Mean Residual Life Model Research Articles

Regression analysis of partially linear transformed mean residual life models

Regression analysis of partially linear transformed mean residual life models

DYNAMIC PREDICTION OF RESIDUAL LIFE WITH LONGITUDINAL COVARIATES USING LONG SHORT-TERM MEMORY NETWORKS.

Sepsis, a complex medical condition that involves severe infections with life-threatening organ dysfunction, is a leading cause of death worldwide. Treatment of sepsis is highly challenging. When making treatment decisions, clinicians and patients desire accurate predictions of mean residual life (MRL) that leverage all available patient information, including longitudinal biomarker data. Biomarkers are biological, clinical, and other variables reflecting disease progression that are often measured repeatedly on patients in the clinical setting. Dynamic prediction methods leverage accruing biomarker measurements to improve performance, providing updated predictions as new measurements become available. We introduce two methods for dynamic prediction of MRL using longitudinal biomarkers. in both methods, we begin by using long short-term memory networks (LSTMs) to construct encoded representations of the biomarker trajectories, referred to as "context vectors." In our first method, the LSTM-GLM, we dynamically predict MRL via a transformed MRL model that includes the context vectors as covariates. In our second method, the LSTM-NN, we dynamically predict MRL from the context vectors using a feed-forward neural network. We demonstrate the improved performance of both proposed methods relative to competing methods in simulation studies. We apply the proposed methods to dynamically predict the restricted mean residual life (RMRL) of septic patients in the intensive care unit using electronic medical record data. We demonstrate that the LSTM-GLM and the LSTM-NN are useful tools for producing individualized, real-time predictions of RMRL that can help inform the treatment decisions of septic patients.

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.

The mean residual life model for the right-censored data in the presence of covariate measurement errors.

In this article, we consider the mean residual life regression model in the presence of covariate measurement errors. In the whole cohort, the surrogate variable of the error-prone covariate is available for each subject, while the instrumental variable (IV), which is related to the underlying true covariates, is measured only for some subjects, the calibration sample. Without specifying distributions of measurement errors but assuming that the IV is missing at random, we develop two estimation methods, the IV calibration and cohort estimators, for the regression parameters by solving estimation equations (EEs) based on the calibration sample and cohort sample, respectively. To improve estimation efficiency, a synthetic estimator is derived by applying the generalized method of moment for all EEs. The large sample properties of the proposed estimators are established and their finite sample performance are evaluated via simulation studies. Simulation results show that the cohort and synthetic estimators outperform the IV calibration estimator and the relative efficiency of the cohort and synthetic estimators mainly depends on the missing rate of IV. In the case of low missing rate, the synthetic estimator is more efficient than the cohort estimator, while the result can be reversed when the missing rate is high. We illustrate the proposed method by application to data from the patients with stage 5 chronic kidney disease in Taiwan.

Generalized mean residual life models for survival data with missing censoring indicators.

The mean residual life (MRL) function is an important and attractive alternative to the hazard function for characterizing the distribution of a time-to-event variable. In this article, we study the modeling and inference of a family of generalized MRL models for right-censored survival data with censoring indicators missing at random. To estimate the model parameters, augmented inverse probability weighted estimating equation approaches are developed, in which the non-missingness probability and the conditional probability of an uncensored observation are estimated by parametric methods or nonparametric kernel smoothing techniques. Asymptotic properties of the proposed estimators are established and finite sample performance is evaluated by extensive simulation studies. An application to brain cancer data is presented to illustrate the proposed methods.

A signature-based approach for reliability modeling and maintenance optimization of a coherent system

In reliability context, mean residual lifetime (MRL) models and proportional hazard (PH) models are widely used for reliability analysis and failure prediction. Since maintenance actions typically are based on aforementioned reliability metrics, recent researches have been focused on the extensions of these two models for accurate decision-making. In this paper, using signature arguments, we propose a state-dependent mean residual life (SDMRL) model and demonstrate its applicability in both reliability and maintenance field. In preference to existing models, the SDMRL modeling can be applied to coherent systems and account both changes in the operating environment and for the natural ageing process of the system. Assuming a bivariate threshold-type policy, the paper aims at minimizing the long-run average maintenance cost per unit time by determining appropriate inspection intervals and optimal replacement policy. The proposed model and the behavior of the optimal solutions as the model parameters vary are illustrated through numerical examples.

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.

Mean Residual Lifetime Frailty Models: A Weighted Perspective

The mean residual life frailty model and a subsequent weighted multiplicative mean residual life model that requires weighted multiplicative mean residual lives are considered. The expression and the shape of a mean residual life for some semiparametric models and also for a multiplicative degradation model are given in separate examples. The frailty model represents the lifetime of the population in which the random parameter combines the effects of the subpopulations. We show that for some regular dependencies of the population lifetime on the random parameter, some aging properties of the subpopulations’ lifetimes are preserved for the population lifetime. We indicate that the weighted multiplicative mean residual life model generates positive dependencies of this type. The copula function associated with the model is also derived. Necessary and sufficient conditions for certain aging properties of population lifetimes in the model are determined. Preservation of stochastic orders of two random parameters for the resulting population lifetimes in the model is acquired.

Partially linear single-index generalized mean residual life models.

Mean residual life (MRL) function defines the remaining life expectancy of a subject who has survived to a time point and is an important alternative to the hazard function for characterizing the distribution of a time-to-event variable. Existing MRL models primarily focus on studying the association between risk factors and disease risks using linear model specifications in multiplicative or additive scale. When risk factors have complex correlation structures, nonlinear effects, or interactions, the prefixed linearity assumption may be insufficient to capture the relationship. Single-index modeling framework offers flexibility in reducing dimensionality and modeling nonlinear effects. In this article, we propose a class of partially linear single-index generalized MRL models, the regression component of which consists of both a semiparametric single-index part and a linear regression part. Regression spline technique is employed to approximate the nonparametric single-index function, and parameters are estimated using an iterative algorithm. Double-robust estimators are also proposed to protect against the misspecification of censoring distribution or MRL models. A further contribution of this article is a nonparametric test proposed to formally evaluate the linearity of the single-index function. Asymptotic properties of the estimators are established, and the finite-sample performance is evaluated through extensive numerical simulations. The proposed models and inference approaches are demonstrated by a New York University Langone Health (NYULH) COVID-19 dataset.

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.

Generalized mean residual life models for case-cohort and nested case-control studies.

Mean residual life (MRL) is the remaining life expectancy of a subject who has survived to a certain time point and can be used as an alternative to hazard function for characterizing the distribution of a time-to-event variable. Inference and application of MRL models have primarily focused on full-cohort studies. In practice, case-cohort and nested case-control designs have been commonly used within large cohorts that have long follow-up and study rare diseases, particularly when studying costly molecular biomarkers. They enable prospective inference as the full-cohort design with significant cost-saving benefits. In this paper, we study the modeling and inference of a family of generalized MRL models under case-cohort and nested case-control designs. Built upon the idea of inverse selection probability, the weighted estimating equations are constructed to estimate regression parameters and baseline MRL function. Asymptotic properties of the proposed estimators are established and finite-sample performance is evaluated by extensive numerical simulations. An application to the New York University Women's Health Study is presented to illustrate the proposed models and demonstrate a model diagnostic method to guide practical implementation.

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

Semiparametric model of mean residual life with biased sampling data

The mean residual life function is an important and attractive alternative to the survival function or the hazard function of survival time in practice. It describes the remaining life expectancy of a subject surviving up to time t. To study the relationship between the mean residual life and its associated covariates, a broad class of mean residual life models under general biased sampling data is proposed in this paper, thereby extending the reach of this flexible and powerful tool. The unknown parameters are estimated by using inverse probability weighting method. An easily used model diagnostic method is also presented to assess the adequacy of the model. Both asymptotic properties and finite sample performances of the proposed estimators are established. Finally the practical appeal of the estimator is shown via two real applications using the Channing House data and the Canadian Study of Health and Aging (CSHA) dementia data.

Estimating equations of additive mean residual life model with censored length-biased data

Estimating equations for additive mean residual life model (AMRL) are proposed through the unique structure of length-biased data. Asymptotic properties of the estimators are stated. Small simulations are also conducted to evaluate their performance in a finite sample.

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.