TY - JOUR
T1 - A bivariate power generalized Weibull distribution
T2 - A flexible parametric model for survival analysis
AU - Jones, M. C.
AU - Noufaily, Angela
AU - Burke, Kevin
N1 - Publisher Copyright:
© The Author(s) 2019.
PY - 2020/8/1
Y1 - 2020/8/1
N2 - We are concerned with the flexible parametric analysis of bivariate survival data. Elsewhere, we argued in favour of an adapted form of the ‘power generalized Weibull’ distribution as an attractive vehicle for univariate parametric survival analysis. Here, we additionally observe a frailty relationship between a power generalized Weibull distribution with one value of the parameter which controls distributional choice within the family and a power generalized Weibull distribution with a smaller value of that parameter. We exploit this relationship to propose a bivariate shared frailty model with power generalized Weibull marginal distributions linked by the BB9 or ‘power variance function’ copula, then change it to have adapted power generalized Weibull marginals in the obvious way. The particular choice of copula is, therefore, natural in the current context, and the corresponding bivariate adapted power generalized Weibull model a novel combination of pre-existing components. We provide a number of theoretical properties of the models. We also show the potential of the bivariate adapted power generalized Weibull model for practical work via an illustrative example involving a well-known retinopathy dataset, for which the analysis proves to be straightforward to implement and informative in its outcomes.
AB - We are concerned with the flexible parametric analysis of bivariate survival data. Elsewhere, we argued in favour of an adapted form of the ‘power generalized Weibull’ distribution as an attractive vehicle for univariate parametric survival analysis. Here, we additionally observe a frailty relationship between a power generalized Weibull distribution with one value of the parameter which controls distributional choice within the family and a power generalized Weibull distribution with a smaller value of that parameter. We exploit this relationship to propose a bivariate shared frailty model with power generalized Weibull marginal distributions linked by the BB9 or ‘power variance function’ copula, then change it to have adapted power generalized Weibull marginals in the obvious way. The particular choice of copula is, therefore, natural in the current context, and the corresponding bivariate adapted power generalized Weibull model a novel combination of pre-existing components. We provide a number of theoretical properties of the models. We also show the potential of the bivariate adapted power generalized Weibull model for practical work via an illustrative example involving a well-known retinopathy dataset, for which the analysis proves to be straightforward to implement and informative in its outcomes.
KW - BB9 copula
KW - Gompertz
KW - log-logistic
KW - power variance frailty
KW - shared frailty
UR - http://www.scopus.com/inward/record.url?scp=85077360073&partnerID=8YFLogxK
U2 - 10.1177/0962280219890893
DO - 10.1177/0962280219890893
M3 - Article
C2 - 31840558
AN - SCOPUS:85077360073
SN - 0962-2802
VL - 29
SP - 2295
EP - 2306
JO - Statistical Methods in Medical Research
JF - Statistical Methods in Medical Research
IS - 8
ER -