Anchors Away: Navigating Unanchored Indirect Comparisons with Multilevel Unanchored Meta-Regression (ML-UMR)

Abstract: Unanchored indirect treatment comparisons using single-arm studies or disconnected evidence are increasingly used in health technology assessment (HTA) when randomized evidence is unavailable. Existing methods, including matching-adjusted indirect comparison (MAIC) and simulated treatment comparison (STC), are generally limited to pairwise settings and typically estimate marginal effects in the comparator study population, which may differ from the decision-relevant population. We propose multilevel unanchored meta-regression (ML-UMR), a Bayesian regression framework for synthesizing individual patient data and aggregate data from fully disconnected evidence. ML-UMR extends multilevel network meta-regression (ML-NMR) to unanchored settings by jointly modeling individual- and aggregate-level data within a unified likelihood, enabling estimation of treatment-specific outcomes and both marginal and conditional effects across multiple treatments, studies, and target populations. ML-UMR distinguishes assumptions required to identify treatment effects from those required to transport results to target populations. As with all unanchored comparisons, valid inference relies on strong and often unverifiable assumptions, including conditional exchangeability, correct specification of the outcome model, and cross-treatment assumptions (e.g., shared prognostic factor assumption (SPFA)). ML-UMR does not lessen these requirements but makes them explicit within a unified framework and facilitates sensitivity analyses. In simulation studies, ML-UMR produced low bias and nominal coverage for comparator-population effects. Transportability to alternative populations depended critically on identifying assumptions: violations of SPFA led to bias under strong effect modification, whereas incorporating subgroup information restored near-unbiased estimation and nominal coverage.

• The paper introduces ML-UMR, a Bayesian framework merging IPD and AgD for unanchored indirect comparisons in health technology assessment.
• It utilizes joint likelihood and quasi–Monte Carlo integration to estimate both conditional and marginal treatment effects across disconnected evidence.
• The method clarifies identification and transport assumptions, supporting robust sensitivity analysis and decision-relevant population inferences.

Multilevel Unanchored Meta-Regression (ML-UMR) for Population-Adjusted Indirect Comparisons

Motivation and Conceptual Framework

The paper "Anchors Away: Navigating Unanchored Indirect Comparisons with Multilevel Unanchored Meta-Regression (ML-UMR)" (2606.20341) addresses methodological limitations in current population-adjusted indirect comparisons (PAICs) used in health technology assessment (HTA), particularly in scenarios where evidence is fully disconnected (i.e., comprising single-arm studies with no shared comparator). Conventional methods, including matching-adjusted indirect comparison (MAIC) and simulated treatment comparison (STC), focus on pairwise contrasts and are typically restricted to estimating treatment effects in the comparator population, with limited support for coherent inference across multiple treatments and populations.

ML-UMR is introduced as a Bayesian outcome-regression framework that generalizes the modeling apparatus of multilevel network meta-regression (ML-NMR) to unanchored settings. ML-UMR allows specification of a unified likelihood that synthesizes individual patient data (IPD) and aggregate data (AgD) from disconnected evidence, facilitating the estimation of both conditional and marginal treatment effects in explicitly defined target populations. The separation of assumptions for identification (treatment effect estimation) from those underpinning transportability (application to target populations) is made explicit, a distinction that is underdeveloped in legacy PAIC approaches.

Statistical Model Structure

ML-UMR operationalizes the outcome regression paradigm for PAIC within a joint likelihood framework. The model specification is as follows:

• For IPD studies of treatment $A$, the standard generalized linear model is fit:

$g(\theta_A(x)) = \alpha_A + x^\top \beta_A$

with $Y_{iA} \sim \pi(\theta_{iA})$ for individual $i$.

• For AgD studies of treatment $B$, observed only as aggregate outcomes and covariate summaries, marginalization over the covariate distribution $f_B(x)$ is performed to yield:

$$\theta_{\bullet B} = \int g^{-1}(\alpha_B + x^\top \beta_B) f_B(x)\, dx$$

The likelihood is computed in terms of the aggregate outcome.

Numerical integration (quasi–Monte Carlo) is used for the marginalization step, with reconstructed covariate distributions to approximate AgD populations. The model is naturally extensible to multiple treatments and studies per treatment, allowing fixed or hierarchical pooling of study-level intercepts.

Identification and Structural Assumptions

Valid inference via ML-UMR (and any unanchored PAIC) is contingent upon strong, often untestable, identification assumptions:

• Conditional exchangeability: All study/population differences influencing outcomes must be captured by measured covariates; unmeasured confounders invalidate causal interpretation.
• Correct outcome model specification: Functional forms and interactions must be appropriately modeled; mis-specification leads to bias.
• Shared Prognostic Factor Assumption (SPFA): Baseline covariate effects must be identical across treatments on the model scale ($\beta_A = \beta_B$); necessary for identification in disconnected single-arm settings.
• Valid reconstruction of AgD covariate distributions: Covariate summary statistics and assumed correlations must accurately reflect true distributions.

The paper explicitly distinguishes the role of these identification assumptions from transportability, emphasizing that transport of treatment effects to population-relevant settings (e.g., HTA jurisdictions) is a distinct modeling step that can be performed via standardization over alternative covariate distributions, provided identification holds.

Extensions and Practical Considerations

ML-UMR supports:

• Non-pairwise comparisons and synthesis of multiple studies per treatment.
• Relaxation of SPFA through incorporation of subgroup-level AgD or via structured sensitivity analysis, enabling treatment-specific covariate effects estimation via hierarchical priors or bias parameterization.
• Survival outcome modeling with marginalization over reconstructed covariate distributions of AgD, employing pseudo-IPD from digitized Kaplan-Meier curves.

Pooling strategies for studies per treatment include fixed study effects (no pooling), complete pooling (common intercepts), and hierarchical models with random intercepts, chosen based on evidence structure and heterogeneity.

Numerical Results and Performance Evaluation

A comprehensive simulation study demonstrates:

• ML-UMR, MAIC, and STC achieve low bias and nominal coverage for effects in the comparator population, even in the presence of strong effect modification or population imbalance.
• Transport of effects to alternative populations (e.g., the index population) is sensitive to violations of SPFA and population differences; bias and undercoverage are observed for MAIC/STC when implicit direct transportability is assumed, with bias up to 0.50 (log odds ratio) under extreme scenarios.
• ML-UMR under SPFA performs well when the assumption holds; bias increases with SPFA violation but can be nearly eliminated by incorporating subgroup AgD.
• Robustness to moderate misspecification of covariate correlation is established; increased sample size does not mitigate structural bias but increases precision and accentuates undercoverage when assumptions are violated.

These results reinforce that comparator-population effects frequently appear robust, yet valid inference in decision-relevant populations (index/jurisdiction) is critically dependent on identification and transport assumptions.

Theoretical and Practical Implications

ML-UMR provides a generalized, coherent modeling approach for unanchored PAIC, offering:

• Explicit delineation of identification versus transport assumptions, enabling analysts to formulate estimands aligned to decision-relevant populations in HTA.
• Formal integration of IPD and AgD, accommodating arbitrary numbers of treatments and studies, multiple population targets, and both conditional and marginal estimands.
• A framework supporting structured sensitivity analysis for violations of SPFA and other critical assumptions, quantification of bias, and propagation of uncertainty to downstream health economic outcomes.
• Improved alignment between statistical modeling and practical HTA requirements, mitigating the risk of unrecognized transport bias in cost-effectiveness modeling and reimbursement decisions.

Methodological directions for future research include quantitative bias analysis for unmeasured confounding, out-of-sample validation strategies in HTA, and extension of ML-UMR to partial networks with both connected randomized trials and disconnected single-arm evidence.

Conclusion

ML-UMR generalizes population-adjusted indirect comparisons for disconnected evidence settings by leveraging a Bayesian outcome-regression framework that synthesizes IPD and AgD from single-arm studies. The method explicitly invokes and clarifies necessary identification (SPFA, model specification, exchangeability) and transportability assumptions, facilitates estimation of treatment effects in both comparator and target populations, and supports structured sensitivity analyses. Numerical evidence demonstrates reliable recovery of comparator-population effects; however, transport to alternative populations is highly sensitive to structural assumptions. ML-UMR offers a robust modeling framework for decision-relevant HTA scenarios, advancing both the methodological rigor and practical applicability of unanchored PAIC.