Meta-analysis of individual patient data with semi-competing risks under the Weibull joint frailty–copula model

Wu, Bo-Hong; Michimae, Hirofumi; Emura, Takeshi

doi:10.1007/s00180-020-00977-1

Cited by 15 publications

(4 citation statements)

References 25 publications

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“…In our data example of gastric cancer patients (Section 5.1), bivariate correlated endpoints are of great interest [55]. Correlations between responses should be employed to improve the efficiency and reduce the bias of univariate analyses [56][57][58][59][60][61][62][63][64][65] and to predict a primary outcome by the secondary outcome [66][67][68][69]. Multivariate shrinkage estimators of multivariate normal means, such as [70,71], can be considered for this extension.…”

Section: Conclusion and Future Extensionsmentioning

confidence: 99%

A Meta-Analysis for Simultaneously Estimating Individual Means with Shrinkage, Isotonic Regression and Pretests

Taketomi

Konno

Chang

et al. 2021

Axioms

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Meta-analyses combine the estimators of individual means to estimate the common mean of a population. However, the common mean could be undefined or uninformative in some scenarios where individual means are “ordered” or “sparse”. Hence, assessments of individual means become relevant, rather than the common mean. In this article, we propose simultaneous estimation of individual means using the James–Stein shrinkage estimators, which improve upon individual studies’ estimators. We also propose isotonic regression estimators for ordered means, and pretest estimators for sparse means. We provide theoretical explanations and simulation results demonstrating the superiority of the proposed estimators over the individual studies’ estimators. The proposed methods are illustrated by two datasets: one comes from gastric cancer patients and the other from COVID-19 patients.

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Section: Conclusion and Future Extensionsmentioning

confidence: 99%

A Meta-Analysis for Simultaneously Estimating Individual Means with Shrinkage, Isotonic Regression and Pretests

Taketomi

Konno

Chang

et al. 2021

Axioms

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“…Figure 3 shows the hazard functions with the increasing (α > 1), constant (α = 1), and decreasing (α < 1) shapes. A number of papers adopted the Weibull distribution for accelerated life data [27,[56][57][58][59], left-truncated data [60,61], breast/colorectal/ovarian cancer data [6,[62][63][64], the AIDS data [65], and others. The Weibull distribution is also useful for creating multivariate survival distributions [66].…”

Section: Weibull Distributionmentioning

confidence: 99%

Parametric Distributions for Survival and Reliability Analyses, a Review and Historical Sketch

et al. 2022

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During its 330 years of history, parametric distributions have been useful for survival and reliability analyses. In this paper, we comprehensively review the historical backgrounds and statistical properties of a number of parametric distributions used in survival and reliability analyses. We provide encyclopedic coverage of the important parametric distributions, which is more extensive than the existing textbooks on survival and reliability analyses. We also explain how these distributions have been adopted in survival and reliability analyses with original and state-of-the-art references. We cover the exponential, Weibull, Rayleigh, lognormal, log-logistic, gamma, generalized gamma, Pareto (types I, II, and IV), Hjorth, Burr (types III and XII), Dagum, exponential power, Gompertz, Birnbaum-Saunders, exponential-logarithmic, piecewise exponential, generalized exponential, exponentiated Weibull, generalized modified Weibull, and spline distributions. We analyze a real dataset for illustration.

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“…Random censoring will be considered as well. We generated event times

S_{i j}

and

T_{i j}

associated with the surrogate and the true endpoints following a Weibull distribution, with a method close to that used in Nelsen (2006), Rotolo, Paoletti, & Michiels (2018), and Wu, Michimae, & Emura (2020) under the Clayton copula function. For the Weibull distribution, we specify the baseline hazard functions by

λ_{0 S} false(t false) = ρ_{S} γ_{S} t^{γ_{S} - 1}, ρ_{S} > 0, γ_{S} > 0; λ_{0 T} false(t false) = ρ_{T} γ_{T} t^{γ_{T} - 1}, ρ_{T} > 0, γ_{T} > 0,

where

ρ_{S}

and

ρ_{T}

are the scale parameters, and

γ_{S}

and

γ_{S}

are the shape parameters.…”

Section: Simulationsmentioning

confidence: 99%

A joint frailty‐copula model for meta‐analytic validation of failure time surrogate endpoints in clinical trials

2020

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In a meta‐analysis framework, the classical approach for the validation of time‐to‐event surrogate endpoint is based on a two‐step analysis. This approach often raises estimation issues. Recently, we proposed a one‐step validation approach based on a joint frailty model. This approach was quite time consuming, despite parallel computing, due to individual‐level frailties used to take into account heterogeneity in the data at the individual level. We now propose an alternative one‐step approach for evaluating surrogacy, using a joint frailty‐copula model. The model includes two correlated random effects treatment‐by‐trial interaction and a shared random effect associated with the baseline risks. At the individual level, the joint survivor functions of time‐to‐event endpoints are linked using copula functions. We used splines for the baseline hazard functions. We estimated parameters and hazard function using a semiparametric penalized marginal likelihood method, considering various numerical integration methods. Both individual‐level and trial‐level surrogacy were evaluated using Kendall's tau and coefficient of determination. The performance of the estimators was evaluated using simulation studies. The model was applied to individual patient data meta‐analyses in advanced ovarian cancer to assess progression‐free survival as a surrogate for overall survival, as part of the evaluation of new therapy. The model showed good performance and was quite robust regarding the integration methods and data variation, regardless of the surrogacy evaluation criteria. Kendall's Tau was better estimated using the Clayton copula model compared to the joint frailty model. The proposed model reduces the convergence and model estimation issues encountered in the two‐step approach.

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Meta-analysis of individual patient data with semi-competing risks under the Weibull joint frailty–copula model

Cited by 15 publications

References 25 publications

A Meta-Analysis for Simultaneously Estimating Individual Means with Shrinkage, Isotonic Regression and Pretests

A Meta-Analysis for Simultaneously Estimating Individual Means with Shrinkage, Isotonic Regression and Pretests

Parametric Distributions for Survival and Reliability Analyses, a Review and Historical Sketch

A joint frailty‐copula model for meta‐analytic validation of failure time surrogate endpoints in clinical trials

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