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<p>Frailty models are widely used in survival analysis to account for unobserved heterogeneity and dependence in clustered time-to-event data. While the gamma frailty remains the most commonly used specification, its limited flexibility may restrict its ability to capture complex dependence structures observed in practice. Motivated by the need for greater modeling flexibility, this paper proposes a new frailty model based on the Jørgensen–Seshadri–Whitmore (JSW) distribution, a flexible extension of the inverse Gaussian family that accommodates varying mixing structures and a broader range of tail behaviors. The proposed frailty specification extends existing inverse Gaussian-based models while preserving analytical tractability. In particular, closed-form expressions for the Laplace transform and its derivatives are obtained, allowing explicit characterization of dependence through Kendall’s <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>. The proposed framework encompasses several classical frailty models as special cases, providing a unified and flexible approach for modeling clustered survival data. Both parametric and semiparametric versions of the model are developed, and parameter estimation is performed via an expectation–maximization algorithm. The finite-sample performance of the proposed estimators is evaluated via Monte Carlo simulations under both correct specification and frailty misspecification. An application to real survival data illustrates that the additional flexibility of the JSW frailty model can lead to improved model fit and a more nuanced assessment of unobserved heterogeneity compared with commonly used frailty distributions.</p>

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A new frailty model based on the jørgensen–seshadri–whitmore distribution

  • 期刊论文

  • 发表日期：

    2026年7月28日

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  • Zohreh Mohammadi,
  • Diego I. Gallardo,
  • Ahad Jamalizadeh

摘要

Frailty models are widely used in survival analysis to account for unobserved heterogeneity and dependence in clustered time-to-event data. While the gamma frailty remains the most commonly used specification, its limited flexibility may restrict its ability to capture complex dependence structures observed in practice. Motivated by the need for greater modeling flexibility, this paper proposes a new frailty model based on the Jørgensen–Seshadri–Whitmore (JSW) distribution, a flexible extension of the inverse Gaussian family that accommodates varying mixing structures and a broader range of tail behaviors. The proposed frailty specification extends existing inverse Gaussian-based models while preserving analytical tractability. In particular, closed-form expressions for the Laplace transform and its derivatives are obtained, allowing explicit characterization of dependence through Kendall’s \(\tau \) τ . The proposed framework encompasses several classical frailty models as special cases, providing a unified and flexible approach for modeling clustered survival data. Both parametric and semiparametric versions of the model are developed, and parameter estimation is performed via an expectation–maximization algorithm. The finite-sample performance of the proposed estimators is evaluated via Monte Carlo simulations under both correct specification and frailty misspecification. An application to real survival data illustrates that the additional flexibility of the JSW frailty model can lead to improved model fit and a more nuanced assessment of unobserved heterogeneity compared with commonly used frailty distributions.