Asymptotic efficiency of a proportional hazards model with cure

Nonparametric estimators of survivor function can be used in the presence of long-term survivors to estimate the probability of cure by the last point of a survivor curve. To explain the presence of long-term survivors the cumulative hazard is assumed bounded but otherwise unspecified to yield an improper survivor function. Within this formulation the PH model is asymptotically fully efficient as compared to a parametric model under certain conditions when estimating the ratio of cure rates. However, this is not the case if estimation of cure rates in absolute terms is of interest. The asymptotic relative efficiency tends to zero as the probability of cure decreases. It also decreases with increase of the coefficient of variation of covariates approaching the value computed under homogeneity. Partial likelihood is shown to be inefficient if the baseline hazard is completely known.

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