title: Bias and precision of methods for estimating the difference in restricted mean survival time from an individual patient data meta-analysis.
abstract: BACKGROUND
  The difference in restricted mean survival time ([Formula: see text]), the area between two survival curves up to time horizon [Formula: see text], 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 [Formula: see text] from an IPD meta-analysis.
  
  
  METHODS
  We compared four methods: the area between Kaplan-Meier curves (experimental vs. control arm) ignoring the trial effect (Naïve 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 [Formula: see text], 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.
  
  
  RESULTS
  The Naïve 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 [Formula: see text], except with non-proportional hazards at [Formula: see text]= 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 [Formula: see text]. Overall, the Pooled Kaplan-Meier method with DerSimonian-Laird random effects formed the best compromise in terms of bias and variance. The [Formula: see text] 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.
  
  
  CONCLUSIONS
  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.
authors.affiliation: Gustave Roussy, Université Paris-Saclay, Service de biostatistique et d'épidémiologie, F-94805, Villejuif, France.|Université Paris-Saclay, Univ. Paris-Sud, UVSQ, CESP, INSERM, F-94085, Villejuif, France.|Ligue Nationale Contre le Cancer meta-analysis platform, Gustave Roussy, F-94085, Villejuif, France.
authors.forename: Béranger
authors.initials: B
authors.lastname: Lueza
authors.affiliation: Gustave Roussy, Université Paris-Saclay, Service de biostatistique et d'épidémiologie, F-94805, Villejuif, France. federico.rotolo@gustaveroussy.fr.|Université Paris-Saclay, Univ. Paris-Sud, UVSQ, CESP, INSERM, F-94085, Villejuif, France. federico.rotolo@gustaveroussy.fr.|Ligue Nationale Contre le Cancer meta-analysis platform, Gustave Roussy, F-94085, Villejuif, France. federico.rotolo@gustaveroussy.fr.
authors.forename: Federico
authors.identifier: http://orcid.org/0000-0003-4837-6501
authors.initials: F
authors.lastname: Rotolo
authors.affiliation: Gustave Roussy, Université Paris-Saclay, Service de biostatistique et d'épidémiologie, F-94805, Villejuif, France.|Université Paris-Saclay, Univ. Paris-Sud, UVSQ, CESP, INSERM, F-94085, Villejuif, France.
authors.forename: Julia
authors.initials: J
authors.lastname: Bonastre
authors.affiliation: Gustave Roussy, Université Paris-Saclay, Service de biostatistique et d'épidémiologie, F-94805, Villejuif, France.|Université Paris-Saclay, Univ. Paris-Sud, UVSQ, CESP, INSERM, F-94085, Villejuif, France.|Ligue Nationale Contre le Cancer meta-analysis platform, Gustave Roussy, F-94085, Villejuif, France.
authors.forename: Jean-Pierre
authors.initials: JP
authors.lastname: Pignon
authors.affiliation: Gustave Roussy, Université Paris-Saclay, Service de biostatistique et d'épidémiologie, F-94805, Villejuif, France.|Université Paris-Saclay, Univ. Paris-Sud, UVSQ, CESP, INSERM, F-94085, Villejuif, France.|Ligue Nationale Contre le Cancer meta-analysis platform, Gustave Roussy, F-94085, Villejuif, France.
authors.forename: Stefan
authors.initials: S
authors.lastname: Michiels
mesh_terms: D000970:Antineoplastic Agents / Q000008:administration & dosage*; D015982:Bias; D002277:Carcinoma; D002986:Clinical Trials as Topic; D003198:Computer Simulation; D018572:Disease-Free Survival; D005260:Female; D006801:Humans; D053208:Kaplan-Meier Estimate; D008297:Male; D015233:Models, Statistical; D000077274:Nasopharyngeal Carcinoma; D009303:Nasopharyngeal Neoplasms / Q000188:drug therapy / Q000401:mortality* / Q000473:pathology; D012680:Sensitivity and Specificity; D013223:Statistics as Topic; D016019:Survival Analysis
chemical_list: D000970:Antineoplastic Agents
keywords: Meta-analysis; Multicenter clinical trial; Restricted mean survival time; Simulation study; Survival analysis; Survival benefit