Transportability of aggregate trial results to an external environment in causally interpretable meta-analysis

In evidence synthesis, multilevel modeling approaches (MMAs) are commonly employed to combine aggregate data (AD) and individual participant data (IPD). These approaches rely on an aggregate outcome model that is ideally obtained by integrating the prespecified individual- level outcome model over the covariate distribution observed in each eligible study. In non- linear settings, such an integration may however be analytically intractable and requires ap- proximations. In this paper, we propose a novel method for incorporating AD into causal meta-analysis of IPD studies that can overcome this challenge. Rather than relying on an ag- gregate outcome model that is difficult to be correctly formulated, we propose modeling the trial membership as a function of baseline covariates. This model allows one to estimate the individual-level outcome model in each AD study by leveraging IPD available in other trials, and then to transport the treatment effects estimated from both AD and IPD trials to an external target population, even when only aggregate covariate data are available for that population. Unlike previous proposals, we do not require pseudo-IPD to be generated from the aggregate data, which helps minimize bias due to incomplete information on the covariate distribution in each AD trial and in the target population.

💡 Research Summary

This paper addresses two persistent challenges in evidence synthesis: (1) the frequent lack of individual participant data (IPD) for many randomized trials, and (2) the limited external validity of trial‐based treatment effects. Traditional multilevel meta‑analysis (MMA) attempts to combine aggregate data (AD) and IPD by integrating an individual‑level outcome model over each trial’s covariate distribution. In non‑linear settings (e.g., logistic models) this integration is analytically intractable, forcing researchers to rely on approximations that can introduce ecological bias.

The authors propose a novel, weighting‑based framework that sidesteps the need for an explicit aggregate outcome model. Instead of modeling the trial‑level mean outcome, they model trial membership—i.e., the probability that a participant belongs to a given study—conditional on baseline covariates (L). By estimating (P(S=s\mid L)) with a logistic model and applying inverse‑probability weighting, they can reconstruct the expected outcome in an AD‑only trial using individuals from an IPD‑available trial. This key identity (Equation 3 in the manuscript) allows the estimation of trial‑specific intercepts and treatment coefficients ((\phi_{0s},\phi_{1s})) for AD studies without generating pseudo‑IPD.

The causal target is the marginal log‑odds ratio (\theta_{0s}) that would be observed in an external target population (S=0). Identification relies on four standard transportability assumptions: (A1) conditional exchangeability of potential outcomes given (L), (A2) positivity of trial‑membership probabilities, (A3) consistency, and (A4) randomization within each trial. Under these assumptions, (\theta_{0s}) can be expressed as a G‑computation integral over the target covariate distribution, which the authors evaluate either by direct simulation (when IPD for the target is available) or by a second stage of inverse weighting (when only summary means and variances of (L) are known).

Methodologically, the approach offers several advantages:

1. No pseudo‑IPD generation – eliminates bias arising from incomplete joint covariate information in AD studies.
2. Avoids complex integrals – works naturally with non‑linear outcome models such as logistic regression.
3. Accommodates treatment‑version heterogeneity – allows trial‑specific intercepts and treatment effects to be treated as random effects.
4. Works with external populations – requires only summary covariate moments for the target, not full IPD.

The authors provide asymptotic theory showing consistency and normality of the estimator, and they conduct extensive simulation studies. When the proportion of AD‑only trials ranges from 30 % to 70 %, the proposed method consistently yields lower bias and mean‑squared error than existing MAIC or pseudo‑IPD approaches, especially when the covariate distribution is only partially known.

A real‑world illustration involves a meta‑analysis of biologic therapies for psoriasis. The dataset comprises five AD‑only small trials and three IPD‑available larger trials. Using only published means and variances of baseline covariates for the AD trials and a summary description of a representative psoriasis cohort (the external target), the method produces calibrated log‑odds ratios for each treatment that are plausibly transportable to routine clinical practice, whereas naïve AD‑only synthesis overstates treatment benefits.

Limitations are acknowledged. The transportability assumption requires that all effect‑modifying covariates be captured in (L); violation can re‑introduce bias. Adequate overlap of covariate distributions across trials and the target is necessary for stable weights. Moreover, estimating high‑dimensional interactions would demand richer summary statistics than those typically reported.

Future work suggested includes Bayesian extensions to propagate uncertainty about the weighting models, integration with electronic health record data to enrich covariate information, and generalization to network meta‑analysis settings with multiple competing treatments.

In sum, the paper delivers a practical, theoretically sound solution for combining AD and IPD in causal meta‑analysis, enabling reliable transport of treatment effects to external populations without the cumbersome step of constructing pseudo‑individual datasets. This contribution is poised to improve the credibility of evidence synthesis in fields where data access is heterogeneous and external validity is paramount.