Modelo Weibull modificado de longa duração
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2011-12-07Autor
Oliveira, Cleyton Zanardo de
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When a group of patients is monitored until a pre-established date for observation of the
recurrence time of an event, it is possible that, at the end of the monitoring period, a parcel of such
group has not yet suffered the event of interest. When that happens, even if the period is extended,
there is evidence that an appropriate model for the theoretical survival function of the time until the
event occurs would be one model able to bear this kind of data. This class of long duration models will
be defined because the form presented by the nonparametric estimation of hazard function in this type
of study indicates that the model should be flexible to allow such function to be increasing, decreasing,
constant or U-shaped. In this report, we present the long duration modified Weibull model (LDMW)
as a proposal to contemplate the issues in the medicine area. The LDMW model has a flexible hazard
curve, which enables adjustment when the hazard is decreasing, increasing, U-shaped, unimodal,
initially decreasing and posteriorly unimodal and constant. The report also particularizes models
already known in the literature that contemplate long duration, such as the long duration Weibull
(LDW), long duration Exponential (LDE) and short duration models, such as the modified Weibull
(MW), Weibull and Exponential. The simulations showed that the odds of coverage reach the nominal
probability of 95% for moderately to big sized samples, that the LDMW p model parameters
estimation is costless when compared to the MW and that the selection criteria of the AIC and BIC
models are not adequate to discriminate the LDMW model adjustment when compared to the LDW
model adjustment for small or moderately sized samples. The LDMW model and its particular cases
were adjusted into two sets of real data considering the Classic and Bayesian Inference. The first data
set is about the time until the seroreversion of children born from HIV-positive mothers and the
second data set is about the recurrence time of breast cancer in women.
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