A multi-parameter Generalized Farlie-Gumbel-Morgenstern bivariate copula family via Bernstein polynomial

Susam, Selim Orhun

doi:10.15672/hujms.993698

Cited by 12 publications

(8 citation statements)

References 16 publications

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“…Another limitation is that only one-parameter copulas are implemented. There are multi-parameter copulas that deserve attention ( [22], [44], [28]).…”

Section: Discussionmentioning

confidence: 99%

Computation of The Mann-Whitney Effect under Parametric Survival Copula Models

Nakazono,

Lin,

Liao

et al. 2024

Preprint

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The Mann-Whitney effect is a measure for comparing survival distributions between two groups. The Mann-Whitney effect is interpreted as the probability that a randomly selected subject in a group survives longer than a randomly selected subject in the other group. Under the independence assumption of two groups, the Mann-Whitney effect can be expressed as the traditional integral formula of survival functions. However, when the survival times in two groups are not independent each other, the traditional expression of the Mann-Whitney effect has to be modified. In this article, we propose a copula-based approach to compute the Mann-Witney effect with parametric survival models under dependence of two groups, which may arise in the potential outcome framework. In addition, we develop a Shiny web app that can implement the proposed method via simple commands (https://nkosuke.shinyapps.io/shiny_survival/). Through a simulation study, we show the correctness of the proposed calculator. We apply the proposed methods to two real datasets.

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“…Another limitation is that only one-parameter copulas are implemented. There are multi-parameter copulas that deserve attention ( [22], [44], [28]).…”

Section: Discussionmentioning

confidence: 99%

Computation of The Mann-Whitney Effect under Parametric Survival Copula Models

Nakazono,

Lin,

Liao

et al. 2024

Preprint

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“…Furthermore, these Archimedean copulas allow simple formulas to compute the CG estimators [ 52 ]. However, there are a large number of non-Archimedean copulas popular in a variety of applications, such as the FGM copula, Gaussian copula, trigonometric copula, and Celebioglu–Cuadras copula [ 82 , 83 , 84 , 85 , 86 , 87 ]. As the CG estimators have not been considered for these non-Archimedean copulas, it is of great interest to develop computational tools for them.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Sensitivity Analysis for Survival Prognostic Prediction with Gene Selection: A Copula Method for Dependent Censoring

2023

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Prognostic analysis for patient survival often employs gene expressions obtained from high-throughput screening for tumor tissues from patients. When dealing with survival data, a dependent censoring phenomenon arises, and thus the traditional Cox model may not correctly identify the effect of each gene. A copula-based gene selection model can effectively adjust for dependent censoring, yielding a multi-gene predictor for survival prognosis. However, methods to assess the impact of various types of dependent censoring on the multi-gene predictor have not been developed. In this article, we propose a sensitivity analysis method using the copula-graphic estimator under dependent censoring, and implement relevant methods in the R package “compound.Cox”. The purpose of the proposed method is to investigate the sensitivity of the multi-gene predictor to a variety of dependent censoring mechanisms. In order to make the proposed sensitivity analysis practical, we develop a web application. We apply the proposed method and the web application to a lung cancer dataset. We provide a template file so that developers can modify the template to establish their own web applications.

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“…The FGM copula was used in applications to survival data, 62 reliability data, 65 chemical data, 66 sports data, 67 and econometric data. 68…”

Section: Declaration Of Conflicting Interestsmentioning

confidence: 99%

“…62 Huang et al 63 also chose the Frank model for modeling dependence between death and readmission in patients with colorectal cancer. Example 3: The Farlie–Gumbel–Morgensterm (FGM) copula (Morgenstern 64 ): The FGM copula produces negative dependence false( θ i < 0 false), positive dependence false( θ i > 0 false), and independence false( θ i = 0 false), having Kendall's tau τ θ i = 2 θ i / 9. The FGM copula was used in applications to survival data, 62 reliability data, 65 chemical data, 66 sports data, 67 and econometric data. 68…”

Section: A1 Examples Of the Copulasmentioning

confidence: 99%

Factorial survival analysis for treatment effects under dependent censoring

Emura,

Ditzhaus,

Dobler

et al. 2023

Stat Methods Med Res

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Factorial analyses offer a powerful nonparametric means to detect main or interaction effects among multiple treatments. For survival outcomes, for example, from clinical trials, such techniques can be adopted for comparing reasonable quantifications of treatment effects. The key difficulty to solve in survival analysis concerns the proper handling of censoring. So far, all existing factorial analyses for survival data have been developed under the independent censoring assumption, which is too strong for many applications. As a solution, the central aim of this article is to develop new methods for factorial survival analyses under quite general dependent censoring regimes. This will be accomplished by combining existing nonparametric methods for factorial survival analyses with techniques developed for survival copula models. As a result, we will present an appealing F-test that exhibits sound performance in our simulation study. The new methods are illustrated in a real data analysis. We implement the proposed method in an R function surv.factorial(.) in the R package compound.Cox.

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A multi-parameter Generalized Farlie-Gumbel-Morgenstern bivariate copula family via Bernstein polynomial

Cited by 12 publications

References 16 publications

Computation of The Mann-Whitney Effect under Parametric Survival Copula Models

Computation of The Mann-Whitney Effect under Parametric Survival Copula Models

Sensitivity Analysis for Survival Prognostic Prediction with Gene Selection: A Copula Method for Dependent Censoring

Factorial survival analysis for treatment effects under dependent censoring

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