Multilevel network meta-regression for multistate models: Population-adjusted joint synthesis of progression and survival data from individual and aggregate evidence

Technical Summary: Multilevel Network Meta-Regression for Multistate Models (ML-NMR-MS)

Problem Statement
In oncology network meta-analysis (NMA), there is a recognized need to synthesize progression-free survival (PFS) and overall survival (OS) jointly rather than separately, as they are functionals of the same underlying disease process. Previous work by Jansen et al. introduced a multistate NMA using a tri-state (stable, progressed, dead) Markov model fitted to aggregate data (AgD). While this provides a coherent joint synthesis and parameterization for state-transition economic models, it cannot adjust for imbalances in effect-modifying covariates across trials. Consequently, relative effects may be biased or irrelevant for specific target populations.

Conversely, Multilevel Network Meta-Regression (ML-NMR) resolves covariate imbalance by integrating individual-level models over aggregate covariate distributions, coherently combining Individual Participant Data (IPD) and AgD. However, existing ML-NMR methods have been limited to single-endpoint outcomes and cannot handle the joint structure of multistate models. The gap lies in the inability to simultaneously perform population adjustment and joint synthesis of PFS/OS data.

Methodology: ML-NMR-MS
The paper introduces Multilevel Network Meta-Regression for Multistate Models (ML-NMR-MS), which embeds the ML-NMR integrated IPD-plus-AgD likelihood inside an illness–death multistate model.

• Model Structure: The method utilizes a general multistate process where transitions (e.g., stable→progression, stable→death, progression→death) are modeled via time-inhomogeneous intensities on the log scale. The model includes study-specific baseline coefficients, treatment effects, prognostic covariate effects, and effect-modifier interactions.
• Data Integration:
  • IPD Studies: Contribute the full multistate likelihood over linked transitions, utilizing observed individual event histories and covariates.
  • AgD Studies: Do not use pseudo-individual reconstruction (which severs the link between progression and death times). Instead, the method computes covariate-marginal state-occupancy probabilities by quasi-Monte-Carlo integration of the transition intensities over a reconstructed covariate distribution (using a Gaussian copula to match reported summaries).
• Likelihood Construction:
  • For AgD, the marginal occupancies are entered into a conditional-survival likelihood.
  • The paper discusses two forms for the aggregate likelihood: a two-binomial composite (treating PFS and OS as independent binomials, default for curve-only evidence) and a multinomial (treating the joint state occupancy as a single multinomial, preferred when joint counts are available).
  • The joint likelihood combines the individual-level contributions from IPD and the marginal contributions from AgD under a shared parameter vector.
• Estimands: The framework produces both conditional effects (for patients with specific covariate values) and marginal effects (population-averaged), as well as absolute quantities. This distinction is crucial due to the non-collapsibility of hazard ratios.
• Estimation: The model is fitted in a Bayesian framework using Hamiltonian Monte Carlo (Stan). The covariate integral is evaluated within the model using quasi-Monte-Carlo integration (Sobol' points), with the number of points determined by a doubling rule to ensure integration error is negligible.

Key Contributions

1. Methodological Unification: The paper embeds the ML-NMR integrated likelihood inside a multistate model. For IPD, it uses the full multistate likelihood; for AgD, it integrates state occupancy over the covariate distribution. This allows for the synthesis of linked transitions (progression and death) while adjusting for covariate imbalances.
2. Population-Adjusted Joint Synthesis: The method yields population-adjusted joint PFS/OS treatment effects for any decision-relevant target population. It produces both conditional and marginal relative effects, which can directly parameterize state-transition economic models without the estimand mismatch often found in partitioned-survival models.
3. Decomposition of Effects: By modeling transitions separately, the method can disentangle a treatment's effect on progression from its effect on post-progression survival. This allows for a mechanistic understanding of how PFS translates to OS.
4. Illustrative Application and Validation: The method is applied to a network of multiple myeloma trials (combining IPD and AgD) and validated through a simulation study with fully known truth.

Results

• Illustrative Example: In the multiple myeloma network, ML-NMR-MS successfully separated the treatment effects. For lenalidomide, the benefit on OS was found to be largely inherited from the delay in progression (stable→progression transition) rather than a direct effect on post-progression survival. The model produced distinct conditional and marginal hazard ratios, demonstrating that marginal effects shift with the target population's covariate distribution due to non-collapsibility.
• Simulation Study:
  • Recovery: Under correct model specification, ML-NMR-MS recovered population-adjusted transition effects with unbiased estimates and near-nominal 95% coverage, comparable to a full-IPD gold standard.
  • Precision: Replacing individual data with aggregate curves incurred a precision penalty (increased standard error) that scaled with the proportion of AgD in the network, but validity (bias and coverage) remained intact.
  • Robustness: The method was robust to misspecification of the covariate reconstruction (Gaussian copula correlation). However, like all methods, it suffered from bias and coverage collapse when an unobserved shared frailty was present (a structural misspecification). It also correctly handled non-proportional hazards when a time-varying coefficient model was specified, whereas a fixed proportional-hazards model became increasingly biased over time.

Significance and Claims
The paper claims that ML-NMR-MS provides a single coherent framework for the population-adjusted synthesis of individual and aggregate progression and survival data. Its primary significance lies in its ability to:

• Resolve the trade-off between joint synthesis (multistate NMA) and population adjustment (ML-NMR).
• Provide the specific building blocks (conditional baseline hazards, prognostic effects, and conditional treatment effects) required to parameterize health-economic state-transition models for target populations, avoiding the bias introduced by applying conditional hazard ratios to marginal reference curves.
• Decompose treatment effects into component transitions, offering a mechanistic view of how PFS impacts OS.

The authors remain modest regarding the scope of their validation, noting that the simulation study was of moderate size and focused on a specific parameterization. They acknowledge that broader questions regarding networks with very thin connectivity or extremely low IPD availability remain open for future investigation. The method is presented as a solution to the specific technical challenge of integrating multistate structures with covariate adjustment in the presence of mixed data types.