Bounds on life expectancy for the Rayleigh and Weibull distributions

Bounds are presented for the life expectancy or the mean residual life of an individual whose lifetime is a random variable X following a Rayleigh distribution or more generally a Weibull distribution. Simple transformations of the variables give inequalities on the Mills' ratio and the incomplete gamma functions. Some numerical computations are also reported to compare the lower and upper bounds with the exact value of the life expectancy function for several values of the parameter. When the lifetime follows a Gompertz distribution, the problem becomes complicated, and it has not been possible to construct bounds on the life expectancy function. The importance of the Gompertz distribution in the dynamics of normal and tumor growth and in the embryonic and postnatal growth of birds and mammals is demonstrated, and life expectancy is evaluated by numerical methods for a number of parameter values.     

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 equations to 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 equations to 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 diabetes mellitus.     

A Study of Log-Logistic Model in Survival Analysis

In survival analysis when the mortality reaches a peak after some finite period and then slowly declines, it is appropriate to use a model which has a nonmonotonic failure rate. In this paper we study the log-logistic model whose failure rate exhibits the above behavior and its mean residual life behaves in the reverse fashion. The maximum likelihood estimation of the parameters is examined and it is proved analytically that unique maximum likelihood estimates exist for the parameters. A lung cancer data set is analyzed. Confidence intervals for the parameters as well as for the critical points of the failure rate and mean residual life functions are obtained for the high performance status (PS) and low PS subgroups, where the term performance status is a measure of general medical status.     

Tests for monotone mean residual life, using randomly censored data

At any age the mean residual life function gives the expected remaining life at that age. Reliabilists and biometricians have found it useful to categorize failure distributions by the monotonicity properties of the mean residual life function. Hollander and Proschan (1975, Biometrika 62, 585-593) have derived tests of the null hypothesis that the underlying failure distribution is exponential, versus the alternative that it has a monotone mean residual life function. These tests are based on a complete sample. Often, however, data are incomplete because of withdrawals from the study and because of survivors at the time the data are analyzed. In this paper we generalize the Hollander-Proschan tests to accommodate randomly censored data. The efficiency loss due to the presence of censoring is also investigated.     

Semiparametric estimation of proportional mean residual life model in presence of censoring

A mean residual life function is the average remaining life of a surviving subject, as it varies with time. The proportional mean residual life model was proposed by Oakes and Dasu (1990, Biometrika77, 409-410) in regression analysis to study its association with related covariates in absence of censoring. In this article, we develop some semiparametric estimation procedures to take censoring into account. The proposed methodology is evaluated via simulation studies, and further applied to a clinical trial of chemotherapy in postoperative radiotherapy of lung cancer patients.     

A penalized spline approach to functional mixed effects model analysis

In this article, we propose penalized spline (P-spline)-based methods for functional mixed effects models with varying coefficients. We decompose longitudinal outcomes as a sum of several terms: a population mean function, covariates with time-varying coefficients, functional subject-specific random effects, and residual measurement error processes. Using P-splines, we propose nonparametric estimation of the population mean function, varying coefficient, random subject-specific curves, and the associated covariance function that represents between-subject variation and the variance function of the residual measurement errors which represents within-subject variation. Proposed methods offer flexible estimation of both the population- and subject-level curves. In addition, decomposing variability of the outcomes as a between- and within-subject source is useful in identifying the dominant variance component therefore optimally model a covariance function. We use a likelihood-based method to select multiple smoothing parameters. Furthermore, we study the asymptotics of the baseline P-spline estimator with longitudinal data. We conduct simulation studies to investigate performance of the proposed methods. The benefit of the between- and within-subject covariance decomposition is illustrated through an analysis of Berkeley growth data, where we identified clearly distinct patterns of the between- and within-subject covariance functions of children's heights. We also apply the proposed methods to estimate the effect of antihypertensive treatment from the Framingham Heart Study data.     

On restricted mean time in favor of treatment

The restricted mean time in favor (RMT-IF) of treatment is a nonparametric effect size for complex life history data. It is defined as the net average time the treated spend in a more favorable state than the untreated over a prespecified time window. It generalizes the familiar restricted mean survival time (RMST) from the two-state life–death model to account for intermediate stages in disease progression. The overall estimand can be additively decomposed into stage-wise effects, with the standard RMST as a component. Alternate expressions of the overall and stage-wise estimands as integrals of the marginal survival functions for a sequence of landmark transitioning events allow them to be easily estimated by plug-in Kaplan–Meier estimators. The dynamic profile of the estimated treatment effects as a function of follow-up time can be visualized using a multilayer, cone-shaped “bouquet plot.” Simulation studies under realistic settings show that the RMT-IF meaningfully and accurately quantifies the treatment effect and outperforms traditional tests on time to the first event in statistical efficiency thanks to its fuller utilization of patient data. The new methods are illustrated on a colon cancer trial with relapse and death as outcomes and a cardiovascular trial with recurrent hospitalizations and death as outcomes. The R-package rmt implements the proposed methodology and is publicly available from the Comprehensive R Archive Network (CRAN).     

Neuroprosthetics of the upper extremity--clinical application in spinal cord injury and future perspectives.

Within the last couple of years, partial restoration of lost motor functions in a larger number of spinal cord injured patients has become possible by the introduction of neuroprostheses into the clinical environment. The Freehand system in particular is the first implantable neuroprosthesis from which a certain group of tetraplegic patients with stable shoulder function, but missing or weak grasp and hold function of the hand do benefit. The system is based on the combination of electrical stimulation and operative tendon transfers and thus represents a multicomponent concept for long-term restoration of the grasp function. The crucial prerequisites for successful use of an implantable neuroprosthesis are the right indication, careful preoperative muscle stimulation, differentiated planning of the surgery and functional training adopted to the individual residual functions. After successful completion of an extensive rehabilitation program, patients are able to use the system for activities of daily living without the need for special additional aids, which enhances their quality of life and independency. In order to extend the group of potential users of neuroprostheses in the future, new technological developments will have to take into account that nowadays the majority of spinal cord injured patients suffer from an incomplete lesion of the spinal cord. For these particular patients who still possess residual functions, modular, "naturally" controllable systems for supporting these functions are needed rather than complex systems to substitute them.     

Robust Discriminant Functions in Assisting Medical Diagnosis. Application to the Chronic Obturative Lung Disease Data

The results of assisting medical diagnosis in bronchial asthma and chronic bronchitis via robust discriminant functions are presented in the paper. The robust discriminant functions are obtained by replacing classical estimates of mean vectors and covariance matrices by their robust equivalents. The new methods were compared with classical ones. These methods resulted in the improvement of automatic diagnosis especially when the “new” data set was classified on the basis of individuals collected earlier.     

中国Holdridge生命地带平均中心的时空分布及其偏移趋势

在分析目前生态地理模型及其实现方法的基础上 ,提出基于 ARC/ INFO与 VC 综合集成的先插值再运行模型的全新研究方法和技术路线 ,克服了以前模型实现过程中所存在的局限性。利用中国 1 96 2～ 2 0 0 2年 735个站点逐日温度与降水量观测数据 ,通过对 Holdridge生命地带模型和生命地带平均中心模型进行模拟运算后获得中国 Holdridge生命地带类型平均中心时空分布图及 2 0世纪 6 0、70、80与 90年代平均中心偏移趋势图。从生命地带类型平均中心时空分布及其偏移趋势分析研究中发现 ,生命地带类型平均中心的时空分布及其偏移趋势与相关气候因子的变化趋势相对应 ,并能够很好地与我国土地覆被类型实际的空间分布及其变化情况相符 ;各种生命地带类型平均面积的变化规律与相应的气候因子的变化趋势 (尤其是降水量、温度 )存在着一定相关性。另外 ,通过对我国生命地带类型平均面积比例大小进行排序分析发现与我国土地覆被类型的实际情况能够很好吻合     

A general theory of life table construction and a precise abridged life table method

"In this paper we lay the foundation of life table construction by unifying the existing life table methods. We also present a new method of constructing current (period) abridged life tables.... The development includes (1) a careful formulation and computation of age-specific death rates, (2) derivation of a new set of formulas for computing the survivorship function from the observed age-specific death rates and populations, (3) estimation of the main life table functions by spline interpolation, integration and differentiation, and (4) use of a quadratic and a Gompertz function to close the life table.... The method is illustrated with construction of abridged life tables using Canadian data."     

An additive‐multiplicative mean residual life model for right‐censored data

Many studies have focused on determining the effect of the body mass index (BMI) on the mortality in different cohorts. In this article, we propose an additive‐multiplicative mean residual life (MRL) model to assess the effects of BMI and other risk factors on the MRL function of survival time in a cohort of Chinese type 2 diabetic patients. The proposed model can simultaneously manage additive and multiplicative risk factors and provide a comprehensible interpretation of their effects on the MRL function of interest. We develop an estimation procedure through pseudo partial score equations to obtain parameter estimates. We establish the asymptotic properties of the proposed estimators and conduct simulations to demonstrate the performance of the proposed method. The application of the procedure to a study on the life expectancy of type 2 diabetic patients reveals new insights into the extension of the life expectancy of such patients.     

The influence of mean climate trends and climate variance on beaver survival and recruitment dynamics

Ecologists are increasingly aware of the importance of environmental variability in natural systems. Climate change is affecting both the mean and the variability in weather and, in particular, the effect of changes in variability is poorly understood. Organisms are subject to selection imposed by both the mean and the range of environmental variation experienced by their ancestors. Changes in the variability in a critical environmental factor may therefore have consequences for vital rates and population dynamics. Here, we examine ≥90‐year trends in different components of climate (precipitation mean and coefficient of variation (CV); temperature mean, seasonal amplitude and residual variance) and consider the effects of these components on survival and recruitment in a population of Eurasian beavers (n = 242) over 13 recent years. Within climatic data, no trends in precipitation were detected, but trends in all components of temperature were observed, with mean and residual variance increasing and seasonal amplitude decreasing over time. A higher survival rate was linked (in order of influence based on Akaike weights) to lower precipitation CV (kits, juveniles and dominant adults), lower residual variance of temperature (dominant adults) and lower mean precipitation (kits and juveniles). No significant effects were found on the survival of nondominant adults, although the sample size for this category was low. Greater recruitment was linked (in order of influence) to higher seasonal amplitude of temperature, lower mean precipitation, lower residual variance in temperature and higher precipitation CV. Both climate means and variance, thus proved significant to population dynamics; although, overall, components describing variance were more influential than those describing mean values. That environmental variation proves significant to a generalist, wide‐ranging species, at the slow end of the slow‐fast continuum of life histories, has broad implications for population regulation and the evolution of life histories.     

基因功能研究方法的新进展

随着生命科学的发展,研究领域的不断开拓,越来越多的未知新基因和基因的新功能被科学家们发现,研究这些未知新基因的功能和已知基因的新功能成为了极其重要的一项内容。本文对基因功能研究的最新方法进行了介绍。     

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

Statistics in Biosciences - The proportional mean residual life model has been discussed by many authors and provides a useful alternative to the commonly used proportional hazards model for...     

Estimation of a monotone percentile residual life function under random censorship

In this paper, we introduce a new estimator of a percentile residual life function with censored data under a monotonicity constraint. Specifically, it is assumed that the percentile residual life is a decreasing function. This assumption is useful when estimating the percentile residual life of units, which degenerate with age. We establish a law of the iterated logarithm for the proposed estimator, and its ‐equivalence to the unrestricted estimator. The asymptotic normal distribution of the estimator and its strong approximation to a Gaussian process are also established. We investigate the finite sample performance of the monotone estimator in an extensive simulation study. Finally, data from a clinical trial in primary biliary cirrhosis of the liver are analyzed with the proposed methods. One of the conclusions of our work is that the restricted estimator may be much more efficient than the unrestricted one.     

Residual electron momentum and energy in a gas ionized by a short high-power laser pulse

A study is made of the nonadiabatic dynamics of photoelectrons produced during interaction of an elliptically polarized, high-power laser pulse with a gas. Expressions for the so-called residual momentum and energy of the electrons (i.e., the mean electron momentum and energy after the passage of the pulse through the gas) are derived. The residual electron momentum and energy are investigated analytically as functions of the gas and laser parameters. A relationship is established between the residual energy and the electron temperature tensor.     

Growth analysis of serradella (Ornithopus sativus Brot.) developed under different soils, methods of sowing and seasons

Growth analysis of French serradella plants was made by classical and functional methods. Relative Growth Rate, Leaf Area Ratio and Unit Leaf Rate were calculated on the basis of weekly measurements of dry matter and leaf area quantities. The dry matter accumulation in above-ground part of serradella plants was described by logistic functions. Their characteristics included the inflection points of the first and the second derivatives, the standard errors of parameters, the determination coefficient and the residual mean squares. The linear function, which was obtained after linearisation of the logistic function, allowed for confirmation of the hypothesis of statistical differentiation among behaviour plants of serradella growing in different conditions within the whole vegetation period.     

Nonparametric analysis of delayed treatment effects using single-crossing constraints

Clinical trials involving novel immuno-oncology therapies frequently exhibit survival profiles which violate the proportional hazards assumption due to a delay in treatment effect, and, in such settings, the survival curves in the two treatment arms may have a crossing before the two curves eventually separate. To flexibly model such scenarios, we describe a nonparametric approach for estimating the treatment arm-specific survival functions which constrains these two survival functions to cross at most once without making any additional assumptions about how the survival curves are related. A main advantage of our approach is that it provides an estimate of a crossing time if such a crossing exists, and, moreover, our method generates interpretable measures of treatment benefit including crossing-conditional survival probabilities and crossing-conditional estimates of restricted residual mean life. Our estimates of these measures may be used together with efficacy measures from a primary analysis to provide further insight into differences in survival across treatment arms. We demonstrate the use and effectiveness of our approach with a large simulation study and an analysis of reconstructed outcomes from a recent combination therapy trial.     

Construction of expanded continuous life tables--a generalization of abridged and complete life tables.

This article extends the recent abridged life-table method of Hsieh. It generalizes the conventional discrete (abridged and complete) life tables into a continuous life table that can produce life-table functions at any age and develops a unified method of life-table construction that simplifies the disparate laborious procedures used in the traditional approach of constructing abridged and complete life tables. A set of precise procedures based on the complete cubic spline for the main body of the table and a mortality law for advanced ages is developed for estimating the basic and nonbasic life-table functions from a given mortality schedule. The proposed method can also produce more life-table functions than other existing methods. The method is illustrated with Canadian data.