On the estimation of interval censored destructive negative binomial cure model

Abstract

In this article, a competitive risk survival model is considered in which the initial number of risks, assumed to follow a negative binomial distribution, is subject to a destructive mechanism. Assuming the population of interest to have a cure component, the form of the data as interval‐censored, and considering both the number of initial risks and risks remaining active after destruction to be missing data, we develop two distinct estimation algorithms for this model. Making use of the conditional distributions of the missing data, we develop an expectation maximization (EM) algorithm, in which the conditional expected complete log‐likelihood function is decomposed into simpler functions which are then maximized independently. A variation of the EM algorithm, called the stochastic EM (SEM) algorithm, is also developed with the goal of avoiding the calculation of complicated expectations and improving performance at parameter recovery. A Monte Carlo simulation study is carried out to evaluate the performance of both estimation methods through calculated bias, root mean square error, and coverage probability of the asymptotic confidence interval. We demonstrate the proposed SEM algorithm as the preferred estimation method through simulation and further illustrate the advantage of the SEM algorithm, as well as the use of a destructive model, with data from a children's mortality study.

A support vector machine-based cure rate model for interval censored data

“…Unlike right-censored data, 32 , 33 interval-censored data occur for a study where subjects are inspected at regular intervals, and not continuously. 34 – 36 If a subject experiences the event of interest, the exact survival time is not observed and is only known that the event has occurred between two consecutive inspections. Interval-censored data marked by cure prospect are often observed in follow-up clinical studies (cancer biochemical recurrence or AIDS drug resistance) dealing with events having low fatality and patients monitored at regular intervals.…”