Generalized log-gamma regression models with cure fraction |
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Authors: | Edwin M M Ortega Vicente G Cancho Gilberto A Paula |
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Institution: | 1. Department of Exact Sciences, Universidade de S?o Paulo (USP), Av. Pádua Dias 11 - Caixa Postal 9, Piracicaba, SP, 13418-900, Brazil 2. Department of Applied Mathematics and Statistics, Universidade de S?o Paulo (USP), Av. Trabalhador S?o-Carlense 400, S?o Carlos, SP, 13560-970, Brazil 3. Department of Statistics, Universidade de S?o Paulo (USP), Rua do Mat?o 1010, S?o Paulo, SP, 05508-090, Brazil
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Abstract: | In this paper, the generalized log-gamma regression model is modified to allow the possibility that long-term survivors may
be present in the data. This modification leads to a generalized log-gamma regression model with a cure rate, encompassing,
as special cases, the log-exponential, log-Weibull and log-normal regression models with a cure rate typically used to model
such data. The models attempt to simultaneously estimate the effects of explanatory variables on the timing acceleration/deceleration
of a given event and the surviving fraction, that is, the proportion of the population for which the event never occurs. The
normal curvatures of local influence are derived under some usual perturbation schemes and two martingale-type residuals are
proposed to assess departures from the generalized log-gamma error assumption as well as to detect outlying observations.
Finally, a data set from the medical area is analyzed. |
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Keywords: | Cure-fraction models Generalized log-gamma distribution Sensitivity analysis Residual analysis Lifetime data |
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