Proportional Mean Residual Life Model Research Articles

Mean residual life cure models for right-censored data with and without length-biased sampling.

We propose a semiparametric mean residual life mixture cure model for right-censored survival data with a cured fraction. The model employs the proportional mean residual life model to describe the effects of covariates on the mean residual time of uncured subjects and the logistic regression model to describe the effects of covariates on the cure rate. We develop estimating equationsto estimate the proposed cure model for the right-censored data with and without length-biased sampling, the latter is often found in prevalent cohort studies. In particular, we propose two estimating equationsto estimate the effects of covariates in the cure rate and a method to combine them to improve the estimation efficiency. The consistency and asymptotic normality of the proposed estimates are established. The finite sample performance of the estimates is confirmed with simulations. The proposed estimation methods are applied to a clinical trial study on melanoma and a prevalent cohort study on early-onset type 2 diabetesmellitus.

Estimation of the Proportional Mean Residual Life Model with Internal and Longitudinal Covariates

Estimation of the Proportional Mean Residual Life Model with Internal and Longitudinal Covariates

Estimating Disability Adjusted Life Years using Survival Models in HIV/ AIDS Risk Groups

Introduction: Advances in human immunodeficiency virus (HIV) treatment have led to greater survival rates and have brought about a shift in the burden of disease from mortality to morbidity. The main purpose of this study is to estimate the Disability Adjusted Life Years (DALYs) of HIV infected patients associated with different modes of transmission. Methods: Non-parametric Kaplan-Meier estimate has been utilised to develop survival function, and the mean residual life model has been utilised to estimate the life expectancy of patients alive at the end of the study. The impact of factors such as age, sex, hepatitis B and syphilis on life expectancy has also been assessed by fitting a proportional mean residual life model. DALYs have been calculated based on the results of both models. Results: Retrospective time to event data of HIV patients undergoing Antiretroviral Therapy (ART) in Dr Ram Manohar Lohia Hospital, New Delhi, India has been utilised to illustrate the modelling technique. The study suggests that in total, 42300.15 DALYs were lost which includes 39765.10 years of life lost due to premature death and 2535.05 years of life lived with disability. When the covariates were taken into consideration, 47592.14 DALYs were found to have been lost with an average of 17.64 DALYs lost per patient. Conclusion: Our results suggest that the high-risk groups such as homosexuals and parent to child transmission are a major cause of concern, which are in accordance with the existing national policies. Also, we would suggest that gender-based and age-based policies should be incorporated to reduce the burden of disease.

Fisher consistent estimation of regression parameter in the proportional mean residual life model with frailty

In the article, we consider the Fisher consistent estimation of the regression parameters in the proportional mean residual life model with arbitrary frailty. It is discussed that conventional estimation procedures, such as the maximum likelihood estimation or Cox’s approach, which are employed in common regression models, may also yield consistent inference in the extended models.

Rank Estimation for Mean Residual Life Transformation Model

This paper proposes a new and important class of mean residual life regression model, which is called the mean residual life transformation model. The link function is assumed to be unknown and increasing in its second argument, but it is permitted to be not differentiable. The mean residual life transformation model encompasses the proportional mean residual life model, the additive mean residual life model, and so on. Under maximum rank correlation estimation, we present the estimation procedures, whose asymptotic and finite sample properties are established. The consistent variance can be estimated by a resampling method via perturbing the U -statistics objective function repeatedly which avoids the usual sandwich choice. Monte Carlo simulations reveal good finite sample performance and the estimators are illustrated with the Oscar data set.

Statistical inference for proportional mean residual life model with continuous auxiliary covariate

In many statistical studies involving failure data, the main covariate is only measured in a validation set due to financial and technical restriction, while some auxiliary information for the main covariate is collected for the full cohort. Making use of the auxiliary information will increase the efficiency of the study. In this paper, we consider statistical inference for the proportional mean residual life model when the primary covariate is measured only for a randomly chosen subcohort and some auxiliary variables are available for the whole study cohort. To further make use of the auxiliary information to improve the efficiency of the study, we propose anestimating equation based on the inverse probability of censoring weighting techniques. The resulting estimators are shown to be consistent and asymptotically normal. Extensive simulations are conducted to evaluate the finite sample performance of the proposed methods. We illustrate the proposed method with a real data set from the Mayo Clinic trial in primary biliary cirrhosis of the liver.

Proportional Mean Residual Life Model with Varying Coefficients for Length-Biased and Right-Censored Data

Length-biased data are encountered in many fields, including economics, engineering and epidemiological cohort studies. There are two main challenges in the analysis of such data: the assumption of independent censoring is violated and the assumed model for the underlying population is no longer satisfied for the observed data. In this paper, a proportional mean residual life varying-coefficient model for length-biased data is considered and a local pseudo likelihood method is proposed for estimating the coefficient functions in the model. Asymptotic properties are investigated for the proposed estimators. The finite sample performance of the proposed methodology is demonstrated by simulation studies. Finally, the method is applied to a real data set concerning the Academy Awards.

Estimating Attributable Life Expectancy Under the Proportional Mean Residual Life Model

In population-based health research, the so-called population attributable fraction is an important quantity that calculates the percentage of excess risk of morbidity and mortality associated with modifiable risk factors for a given population. While the concept of “risk” is usually measured by event probabilities, in practice it may be of a more direct interest to know the excess life expectancy associated with the modifiable risk factors instead, particularly when mortality is of the ultimate concern. In this paper, we thus propose to study a novel quantity, termed “attributable life expectancy,” to measure the population attributable fraction of life expectancy. We further develop a model-based approach for the attributable life expectancy under the Oakes–Dasu proportional mean residual life model, and establish its asymptotic properties for inferences. Numerical studies that include Monte-Carlo simulations and an actual analysis of the mortality associated with smoking cessation in an Asia Cohort Consortium are conducted to evaluate the performance of our proposed method.

Reliability Aspects of Proportional Mean Residual Life Model Using Quantile Functions

Reliability Aspects of Proportional Mean Residual Life Model Using Quantile Functions

Analysis of combined incident and prevalent cohort data under a proportional mean residual life model.

The Nun Study, a longitudinal study to examine risk factors for the progression of dementia, consists of subjects who were already diagnosed with dementia (ie, prevalent cohort) and those who do not have dementia (ie, incident cohort) at study enrollment. When assessing the risk factors' effects on the survival time from dementia diagnosis until death, utilizing data from both cohorts supports more efficient statistical inference because the two cohorts provide valuable complementary information. A major challenge in analyzing the combined cohort data is that the prevalent cases are not representative of the target population. Moreover, the dates of dementia diagnosis are not ascertained for the prevalent cohort in the Nun Study. Hence, the survival time for the prevalent cohort is only partially observed from study enrollment until death or censoring, with the time from dementia diagnosis to study enrollment missing. In this paper, we propose an efficient estimation method that uses both incident and prevalent cohorts under the proportional mean residual life model. By assuming proportionality of the mean residual life time with covariates in the incident cohort, we can utilize the natural relationship between the mean residual life function and the hazard function of the survival time measured from enrollment until death for the prevalent cohort. We evaluate the efficiency gain from using the combined cohort data through simulations and demonstrate that the proposed method is valid and efficient.

Proportional mean residual life model with censored survival data under case-cohort design

Proportional mean residual life model is studied for analysing survival data from the case-cohort design. To simultaneously estimate the regression parameters and the baseline mean residual life function, weighted estimating equations based on an inverse selection probability are proposed. The resulting regression coefficients estimates are shown to be consistent and asymptotic normal with easily estimated variance-covariance. Simulation studies show that the proposed estimators perform very well. An application to a real dataset from the South Welsh nickel refiners study is also given to illustrate the methodology.

Analysis of proportional mean residual life model with latent variables.

End-stage renal disease (ESRD) is one of the most serious diabetes complications. Numerous studies have been devoted to revealing the risk factors of the onset time of ESRD. In this article, we propose a proportional mean residual life (MRL) model with latent variables to assess the effects of observed and latent risk factors on the MRL function of ESRD in a cohort of Chinese type 2 diabetic patients. The proposed model generalizes the conventional proportional MRL model to accommodate the latent risk factor that cannot be measured by a single observed variable. We employ a factor analysis model to characterize the latent risk factors via multiple observed variables. We develop a borrow-strength estimation procedure, which incorporates the expectation-maximization algorithm and an extended estimating equation approach. The asymptotic properties of the proposed estimators are established. Simulation shows that the performance of the proposed methodology is satisfactory. The application to the study of type 2 diabetes reveals insights into the prevention of ESRD. Copyright © 2016 John Wiley & Sons, Ltd.

General proportional mean residual life model

By considering a covariate random variable in the ordinary proportional mean residual life (PMRL) model, we introduce and study a general model, taking more situations into account with respect to the ordinary PMRL model. We investigate how stochastic structures of the proposed model are affected by the stochastic properties of the baseline and the mixing variables in the model. Several characterizations and preservation properties of the new model under different stochastic orders and aging classes are provided. In addition, to illustrate different properties of the model, some examples are presented.

Semiparametric inference for the proportional mean residual life model with right-censored length-biased data

Semiparametric inference for the proportional mean residual life model with right-censored length-biased data

Semiparametric Proportional Mean Residual Life Model With Censoring Indicators Missing at Random

For right-censored survival data, the information that whether the observed time is survival or censoring time is frequently lost. This is the case for the competing risk data. In this article, we consider statistical inference for the right-censored survival data with censoring indicators missing at random under the proportional mean residual life model. Simple and augmented inverse probability weighted estimating equation approaches are developed, in which the nonmissingness probability and some unknown conditional expectations are estimated by the kernel smoothing technique. The asymptotic properties of all the proposed estimators are established, while extensive simulation studies demonstrate that our proposed methods perform well under the moderate sample size. At last, the proposed method is applied to a data set from a stage II breast cancer trial.

An Additive–Multiplicative Restricted Mean Residual Life Model

AbstractThe mean residual life measures the expected remaining life of a subject who has survived up to a particular time. When survival time distribution is highly skewed or heavy tailed, the restricted mean residual life must be considered. In this paper, we propose an additive–multiplicative restricted mean residual life model to study the association between the restricted mean residual life function and potential regression covariates in the presence of right censoring. This model extends the proportional mean residual life model using an additive model as its covariate dependent baseline. For the suggested model, some covariate effects are allowed to be time‐varying. To estimate the model parameters, martingale estimating equations are developed, and the large sample properties of the resulting estimators are established. In addition, to assess the adequacy of the model, we investigate a goodness of fit test that is asymptotically justified. The proposed methodology is evaluated via simulation studies and further applied to a kidney cancer data set collected from a clinical trial.

Semiparametric regression for restricted mean residual life under right censoring

A mean residual life function (MRLF) is the remaining life expectancy of a subject who has survived to a certain time point. In the presence of covariates, regression models are needed to study the association between the MRLFs and covariates. If the survival time tends to be too long or the tail is not observed, the restricted mean residual life must be considered. In this paper, we propose the proportional restricted mean residual life model for fitting survival data under right censoring. For inference on the model parameters, martingale estimating equations are developed, and the asymptotic properties of the proposed estimators are established. In addition, a class of goodness-of-fit test is presented to assess the adequacy of the model. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and the approach is applied to a set of real life data collected from a randomized clinical trial.

Semiparametric proportional mean residual life model with covariates missing at random

In this paper, we consider statistical inference for the proportional mean residual life model when some covariates are missing at random. Simple and augmented inverse probability-weighted estimating equations are used to obtain the estimators of the regression coefficients and baseline mean residual life function. The unknown non-missingness probability and some unknown conditional expectations are estimated by the kernel smoothing technique. We show that the simple inverse probability-weighted estimator with estimated non-missingness probability is more efficient than that with the true non-missingness probability, while the augmented inverse probability-weighted estimator with estimated non-missingness probability and that with the true non-missingness probability have the same efficiency. The asymptotic properties of all the proposed estimators are established. Extensive simulation studies are conducted to examine the finite sample performance of the proposed estimator. At last, the proposed method is applied to the mouse leukaemia data.

ON DYNAMIC PROPORTIONAL MEAN RESIDUAL LIFE MODEL

Recently, proportional mean residual life model has received a lot of attention after the importance of the model was discussed by Zahedi [17]. In this paper, we define dynamic proportional mean residual life model and study its properties for different aging classes. The closure of this model under different stochastic orders is also discussed. Many examples are presented to illustrate different properties of the model.

On the Mixture Proportional Mean Residual Life Model

In this article, we propose a new mixture model induced by the model of proportional mean residual life. Under some appropriate assumptions, it is shown that the mixing and overall variables in the model admit the positive likelihood ratio dependence structure. To see how the overall variable is affected by the stochastic variation of the mixing variable, we study some stochastic comparisons using these variables. Finally, some useful bounds for tail probability of the overall variable for large values of the mixing variable are derived.