Abstract

The difference in restricted mean survival time ( $$ rmstD\left({t}^{\ast}\right) $$ ), the area between two survival curves up to time horizon $$ {t}^{\ast } $$ , is often used in cost-effectiveness analyses to estimate the treatment effect in randomized controlled trials. A challenge in individual patient data (IPD) meta-analyses is to account for the trial effect. We aimed at comparing different methods to estimate the $$ rmstD\left({t}^{\ast}\right) $$ from an IPD meta-analysis. We compared four methods: the area between Kaplan-Meier curves (experimental vs. control arm) ignoring the trial effect (Naive Kaplan-Meier); the area between Peto curves computed at quintiles of event times (Peto-quintile); the weighted average of the areas between either trial-specific Kaplan-Meier curves (Pooled Kaplan-Meier) or trial-specific exponential curves (Pooled Exponential). In a simulation study, we varied the between-trial heterogeneity for the baseline hazard and for the treatment effect (possibly correlated), the overall treatment effect, the time horizon $$ {t}^{\ast } $$ , the number of trials and of patients, the use of fixed or DerSimonian-Laird random effects model, and the proportionality of hazards. We compared the methods in terms of bias, empirical and average standard errors. We used IPD from the Meta-Analysis of Chemotherapy in Nasopharynx Carcinoma (MAC-NPC) and its updated version MAC-NPC2 for illustration that included respectively 1,975 and 5,028 patients in 11 and 23 comparisons. The Naive Kaplan-Meier method was unbiased, whereas the Pooled Exponential and, to a much lesser extent, the Pooled Kaplan-Meier methods showed a bias with non-proportional hazards. The Peto-quintile method underestimated the $$ rmstD\left({t}^{\ast}\right) $$ , except with non-proportional hazards at $$ {t}^{\ast } $$ = 5 years. In the presence of treatment effect heterogeneity, all methods except the Pooled Kaplan-Meier and the Pooled Exponential with DerSimonian-Laird random effects underestimated the standard error of the $$ rmstD\left({t}^{\ast}\right) $$ . Overall, the Pooled Kaplan-Meier method with DerSimonian-Laird random effects formed the best compromise in terms of bias and variance. The $$ rmstD\left({t}^{\ast },=,10,\kern0.5em ,\mathrm{years}\right) $$ estimated with the Pooled Kaplan-Meier method was 0.49 years (95 % CI: [−0.06;1.03], p = 0.08) when comparing radiotherapy plus chemotherapy vs. radiotherapy alone in the MAC-NPC and 0.59 years (95 % CI: [0.34;0.84], p < 0.0001) in the MAC-NPC2. We recommend the Pooled Kaplan-Meier method with DerSimonian-Laird random effects to estimate the difference in restricted mean survival time from an individual-patient data meta-analysis.

Highlights

  • The difference in restricted mean survival time, the area between two survival curves up to time horizon tÃ, is often used in cost-effectiveness analyses to estimate the treatment effect in randomized controlled trials

  • Methods for estimating the difference in restricted mean survival time We investigated four methods for estimating the difference in restricted mean survival time rmstDðtÃÞ from an individual patient data (IPD) meta-analysis: 1) the Naïve Kaplan-Meier, which pools the data, ignoring the trial effect, 2-3) the Pooled Kaplan-Meier and Pooled Exponential methods, which use a two-stage approach to combine rmstDjðtÃÞ estimated in each trial j, and 4) the Peto-quintile method, which uses survival functions derived from a pooled hazard ratio estimated with a two-stage approach in order to take into account the trial effect

  • The difference in restricted mean survival time is an appealing alternative to the hazard ratio to measure the treatment effect in a meta-analysis of time-to-event outcomes, as it is free of the proportional hazards assumption and its interpretation is more intuitive

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Summary

Introduction

The difference in restricted mean survival time (rmstDðtÃÞ), the area between two survival curves up to time horizon tÃ, is often used in cost-effectiveness analyses to estimate the treatment effect in randomized controlled trials. In cost-effectiveness analysis, a commonly used survival measure is the restricted mean survival time (RMST) It estimates the life expectancy for one treatment arm up to a certain time horizon tà [1,2,3,4]. Recent studies have compared methods to estimate the RMST including extrapolation beyond the trial followup [7,8,9,10] These studies focused on the use of a single randomized clinical trial and not on multicenter clinical trials nor meta-analyses

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