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arxiv: 2605.30517 · v1 · pith:YCSR2HORnew · submitted 2026-05-28 · 📊 stat.ME · stat.CO

Restricted mean time lost for survival and competing risks data using mets in R

Thomas Harder Scheike , Klaus K\"ahler Holst This is my paper

Pith reviewed 2026-06-29 05:35 UTC · model grok-4.3

classification 📊 stat.ME stat.CO
keywords restricted mean survival timerestricted mean time lostcompeting risksIPCWinfluence functionsR packageaverage treatment effects
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The pith

The mets R package supplies non-parametric and IPCW regression estimates of restricted mean survival time and time lost, with influence functions for standard errors across all time horizons.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper describes an R package that computes restricted mean survival time and restricted mean time lost for ordinary survival data and for data with competing risks. The implementation returns the non-parametric estimates together with their standard errors for every possible time horizon in a single pass. Regression models rely on inverse probability of censoring weighting, and the package supplies the influence functions that make variance estimation and further statistical constructions possible.

Core claim

The mets package implements IPCW-based estimating equations for RMST and RMTL, including cause-specific RMTL in the competing-risks setting, supplies the corresponding influence functions, and adds G-computation procedures that yield average treatment effect estimates; all computations scale linearly with the number of observations.

What carries the argument

IPCW adjusted estimating equations together with their influence functions, which deliver both point estimates and variance estimates while permitting the RMST quantities to be used as inputs to more complex statistics.

If this is right

  • Non-parametric RMST and RMTL estimates together with standard errors become available for every time horizon without separate runs.
  • Influence functions allow the RMST estimates to be inserted directly into more elaborate statistics such as while-alive summaries for recurrent events.
  • G-computation routines produce average treatment effect estimates for RMST and RMTL under the competing-risks model.
  • The linear scaling makes the procedures practical for data sets with tens or hundreds of thousands of observations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same influence functions could be reused to construct joint confidence regions across several time horizons without additional resampling.
  • The package output could serve as input to meta-analytic models that pool RMST differences across studies while accounting for within-study dependence.
  • Because the estimates are already equipped with influence functions, they can be combined with other estimating equations in a single sandwich variance calculation.

Load-bearing premise

The censoring mechanism can be modeled correctly so that the inverse probability weights are consistent.

What would settle it

A Monte Carlo experiment in which the true RMST value is known but the coverage rate of the influence-function-based intervals falls substantially below the nominal level would falsify the variance estimator.

Figures

Figures reproduced from arXiv: 2605.30517 by Klaus K\"ahler Holst, Thomas Harder Scheike.

Figure 1
Figure 1. Figure 1: RMST for all time-horizons with 95 % confidence intervals. [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: RMTL for TRM and relapse for all time-horizons with 95 % confidence intervals. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
read the original abstract

This paper introduces software implemented in the mets R-package for calculating non-parametric and regression estimates of Restricted Mean Survival Time (RMST) and Restricted Mean Time Lost (RMTL), including RMTL due to specific causes. A unique feature is the ability to compute the non-parametric estimates of RMST and RMTL, as well as their standard errors, for all time horizons simultaneously. Regression modeling in mets is based on Inverse Probability of Censoring Weighting (IPCW) methods. The package implements different versions of IPCW adjusted estimating equations. A critical technical contribution is the provision of influence functions for all models, which enables the computation of standard errors and allows the estimates to be used as building blocks for more complex statistics, such as the while-alive estimate in recurrent events settings. To expand capabilities in causal inference, the mets package also implements methods for standardization estimates (G-computation) and the estimation of Average Treatment Effects (ATE) for both RMST and RMTL in the competing risks setting. Importantly, the computations scale linearly with the number of observations, making the software efficient for use with large datasets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript describes the mets R package for non-parametric and IPCW-based regression estimation of restricted mean survival time (RMST) and restricted mean time lost (RMTL), including cause-specific RMTL under competing risks. It highlights simultaneous computation of estimates and standard errors across all time horizons, provision of influence functions for variance estimation and downstream use (e.g., while-alive estimators), extensions to G-computation and ATE via standardization, and linear scaling with sample size.

Significance. If the implementations are correct, the package supplies a practical, efficient tool for RMST/RMTL analysis in competing-risks settings. The explicit influence functions are a useful technical feature that supports standard-error calculation and modular use in more complex estimators; linear scaling addresses a common practical limitation with large data.

minor comments (3)
  1. The abstract states that influence functions are provided for all models, but the manuscript should include a brief explicit statement (with reference to the relevant estimating equations) confirming that these functions are derived and exported for the IPCW regression estimators as well as the non-parametric estimators.
  2. The description of the different IPCW estimating-equation variants would benefit from a short table or enumerated list that maps each variant to the corresponding function name and the precise form of the censoring model it employs.
  3. Standard references for the original RMST/RMTL IPCW estimators (e.g., the foundational papers on IPCW for RMST) should be cited in the introduction or methods section to situate the software contribution.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary and recommendation of minor revision. No major comments were provided in the report, so there are no specific points requiring point-by-point response or manuscript changes at this stage.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The manuscript presents an R package implementing established IPCW regression and influence-function variance estimation for RMST/RMTL quantities. No derivation is claimed that reduces by construction to fitted inputs, self-citation chains, or renamed empirical patterns; the influence functions are supplied as a computational feature whose validity rests on standard semiparametric theory rather than on any internal redefinition or self-referential premise. The work is therefore self-contained against external statistical benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

This is a software implementation paper; the central claims rest on standard survival analysis assumptions rather than new free parameters or invented entities.

axioms (1)
  • domain assumption IPCW methods require correct modeling of the censoring distribution or proper estimation of weights.
    The abstract states that regression modeling is based on IPCW methods.

pith-pipeline@v0.9.1-grok · 5731 in / 1274 out tokens · 30781 ms · 2026-06-29T05:35:58.556175+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages · 1 internal anchor

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    Birkhäuser, Boston. Sachs MC, Gabriel EE (2022). “Event History Regression with Pseudo-Observations: Compu- tational Approaches and an Implementation in R.”Journal of Statistical Software,102(9), 1–34.doi:10.18637/jss.v102.i09. Sachs MC, Gabriel EE (2025).eventglm: Regression Models for Event History Outcomes. R package version 1.4.5, URLhttps://cran.r-pr...

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