A flexible-hazards cure model with application to patients with soft tissue sarcoma

In medical research, it is often of great interest to have an accurate estimation of cure rates by different treatment options and for different patient groups. If the follow-up time is sufficiently long and the sample size is large, the proportion of cured patients will make the Kaplan-Meier estimator of survival function have a flat plateau at its tail, whose value indicates the overall cure rate. However, it may be difficult to estimate and compare the cure rates for all the subsets of interest in this way, due to the limit of sample sizes and curse of dimensionality. In the current literature, most regression models for estimating cure rates assume proportional hazards (PH) between different subgroups. It turns out that the estimation of cure rates for subgroups is highly sensitive to this assumption, so more flexible models are needed, especially when this PH assumption is clearly violated. We propose a new cure model to simultaneously incorporate both PH and non-PH scenarios for different covariates. We develop a stable and easily implementable iterative procedure for parameter estimation through maximization of the nonparametric likelihood function. The covariance matrix is estimated by adding perturbation weights to the estimation procedure. In simulation studies, the proposed method provides unbiased estimation for the regression coefficients, survival curves, and cure rates given covariates, while existing models are biased. Our model is applied to a study of stage III soft tissue sarcoma and provides trustworthy estimation of cure rates for different treatment and demographic groups.