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BMC Med Res Methodol. 2016 Mar 29;16:37. doi: 10.1186/s12874-016-0137-z.

Bias and precision of methods for estimating the difference in restricted mean survival time from an individual patient data meta-analysis.

Lueza B1,2,3, Rotolo F4,5,6, Bonastre J1,2, Pignon JP1,2,3, Michiels S1,2,3.

Author information

1
Gustave Roussy, Université Paris-Saclay, Service de biostatistique et d'épidémiologie, F-94805, Villejuif, France.
2
Université Paris-Saclay, Univ. Paris-Sud, UVSQ, CESP, INSERM, F-94085, Villejuif, France.
3
Ligue Nationale Contre le Cancer meta-analysis platform, Gustave Roussy, F-94085, Villejuif, France.
4
Gustave Roussy, Université Paris-Saclay, Service de biostatistique et d'épidémiologie, F-94805, Villejuif, France. federico.rotolo@gustaveroussy.fr.
5
Université Paris-Saclay, Univ. Paris-Sud, UVSQ, CESP, INSERM, F-94085, Villejuif, France. federico.rotolo@gustaveroussy.fr.
6
Ligue Nationale Contre le Cancer meta-analysis platform, Gustave Roussy, F-94085, Villejuif, France. federico.rotolo@gustaveroussy.fr.

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.

KEYWORDS:

Meta-analysis; Multicenter clinical trial; Restricted mean survival time; Simulation study; Survival analysis; Survival benefit

PMID:
27025706
PMCID:
PMC4812643
DOI:
10.1186/s12874-016-0137-z
[Indexed for MEDLINE]
Free PMC Article

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