A Nonparametric Mixture Model for Cure Rate Estimation

Abstract

Nonparametric methods have attracted less attention than their parametric counterparts for cure rate analysis. In this paper, we study a general nonparametric mixture model. The proportional hazards assumption is employed in modeling the effect of covariates on the failure time of patients who are not cured. The EM algorithm, the marginal likelihood approach, and multiple imputations are employed to estimate parameters of interest in the model. This model extends models and improves estimation methods proposed by other researchers. It also extends Cox's proportional hazards regression model by allowing a proportion of event-free patients and investigating covariate effects on that proportion. The model and its estimation method are investigated by simulations. An application to breast cancer data, including comparisons with previous analyses using a parametric model and an existing nonparametric model by other researchers, confirms the conclusions from the parametric model but not those from the existing nonparametric model.

A SAS macro for parametric and semiparametric mixture cure models

“…A more detailed presentation can be found in Peng and Dear [6] and Sy and Taylor [7]. and if δ i = 0 then u i is not observed, where u i is the value taken by the random variable U i .…”

A dynamic Mover–Stayer model for recurrent event processes subject to resolution

“…Kuk and Chen (1992) extended the cure rate model to accommodate a semiparametric proportional hazard model for the survival time and proposed estimation via an expectation-maximization (EM) algorithm. Peng and Dear (2000) further studied the semiparametric approach by allowing covariate effects on the cure rate. A zero-tail constraint was introduced by Sy and Taylor (2000) to deal with identifiability issues.…”

Semiparametric accelerated failure time cure rate mixture models with competing risks

“…To analyze such data, one can use cure fraction models that have been developed to manipulate and analyze survival data with a high survivor rate. [1][2][3][4][5][6][7][8][9] Cure rate models focus on the proportion of patients who survive for a long time following the disease diagnosis. Additionally, these models work on the survival probability of the uncured patients up to a given point in time.…”

“…This leads to the 2-mixture cure models that formulate the overall survival function as S T (t) = 0 + 1 S 1 (t), where 0 is the cure fraction and S 1 (t) is the conditional survival function for the uncured subgroup with probability 1 = 1 − 0 . Studies of parametric and semiparametric treatments of these models are well represented in the literature (eg, Peng and Dear, 2 Lu and Ying, 3 Lu, 7 and Choi and Huang 8 ). For 2 mutually-exclusive competing risks problems, this model can be naturally expanded to S T (t) = 1 S 1 (t) + 2 S 2 (t),…”