Heather Hufstedler and Alexander M. Danzer and Valentijn Marnix Theodoor de Jong and Till Bärnighausen},
journal = {Research Synthesis Methods},
year = {2026},
month = jun,
doi = {10.1017/rsm.2026.10103},
url = {https://doi.org/10.1017/rsm.2026.10103},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Mixed-effects two-stage residual inclusion methods for individual patient data meta-analysis: A methodological framework for causal inference in survival analysis
AU - Heather Hufstedler
AU - Alexander M. Danzer
AU - Valentijn Marnix Theodoor de Jong
AU - Till Bärnighausen
PY - 2026
DA - 2026/06/29
JO - Research Synthesis Methods
DO - 10.1017/rsm.2026.10103
UR - https://doi.org/10.1017/rsm.2026.10103
AB - Individual patient data meta-analyses (IPDMAs) provide powerful tools for synthesizing evidence across studies, yet methods for addressing unmeasured confounding in observational IPDMAs with survival outcomes are rarely implemented. Instrumental variable (IV) approaches offer causal inference capabilities but face practical challenges in hierarchical data structures, particularly the lack of standard diagnostics for instrument strength in nonlinear mixed-effects models. We adapt and evaluate a frequentist mixed-effects two-stage residual inclusion (2SRI) framework for survival IPDMAs, extending traditional IV methods to accommodate study-level and temporal clustering while handling time-to-event outcomes through Cox proportional hazards models. Because classical F-statistics are unavailable for logistic mixed-effects first-stage models, we propose the Wald χ2chi squared statistic as a practical instrument-strength diagnostic and empirically characterize its relationship to estimator performance. Through a comprehensive simulation study with 48 scenarios—varying unmeasured confounding (weak to very strong), instrument–treatment association strength (0.3–1.0), and cross-study IV allocation patterns—we evaluated 2SRI against naive mixed-effects Cox models using bias, coverage, variance, and mean squared error. The design was anchored to realistic IPDMA structure (10 studies, N≈4,357upper N almost equals 4 comma 357 ) from pooled Ebola data, with 1,000 replications per scenario. Results show that under weak confounding, naive models dominate on all metrics. With moderate-to-strong confounding and realized Wald χ2chi squared exceeding 150–200, mixed-effects 2SRI substantially reduces bias and achieves near-nominal coverage, though with inflated variance. We provide empirical guideposts linking realized first-stage strength to expected performance, enabling analysts to judge when 2SRI will outperform conventional approaches in hierarchical survival IPDMAs. All simulations assume a common treatment effect across studies. Performance under heterogeneous effects remains to be established.
SN - 1759-2879
SN - 1759-2887
ER -