Presentation (CTI)

OBJECTIVES: Multilevel network meta-regression (ML-NMR) synthesizes individual patient and aggregate data for population-adjusted indirect treatment comparisons by marginalizing an individual-level model over each aggregate study’s covariate distribution. In multinma this requires numerical integration within Hamiltonian Monte Carlo and dominates per-gradient cost. We sought posterior-preserving accelerations, validated per gradient.
METHODS: We developed three accelerations, graded by effect on the target. Two are exact, leaving the posterior invariant up to floating-point reassociation. Integration-block deduplication exploits invariance of the aggregate design block across an arm’s reconstructed pseudo-individuals, evaluating the per-arm linear predictor, exponential, and M-spline softmax on unique blocks and gathering results. Tie aggregation applies the distributive law to pseudo-individuals with identical likelihood inputs, replacing repeated evaluations with a count-weighted term. One is same-estimand: structure-exploiting quadrature marginalizes discrete covariates by exact enumeration and continuous covariates by Gauss-Hermite cubature with copula-consistent weights. Exactness was verified by log-density and gradient agreement to 1e-9 at shared unconstrained parameters and bit-exact reductions. Posterior agreement used standardized differences for treatment and regression estimands.
RESULTS: In the survival network (NDMM), Kaplan-Meier reconstruction replicated the integration block about 700-fold. Deduplication removed this redundancy exactly, halving per-gradient cost while preserving estimands within Monte Carlo error and producing no divergent transitions, reaching 4.79x speedup. Tie aggregation was exact and complementary, with data-dependent gain: about 1.3-fold block reduction under continuous event times and larger gains under coarsened times, leading to 1.08x speedup alone and 5.41x with deduplication. Structure-exploiting quadrature eliminated Monte Carlo error on the discrete margin and was advantageous when discrete covariates dominate.
CONCLUSIONS: ML-NMR admits substantial, independently verifiable acceleration without altering the posterior. Deduplication is the dominant exact lever under data reconstruction; tie aggregation augments it; structure-exploiting quadrature is a regime-conditional, same-estimand alternative for feasible population-adjusted inference.