Tocqueville Today? Contexts, Interpretations and Usages

Geenens, Raf; Dijn, Annelien de

doi:10.1057/9780230599123_1

Cited by 2 publications

(2 citation statements)

References 2 publications

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“…According to [21], any bivariate distribution function for (T 1 , T 2 ) can be formulated by using a copula. A bivariate copula is a bivariate distribution function for two uniform variables on [0, 1] ( [22], [23]). Let T 1 and T 2 be continuous survival times with marginal survival functions S 1 and S 2 , respectively.…”

Section: Copula Models For Dependent Survival Timementioning

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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Section: Copula Models For Dependent Survival Timementioning

confidence: 99%

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

Nakazono,

Lin,

Liao

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

“…According to Sklar [23], any bivariate distribution function for (T 1 , T 2 ) can be formulated by using a copula. A bivariate copula is a bivariate distribution function for two uniformly distributed variables on [0, 1] [24,25]. In many applications of copulas on survival analysis, bivariate survival functions are modeled via survival copulas [20,24,26,27].…”

Section: Survival Copula Models For Dependent Survival Timementioning

confidence: 99%

Computation of the Mann–Whitney Effect under Parametric Survival Copula Models

Nakazono,

Lin,

Liao

et al. 2024

Mathematics

View full text Add to dashboard Cite

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 of each other, the traditional formula of the Mann–Whitney effect has to be modified. In this article, we propose a copula-based approach to compute the Mann–Whitney 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 . Through a simulation study, we show the correctness of the proposed calculator. We apply the proposed methods to two real datasets.

show abstract

Tocqueville Today? Contexts, Interpretations and Usages

Cited by 2 publications

References 2 publications

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

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

Computation of the Mann–Whitney Effect under Parametric Survival Copula Models

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