Surviving and non surviving fraction regression models based on the beta modified Weibull distribution

Abstract

We propose two regression models based on the beta modified Weibull distribution. The first one is the long-term mixture lifetime regression applied to survival data when some individuals may never experience the event of interest for possible presence of long-term survivors in the data. This regression attempts to estimate the effects of covariates on the surviving fraction. The second one is regression model based on the log-beta modified Weibull distribution as an alternative to the log-modified Weibull regression. This model aims to estimate the effects of covariates on the survival times. These new models generalize some existing regressions in the literature. For both cases, the model parameters are estimated by the method of maximum likelihood for censored data. We derive the appropriate matrices for assessing the local influence on parameter estimates under different perturbation schemes and present a global sensitivity analysis. A model check based on the quantile residuals is performed to select the appropriate regressions. We reanalyze two data sets available in the literature, one for each regression.