Abstract
The interest in estimating the probability of cure has been increas ing in cancer survival analysis as the cure of some cancer sites is becoming a reality. Mixture cure models have been used to model the failure time data with the existence of long-term survivors. The mixture cure model assumes that a fraction of the survivors are cured from the disease of interest. The failure time distribution for the uncured individuals (latency) can be mod eled by either parametric models or a semi-parametric proportional hazards model. In the model, the probability of cure and the latency distribution are both related to the prognostic factors and patients’ characteristics. The maximum likelihood estimates (MLEs) of these parameters can be obtained using the Newton-Raphson algorithm. The EM algorithm has been proposed as a simple alternative by Larson and Dinse (1985) and Taylor (1995). in various setting for the cause-specific survival analysis. This approach is ex tended here to the grouped relative survival data. The methods are applied to analyze the colorectal cancer relative survival data from the Surveillance, Epidemiology, and End Results (SEER) program.
Highlights
In the study of cancer incidence and mortality of the population, mixture cure models Boag (1949) have been used for failure time data with long term survivors
This paper provides an EM algorithm to fit the mixture cure model to the grouped relative survival data
It can fit both a parametric or a semi-parametric mixture cure model. This algorithm utilizes the standard statistical software to achieve the M-step and is easier to implement than the Newton-Raphson
Summary
In the study of cancer incidence and mortality of the population, mixture cure models Boag (1949) have been used for failure time data with long term survivors. These models assume that a fraction of the patients are cured from the disease of interest. The additive hazards model implies that pij(θ; xi, Eij) = rij(θ; xi)Eij. The loglikelihood function for the grouped relative survival data (x, s, d, E) = {(xi, sij, dij, Eij), i = 1, ..., I, j = 1, ..., J} is IJ (θ|x, s, d, E) =. We provide a simple alternative, the EM algorithm, to estimate the mixture cure model for grouped relative survival data.
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