No aggregate-data bridge exists for disconnected survival networks
Statement
Every published aggregate-data bridge for disconnected networks, random effects on baseline, reference prediction and aggregate-level matching, is formulated for single-time-point generalized linear models in which the bridged quantity is a scalar baseline parameter such as a log odds. For a time-to-event outcome the bridged quantity is an entire baseline hazard or survival function, and no method specifies how to make baseline hazards exchangeable across subnetworks, how to match a disconnected trial’s hazard function to a connected trial’s, or how to partition heterogeneity across the gap when the treatment effect is itself time-varying, as in fractional-polynomial or spline network meta-analysis. The extension is declined rather than overlooked: after modifying both bridges and evaluating them by deletion and simulation, extension to count and continuous outcomes is described as straightforward while time-to-event network meta-analysis such as fractional polynomials, common in oncology, is said to require more significant modification (Thom et al. 2022, doi:10.1177/0272989X221097081). That same evaluation shows how much accuracy is at stake in the easier scalar case: for disconnected treatments bias ran from -0.16 to 0.392 for aggregate-level matching and from -0.102 to 0.40 for reference prediction against a true effect of 0.5, with coverage as low as 0.30 and 0.64 respectively. Disconnected oncology networks with time-to-event endpoints are the case health technology assessment most often faces, and what decisions there need is a survival curve and a restricted mean rather than a single contrast, so a bridge that returns only a hazard ratio would not close the gap even if it existed.
Why it is open
A hazard function is infinite-dimensional, so a bridge for it needs an exchangeability model over functions rather than over a scalar: a shared shape with study-specific scale, a hierarchical spline or fractional-polynomial coefficient vector, or a process prior, and each choice imposes a different and untestable restriction on the unobserved cross-gap comparison. Follow-up durations, censoring patterns and administrative cutoffs differ across subnetworks, so two baseline hazards are rarely reported on comparable time supports and matching them requires extrapolating at least one into a region with no data. Aggregate survival evidence usually enters through digitized published curves, which introduces reconstruction error that no bridge currently propagates, and a time-varying treatment effect makes the cross-gap quantity a function of time, so a single bias or coverage number does not describe the failure. The scalar bridges are themselves badly biased and undercovered for disconnected treatments, which weakens the incentive to build the harder version before the easier one works.
What has been tried
| Work | What it contributes |
|---|---|
| Thom et al. 2022, Medical Decision Making | modifies reference prediction and aggregate-level matching for disconnected trials and single-arm studies, evaluates them by bridge deletion and a 96-scenario simulation, and states that time-to-event network meta-analysis would require significant further modification while count and continuous outcomes would not |
| Beliveau et al. 2017, Research Synthesis Methods | fits random baseline treatment effects to bridge disconnected components and validates by deleting links from connected networks, entirely within the scalar baseline parameterization |
| Ouwens et al. 2010, Research Synthesis Methods | gives network meta-analysis of parametric survival curves, where each study contributes shape and scale parameters, which is the natural object a survival bridge would have to make exchangeable |
| Jansen 2011, BMC Medical Research Methodology | gives fractional-polynomial network meta-analysis with time-varying hazard ratios, the model class named as the hard case for a bridge because the cross-gap quantity becomes a function of time |
| Guyot et al. 2012, BMC Medical Research Methodology | reconstructs individual event times from published Kaplan-Meier curves, the route by which aggregate survival evidence enters a network and the source of reconstruction error a bridge would have to carry |
| Freeman and Carpenter 2017, Research Synthesis Methods | fits one-step Bayesian individual-data network meta-analysis of time-to-event outcomes with Royston-Parmar models, showing that flexible baseline hazards can be estimated jointly across a connected network |
| Phillippo et al. 2025, Journal of the Royal Statistical Society Series A | extends multilevel network meta-regression to general likelihoods with flexible baseline hazards, supplying absolute-scale survival quantities for connected networks with at least one individual-data study; the disconnected case is not covered |
| Raja Rajeeswari et al. 2026, Value in Health (ISPOR abstract CO184) | reports work extending multilevel network meta-regression to disconnected networks for time-to-event outcomes in myeloma, evidence that the gap is being worked on but as a conference abstract without a published method or independent evaluation |
Probable solution or research direction
Specify the bridged object explicitly: pick a representation of the baseline hazard, piecewise constant, M-spline or fractional polynomial, make its coefficient vector the exchangeable quantity across subnetworks with a declared covariance, and derive what that exchangeability implies for the cross-gap survival contrast at each time point. Build the matching analogue by defining a distance between reported hazard or survival functions on a common time support, with the admissible region declared before matching, rather than matching on scalar baseline summaries that discard the shape. Score on the quantities decisions use, survival probability error at fixed horizons, restricted mean survival difference and extrapolation error, and validate by bridge deletion on connected oncology networks where the cross-gap answer is known. Propagate Kaplan-Meier reconstruction uncertainty through the bridge, since a digitized curve is the input on both sides of the gap and its error is currently absorbed into the point estimate.
Verification
Verdict. Confirmed open. One reader proposed it from a single paper whose discussion names the extension and declines it, and the reviewer accepted that a scalar baseline bridge does not supply a bridge for an entire baseline hazard function. The basis is that one paper plus a conference abstract announcing work in the same direction, which is a weaker foundation than a record of published attempts.
Source
Derived from reading:nma-18 of the reviewed corpus.