Abstract
In this paper the log-exponentiated-Weibull regression model is modified to allow the possibility that long term survivors are present in the data. The modification leads to a log-exponentiated-Weibull regression model with cure rate, encompassing as special cases the log-exponencial regression and log-Weibull regression models with cure rate typically used to model such data. The models attempt to estimate simultaneously the effects of covariates on the acceleration/deceleration of the timing of a given event and the surviving fraction; that is, the proportion of the population for which the event never occurs. Assuming censored data, we consider a classic analysis and Bayesian analysis for the parameters of the proposed model. The normal curvatures of local influence are derived under various perturbation schemes and two deviance-type residuals are proposed to assess departures from the log-exponentiated-Weibull error assumption as well as to detect outlying observations. Finally, a data set from the medical area is analyzed.
Highlights
Models for survival analysis typically assume that all units under study are susceptible to the event and will eventually experience this event if the follow-up is sufficiently long
The log-exponentiated-Weibull regression (LEWR) model was modified in order to include long-term individuals
Continuing with modeling investigation, we applied local influence theory (Cook (1986) and Thomas and Cook (1990)) and conducted a study based on martingale and deviance residuals in a survival model with a cure fraction
Summary
Models for survival analysis typically assume that all units under study are susceptible to the event and will eventually experience this event if the follow-up is sufficiently long. Cure rate models have been applied to estimate the possibility of a cured fraction These models extend the understanding of time-to-event data by allowing the formulation of more accurate and informative conclusions. The literature presents many applications of the survival models with cure rate considering the Weibull family of distributions (see, Ibrahim et al, 2001; Maller and Zhou , 1996). This family is suitable in situations where the failure rate function is constant or monotone.
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