EXTENDED EXPONENTIAL-WEIBULL REGRESSION MODEL FOR HANDLING SURVIVAL DATA IN THE PRESENCE OF COVARIATES

Abstract

Incorporating covariates into the future lifetime distribution is crucial to the survival analysis. In this thesis a novel version of the exponential-Weibull distribution known as the extended exponential-Weibull (ExEW) distribution is developed and examined using the Lehmann alternative II (LAII) technique. The basic mathematical properties of the new ExEW distribution are derived. The maximum likelihood estimation (MLE) technique is used to estimate the unknown parameters of the ExEW distribution. The estimators' performance is further assessed using Monte Carlo simulations. Two real-world data sets are utilized to show the applicability of the new distribution. Moreover, a fully parametric accelerated failure time (AFT) model with a exible, novel modi ed exponential Weibull baseline distribution called the extended exponential Weibull accelerated failure time (ExEW-AFT) model is developed. The model is presented using the multi-parameter survival regression model, where more than one distributional parameter is linked to the covariates. The model formulation, probabilistic functions, and some of its sub-models are derived. The parameters of the developed model are estimated using the maximum likelihood approach. An extensive simulation study is used to assess the estimates' performance using di erent scenarios based on the baseline hazard shape. The developed model is applied to a real-life right-censored COVID-19 data set from Sudan to illustrate the practical applicability of the developed ExEW-AFT model. A mixture cure model with ExEW distribution is presented to include the fraction of unsusceptible (cured) individuals in the study. The developed models are compared with existing mode