Change-point Hazard Research Articles

Cpsurvsim: An R Package for Simulating Data from Change-Point Hazard Distributions

Change-point hazard models have several practical applications, including modeling processes such as cancer mortality rates and disease progression. While the inverse cumulative distribution function (CDF) method is commonly used for simulating data, we demonstrate the shortcomings of this approach when simulating data from change-point hazard distributions with more than a scale parameter. We propose an alternative method of simulating this data that takes advantage of the memoryless property of survival data and introduce the R package cpsurvsim which implements both simulation methods. The functions of cpsurvsim are discussed, demonstrated, and compared.

Testing for Phases of Dropout Attrition Using Change-Point Hazard Models

Abstract While web-based surveys are a convenient research tool, the ease of dropping out in the online setting has become a growing issue in ensuring data quality. One theory is that dropout, or attrition, occurs in phases that can be generalized to phases of high dropout and phases of stable use. In order to detect these phases, survey dropout is considered as a time-to-event outcome and tests within change-point hazard models are introduced. Here, we apply the multiple change-point exponential model and extend the single change-point Weibull model to account for multiple change-points. We also introduce a likelihood ratio test to aid in determining the number of distinct phases, using Monte Carlo simulations of the null hypothesis of no attrition phases or change-points against the alternative hypothesis that distinct attrition phases exist (at least one change-point). The performances of these change-point hazard models are compared using both a simulation study and also with application to survey data on patient cancer screening preferences, as well as compared to previous work with discrete models.

Estimation in the single change-point hazard function for interval-censored data with a cure fraction

ABSTRACTIn reliability or survival analysis, the hazard function plays a significant part for it can display the instantaneous failure rate at any time point. In practice, the abrupt change in hazard function at an unknown time point may occur after a maintenance activity or major operation. Under these circumstances, identifying the change point and estimating the size of the change are meaningful. In this paper, we assume that the hazard function is piecewise constant with a single jump at an unknown time. We propose the single change-point model for interval-censored survival data with a cure fraction. Estimation methods for the proposed model are investigated, and large-sample properties of the estimators are established. Simulation studies are carried out to evaluate the performance of the estimating method. The liver cancer data and breast cancer data are analyzed as the applications.

Estimation in a change-point hazard regression model with long-term survivors

This paper estimates the change-point for a piecewise hazard regression model in the presence of right censoring and long-term survivors. The maximum likelihood estimators of the change point and other parameters are shown to be consistent. The proposed method is illustrated through analyzing the kidney infection recurrence data.

A Test for Constant Hazard Against a Change-Point Alternative

In this article, we consider the change-point hazard rate model which arises quite commonly in mechanical or biological systems, which experience a high hazard rate early in their lifetime due to infant mortality and then a constant or steady hazard rate after the threshold time. We first derive the corresponding mean residual life function (MRLF) and observe that the MRLF is initially increasing and then constant. Here, we derive a test statistic for exponentiality against Increasing Initially then Constant Mean Residual Life (ICMRL). We also derive the asymptotic distribution of the test statistic and compare the power of the test with other existing tests such as likelihood ratio, Weibull, and Log gamma tests considered in the literature. The test performs quite well as compared to other alternatives studied.

Bayesian Analysis of Change-Point Hazard Rate Problem

Abstract Change-point hazard rate models arise, for example, in applying “burn-in” techniques to screen defective items and in studying times until undesirable side effects occur in clinical trials. The classical approach develops estimates of model parameters, with particular interest in the threshold or change-point parameter, but exclusively in terms of asymptotic properties. Such asymptotics can be poor for small to moderate sample sizes often encountered in practice. We propose a Bayesian approach, avoiding asymptotics, to provide more reliable inference conditional only upon the data actually observed. The Bayesian models can be fitted using simulation methods. We develop a very general formulation of the model but also look at special cases which offer particularly simple fitting. We illustrate with an application involving failure times of electrical insulation.

Estimation in a change-point hazard regression model

In this paper, we consider a parametric survival regression model with a change-point in both hazard and regression parameters. Change-point occurs at an unknown time point. Estimators of the change-point, hazard and regression parameters are proposed and shown to be consistent.

Estimation in change-point hazard function models

In this paper, we consider hazard function models with a change-point allowing for random censoring when the base-line hazard function is unknown with some parameters. A non-parametric estimator of the change-point is proposed in the context of counting process. The estimators of change-point and other parameters are shown to be consistent.

Bootstrapping the change-point of a hazard rate

This paper concerns the asymptotic validity of the bootstrap method in a non-regular model. Specifically, it is shown that the parametric bootstrap of the change-point parameter in the change-point hazard rate model works.

Statistical Modelling of the AIDS Epidemic for Forecasting Health Care Needs

The objective of this paper is to develop statistical methods for estimating current and future numbers of individuals in different stages of the natural history of the human immunodeficiency (AIDS) virus infection and to evaluate the impact of therapeutic advances on these numbers. The approach is to extend the method of back-calculation to allow for a multistage model of natural history and to permit the hazard functions of progression from one stage to the next to depend on calendar time. Quasi-likelihood estimates of key quantities for evaluating health care needs can be obtained through iteratively reweighted least squares under weakly parametric models for the infection rate. An approach is proposed for incorporating into the analysis independent estimates of human immunodeficiency virus (HIV) prevalence obtained from epidemiologic surveys. The methods are applied to the AIDS epidemic in the United States. Short-term projections are given of both AIDS incidence and the numbers of HIV-infected AIDS-free individuals with CD4 cell depletion. The impact of therapeutic advances on these numbers is evaluated using a change-point hazard model. A number of important sources of uncertainty must be considered when interpreting the results, including uncertainties in the specified hazard functions of disease progression, in the parametric model for the infection rate, in the AIDS incidence data, in the efficacy of treatment, and in the proportions of HIV-infected individuals receiving treatment.

A Problem with the Likelihood Ratio Test for a Change-Point Hazard Rate Model

A Problem with the Likelihood Ratio Test for a Change-Point Hazard Rate Model

Strong consistency of the maximum likelihood estimators in the change-point hazard bate model

A procedure for estimating the parameters in the change point hazard rate model by maximizing the likelihood over suitable random compact sets is proposed- The estimates are shown to be strongly consistent under quite general conditions and their asymptotic distributions are given

A problem with the likelihood ratio test for a change-point hazard rate model

A likelihood ratio test for constant hazard against a step change alternative has received considerable attention in recent years. Additional information in the maximum likelihood estimate of the change-point can seriously affect interpretation of test results. Some simple modifications are considered for which exact percentage points can be derived. Monte Carlo power and mean squared error comparisons are encouraging.

A parametric approach to theory of competing risks when the time of death from each cause follows a change-point hazard rate model

The paper a t tempts t o make i n f e r e n c e about the component parameters, based on data from a series system, when the components each follow a different changepoint hazard r a t e model.The paper extends the result of Nattbews and Farewell (1982) to the competing risk framework.

On a Singularity in the Likelihood for a Change-Point Hazard Rate Model

A singularity identified by Nguyen, Rogers & Walker (1984) in the log likelihood function for a change-point hazard rate model is eliminated if the likelihood function is appropriately defined.

On a singularity in the likelihood for a change-point hazard rate model

A singularity identified by Nguyen, Rogers & Walker (1984) in the log likelihood function for a change-point hazard rate model is eliminated if the likelihood function is appropriately defined.

Estimation in change-point hazard rate models

SUMMARY This paper discusses the estimation of parameters in hazard rate models with a changepoint. Due to the irregularity of the models, the classical maximum likelihood method and the method of moments cannot be used. A consistent estimator of the change-point is obtained by examining the properties of the density represented as a mixture. The performance of the estimator is checked via simulation.