No rule selects the common RMST horizon across unequal follow-up
Statement
A synthesis on the restricted mean survival time scale requires one restriction time t* shared by every trial contributing to a contrast, and networks routinely contain trials whose observed follow-up differs by years. Any choice either extrapolates the arms whose last event precedes t, importing model-dependent area under the curve that the hazard-ratio analysis never used, or is pulled back toward the shortest common follow-up, discarding observed events and possibly landing short of the horizon a reimbursement decision needs. The first RMST-based network meta-analysis, 20 nasopharyngeal carcinoma trials and 5144 patients across 26 trial comparisons, set t to 10 years and found that 20 of the 44 trial arms (45.5%) had their last event before the horizon and required extrapolation over a mean of 1.8 years; the 5-year alternative needed no extrapolation but forced the hazard-ratio comparator to be censored at 5 years, an acknowledged loss of information. Under crossing or delayed-effect curves the sign of an RMST difference can itself depend on t, so the horizon is part of the estimand rather than a display setting. No selection rule, admissibility criterion, sensitivity convention or reporting requirement governs t in evidence synthesis, and no method propagates the extrapolation uncertainty the choice creates into the pooled interval or into the treatment ranking.
Why it is open
The tradeoff is structural rather than unexplored: observed information in the longest-followed trials and freedom from extrapolation in the shortest cannot both be had, so no criterion can be optimal on both counts and the choice has to be defended on grounds outside the data. Survival beyond a trial’s last observed event is not identified from that trial, so the imported area is a function of the assumed tail; the resulting uncertainty is model-assumption uncertainty that a within-trial variance does not carry and that current pooling treats as absent. The single-study work on window choice solves a different problem: it establishes how large a t may be given one censoring distribution and how to make inference when t is chosen from the data, whereas a network has as many censoring distributions as trials and needs one t* admissible under all of them simultaneously. The only guidance offered is to prespecify t* by clinical interest, which is a governance answer: it does not say which value is defensible when trials disagree on follow-up and it prices nothing. Because RMST is being promoted as the replacement for the hazard ratio in HTA-facing survival synthesis, the horizon has become a free parameter that can move a reported benefit, including its sign, with no procedure constraining it.
What has been tried
| Work | What it contributes |
|---|---|
| Petit, Blanchard, Pignon and Lueza 2019, Individual patient data network meta-analysis using either restricted mean survival time difference or hazard ratios: is there a difference? A case study on locoregionally advanced nasopharyngeal carcinomas, Systematic Reviews 8:96 | first network meta-analysis run on the RMST difference; documents the horizon problem concretely, with 20 of 44 arms extrapolated by a mean of 1.8 years at t* of 10 years, no extrapolation but censored hazard ratios at 5 years, and 5 of 32 league-table comparisons changing interpretation between the two scales; its only guidance is to prespecify t* on clinical grounds |
| Tian, Jin, Uno, Lu, Huang, Anderson and Wei 2020, On the empirical choice of the time window for restricted mean survival time, Biometrics 76(4):1157-1166 | gives the single-study version of the problem a formal treatment: inference for an RMST whose window is itself data-dependent, and a mild condition on the censoring distribution under which t may run to the largest observed or censored follow-up time; it is stated for one comparative study and does not address a horizon common to trials with different censoring distributions |
| Wei, Royston, Tierney and Parmar 2015, Meta-analysis of time-to-event outcomes from randomized trials using restricted mean survival time: application to individual participant data, Statistics in Medicine 34(21):2881-2898 | establishes RMST-based individual participant data meta-analysis as an alternative to the hazard ratio under non-proportional hazards and supplies a diagnostic for the overall proportional-hazards assumption; the restriction time is chosen per application rather than by a stated rule |
| Lueza, Rotolo, Bonastre, Pignon and Michiels 2016, Bias and precision of methods for estimating the difference in restricted mean survival time from an individual patient data meta-analysis, BMC Medical Research Methodology 16:37 | compares estimators of the pooled RMST difference from individual patient data and identifies the pooled Kaplan-Meier approach with random effects as the best bias-variance compromise; it evaluates estimators at a fixed horizon and does not treat the horizon as a quantity to be selected |
| Hua, Wang and Hong 2025, Network Meta-Analysis of Time-to-Event Endpoints With Individual Participant Data Using Restricted Mean Survival Time Regression, Biometrical Journal 67(1) | extends RMST network meta-analysis beyond two-step aggregation by fitting RMST regression on individual participant data so that covariate moderation and subgroup effects can be estimated; its contribution is the regression structure, and the restriction time is taken as given |
| Phillippo, Dias, Ades and Welton 2025, Multilevel network meta-regression for general likelihoods: synthesis of individual and aggregate data with applications to survival analysis, Journal of the Royal Statistical Society Series A | delivers restricted means in a target population by integrating a marginal survival function to a horizon, which is the population-adjusted route to the same estimand; the horizon is supplied by the analyst and no admissibility or sensitivity requirement attaches to it |
Probable solution or research direction
Start with the estimand: for stated survival families, write the RMST contrast as a function of t* and characterize the horizons at which it changes sign, so that a network reports the leverage of the horizon rather than assuming it away. Define an admissible-horizon set for a network by generalizing the single-study censoring condition, for example the largest t* at which every contributing arm retains a stated minimum at-risk set, and report where the chosen t* sits in that set. Price the extrapolation instead of hiding it: report the extrapolated share of each arm’s restricted mean and propagate tail-model uncertainty into the pooled interval by refitting under alternative tail families or by placing a prior on the tail, rather than passing an extrapolated area forward as observed data. Standardize the reporting minimum: the horizon, which arms were extrapolated to reach it, the mean extrapolation time, and the contrast and ranking at a prespecified set of horizons, so a reader can see whether the conclusion is horizon-stable. Settle the operating characteristics by simulation under crossing and delayed-effect mechanisms with unequal administrative censoring, scoring candidate rules against the truncate-to-shortest and extrapolate-to-clinical-horizon extremes on bias, coverage and rank stability.
Verification
Verdict. Partially addressed. One reader proposed this from a single paper, the first RMST-based network meta-analysis, and the reviewer accepted it on the ground that a common horizon determines both the information discarded and the extrapolation introduced and can alter the estimand under non-proportional hazards. It is partially addressed rather than untouched because the single-study version of horizon choice has a formal treatment, including an admissibility condition tied to the censoring distribution; the network-level selection rule and the propagation of extrapolation uncertainty do not exist.
Source
Derived from reading:nma-28 of the reviewed corpus.