Extending the long-term survivor mixture model with random effects for clustered survival data

To provide a class of hazard functions in analyzing survival data, the power family of transformations has been proposed in the literature. Our work in this paper considers the existence of cured patients and random effects due to clustering of survival data in a long-term survivor model setting. A power family of transformations is assumed for the relative risk in the hazard function component. Such an extension allows us to flexibly base the inferences on various hazard function assumptions, particularly taking exponential and linear relative risk as two special cases. The parameter governing the power transformation could be determined by means of a modified Akaike information criterion (AIC). Applications to two sets of survival data illustrate the use of the proposed long-term survivor mixture model. A simulation study is carried out to examine the performance of the estimators under the proposed numerical estimation scheme.