Generalized inverse-Gaussian frailty models with application to TARGET neuroblastoma data
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Generalized inverse‑Gaussian frailty models with application to TARGET neuroblastoma data Luiza S. C. Piancastelli1,3 · Wagner Barreto‑Souza2,3 · Vinícius D. Mayrink3 Received: 11 April 2020 / Revised: 3 October 2020 / Accepted: 13 October 2020 © The Institute of Statistical Mathematics, Tokyo 2020
Abstract A new class of survival frailty models based on the generalized inverse-Gaussian (GIG) distributions is proposed. We show that the GIG frailty models are flexible and mathematically convenient like the popular gamma frailty model. A piecewiseexponential baseline hazard function is employed, yielding flexibility for the proposed class. Although a closed-form observed log-likelihood function is available, simulation studies show that employing an EM-algorithm is advantageous concerning the direct maximization of this function. Further simulated results address the comparison of different methods for obtaining standard errors of the estimates and confidence intervals for the parameters. Additionally, the finite-sample behavior of the EM-estimators is investigated and the performance of the GIG models under misspecification assessed. We apply our methodology to a TARGET (Therapeutically Applicable Research to Generate Effective Treatments) data about the survival time of patients with neuroblastoma cancer and show some advantages of the GIG frailties over existing models in the literature. Keywords EM-algorithm · Frailty · Generalized inverse-Gaussian models · Neuroblastoma · Robustness
1 Introduction When dealing with time to event data, the most popular statistical approach is the proportional hazards model by Cox (1972). This model is based on the hazard function and accommodates well censored and truncated data, which are key elements in survival analysis.
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s1046 3-020-00774-z) contains supplementary material, which is available to authorized users. * Wagner Barreto‑Souza [email protected] Extended author information available on the last page of the article
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One situation in which the proportional hazards model can be deficient occurs when unobserved sources of heterogeneity are present in the data. This might be explained by the lack of important covariates in the study, which are difficult to measure or were not collected because the researcher did not know its importance in the first place. In this case, the deficiency of the proportional hazards model is the assumption of a homogeneous population. Another common situation in which the proportional hazards model is problematic occurs when there is correlated survival data. The correlation arises, for example, when repeated measures are collected for each individual or when some common traits such as biological or environmental factors are shared. The described situations are usually treated by assuming a frailty model configured as a natural extension to the Cox model. This approach introd
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