Abstract
Cure rate models are useful while modelling lifetime data involving long time survivors. In this work, we discuss a flexible cure rate model by assuming the number of competing causes for the event of interest to follow the Conway-Maxwell Poisson distribution and the lifetimes of the non-cured individuals to follow a proportional odds model. The baseline distribution is considered to be either Weibull or log-logistic distribution. Under right censoring, we develop the maximum likelihood estimators using EM algorithm. Model discrimination among some well-known special cases are discussed under both likelihood- and information-based criteria. An extensive simulation study is carried out to examine the performance of the proposed model and the inferential methods. Finally, a cutaneous melanoma dataset is analyzed for illustrative purpose.
Highlights
Statistical models accommodating a surviving fraction are known as cure rate models
Cure data have been analyzed in the literature by the structure of the underling survival model of the non-cured individuals Ss(t) as proportional hazards (PH) mixture cure model [20] [15] [24], accelerated failure time (AFT) mixture cure rate model [25] [17] [14], accelerated hazards (AH) mixture cure rate model [26], and proportional odds (PO) mixture cure rate model [10] [18]
We consider two baseline distributions for the proportional odds survival model corresponding to the timeto-event random variable, namely, Weibull and log-logistic distributions
Summary
The cure rate model was first introduced by [8] and [7], and have been subsequently studied by many authors. Where p0 is the probability of cure and Ss(t) is the survival function of the non-cured or susceptible individuals in the population. PROPORTIONAL ODDS UNDER CONWAY-MAXWELL-POISSON CURE RATE MODEL (c.d.f) F (w) = 1 − S(w). Where W0 is corresponding to the individual who are not susceptible to the event occurrence (namely, with infinite lifetime). This leads to a proportion of the cured group, known as cure rate. We assume a proportional odds model for the distribution of Wj, with a parametric assumption on the baseline odds function.
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