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A two‐way flexible generalized gamma transformation cure rate model

We propose a two‐way flexible cure rate model. The first flexibility is provided by considering a family of Box‐Cox transformation cure models that include the commonly used cure models as special cases. The second flexibility is provided by proposing the wider class of generalized gamma distributions to model the associated lifetime. The advantage of this two‐way flexibility is that it allows us to carry out tests of hypotheses to select an adequate cure model (within the family of Box‐Cox transformation cure models) and a suitable lifetime distribution (within the wider class of generalized gamma distributions) that jointly provides the best fit to a given data. First, we study the maximum likelihood estimation of the generalized gamma Box‐Cox transformation (GGBCT) model parameters. Then, we use the flexibility of our proposed model to carry out power studies to demonstrate the power of likelihood ratio test in rejecting mis‐specified models. Furthermore, we study the bias and efficiency of the estimators of the cure rates under model mis‐specification. Our findings strongly suggest the importance of selecting a correct lifetime distribution and a correct cure rate model, which can be achieved through the proposed two‐way flexible model. Finally, we illustrate the applicability of our proposed model using a data from a breast cancer study and show that our model provides a better fit than the existing semiparametric Box‐Cox transformation cure model with piecewise exponential approximation to the lifetime distribution.