Locally efficient estimation of the quality-adjusted lifetime distribution with right-censored data and covariates

Zhao and Tsiatis (1997) consider the problem of estimation of the distribution of the quality-adjusted lifetime when the chronological survival time is subject to right censoring. The quality-adjusted lifetime is typically defined as a weighted sum of the times spent in certain states up until death or some other failure time. They propose an estimator and establish the relevant asymptotics under the assumption of independent censoring. In this paper we extend the data structure with a covariate process observed until the end of follow-up and identify the optimal estimation problem. Because of the curse of dimensionality, no globally efficient nonparametric estimators, which have a good practical performance at moderate sample sizes, exist. Given a correctly specified model for the hazard of censoring conditional on the observed quality-of-life and covariate processes, we propose a closed-form one-step estimator of the distribution of the quality-adjusted lifetime whose asymptotic variance attains the efficiency bound if we can correctly specify a lower-dimensional working model for the conditional distribution of quality-adjusted lifetime given the observed quality-of-life and covariate processes. The estimator remains consistent and asymptotically normal even if this latter submodel is misspecified. The practical performance of the estimators is illustrated with a simulation study. We also extend our proposed one-step estimator to the case where treatment assignment is confounded by observed risk factors so that this estimator can be used to test a treatment effect in an observational study.     

Semiparametric analysis of zero-inflated count data

Medical and public health research often involve the analysis of count data that exhibit a substantially large proportion of zeros, such as the number of heart attacks and the number of days of missed primary activities in a given period. A zero-inflated Poisson regression model, which hypothesizes a two-point heterogeneity in the population characterized by a binary random effect, is generally used to model such data. Subjects are broadly categorized into the low-risk group leading to structural zero counts and high-risk (or normal) group so that the counts can be modeled by a Poisson regression model. The main aim is to identify the explanatory variables that have significant effects on (i) the probability that the subject is from the low-risk group by means of a logistic regression formulation; and (ii) the magnitude of the counts, given that the subject is from the high-risk group by means of a Poisson regression where the effects of the covariates are assumed to be linearly related to the natural logarithm of the mean of the counts. In this article we consider a semiparametric zero-inflated Poisson regression model that postulates a possibly nonlinear relationship between the natural logarithm of the mean of the counts and a particular covariate. A sieve maximum likelihood estimation method is proposed. Asymptotic properties of the proposed sieve maximum likelihood estimators are discussed. Under some mild conditions, the estimators are shown to be asymptotically efficient and normally distributed. Simulation studies were carried out to investigate the performance of the proposed method. For illustration purpose, the method is applied to a data set from a public health survey conducted in Indonesia where the variable of interest is the number of days of missed primary activities due to illness in a 4-week period.     

Analysis of experimental data with repeated measurements

Summary. Experimental data often consist of serial measurements on subjects after a treatment. Typical questions concerning such data are: (A) Do subjects really react to treatment or are the fluctuations just random? (B) What are the numerical characteristics of the response? (C) Is the response identical in all groups? Differences between the individuals in the dynamics of the reaction make it difficult to apply standard statistical procedures. This paper proposes to answer questions (A) and (B) at the individual level, then to give an answer to (C) on the basis of this information. This kind of analysis may be useful since it can separate subjects giving response from those that do not and can identify individual response patterns and compare treatments with respect to each numerical characteristic separately. To answer question (A), a permutation test is proposed and its power is evaluated by simulation.     

Curve fitting of germination data using the Richards function

Abstract. The fitting of the generalized Richards function to germination data by using two nested iterative and least squares regression procedures to estimate the four parameters (all of which can be associated with features of biological growth) is demonstrated. The program also involves a procedure of parallel curve analysis which makes comparisons between two curves by examining the whole process represented by the curve and not just a point or portion thereof. Excellent agreement between observed and expected values was obtained by analyzing data which defined patterns of germination exhibiting a range of rates and final percentages. The program also calculates a number of derived quantities including maximum daily rate of germination and time to 50% of final germination.     

相互干扰的捕食与被捕食者种群的Hassall模型定性分析

本文证明了Hassall模型的渐近稳定性、有界性、全局稳定性。解决了文献[1]对该模型的三个猜想：（1）模型在某种条件下,正平衡点（x^*,y^*）是渐近稳定的;（2）模型的一切正初始条件的解有界;（3）模型在一定条件下,正平衡点（x^*,y^*）是全局稳定的。     

Estimating the accuracy of psychological scales using longitudinal data

This article presents a method for estimating the accuracy of psychological screening scales using receiver operating characteristic curves and associated statistics. Screening scales are typically semicontinuous within a known range with distributions that are nearly symmetric when the target condition is present and highly skewed when the condition is absent. We model screening scale outcomes using truncated normal distributions that accommodate these different distributional shapes and use subject-specific random effects to adjust for multiple assessments within individuals. Using the proposed model, we estimate the accuracy of the Symptom Checklist as a measure of major depression from a repeatedly screened sample of patients.     

Order-restricted inference for clustered ROC data with application to fingerprint matching accuracy

Receiver operating characteristic (ROC) curve is commonly used to evaluate and compare the accuracy of classification methods or markers. Estimating ROC curves has been an important problem in various fields including biometric recognition and diagnostic medicine. In real applications, classification markers are often developed under two or more ordered conditions, such that a natural stochastic ordering exists among the observations. Incorporating such a stochastic ordering into estimation can improve statistical efficiency (Davidov and Herman, 2012). In addition, clustered and correlated data arise when multiple measurements are gleaned from the same subject, making estimation of ROC curves complicated due to within-cluster correlations. In this article, we propose to model the ROC curve using a weighted empirical process to jointly account for the order constraint and within-cluster correlation structure. The algebraic properties of resulting summary statistics of the ROC curve such as its area and partial area are also studied. The algebraic expressions reduce to the ones by Davidov and Herman (2012) for independent observations. We derive asymptotic properties of the proposed order-restricted estimators and show that they have smaller mean-squared errors than the existing estimators. Simulation studies also demonstrate better performance of the newly proposed estimators over existing methods for finite samples. The proposed method is further exemplified with the fingerprint matching data from the National Institute of Standards and Technology Special Database 4.     

Estimators Asymptotically Minimax in Wide Sense

Estimators of location are considered. Huber (1964) introduced estimators asymptotically minimax on the set ?? of all regular M-estimators, for a given contamination ε and for the set Q of all regular symmetric alternative data sources. We extend his concept by admitting arbitrary sets ?? of regular M-estimators and arbitrary sets Q or regular symmetric alternative sources, and also by replacing the singletons [ε] ? (0, 1) by arbitrary subsets ?? ? (0, 1). The resulting estimator cannot in general be evaluated explicitly. But for finite T it exists and, if ?? and Q are finite too, it may be chosen by a computer. This extra burden is justified in some cases since more than 100% relative efficiency gain against all Huber's Hk is achievable in this manner. Such gains are achieved for a nontrivial family Q by the estimator proposed in Vajda (1984), with redescending influence curve, which is shown to be asymptotically minimax in wide sense.     

渐近周期的Logistic方程

主要研究了渐近周期的Logistic方程,得到了渐近周期解的存在唯一性,全局吸引性;进一步得到渐近周期函数对加减乘除,导数,微分,复合函数运算的封闭性;渐近周期函数空间是Banach空间,并得到高维系统下的渐近周期函数空间是Banach空间．     

基于秦岭样区的四种时序EVI函数拟合方法对比研究

函数曲线拟合方法是植被指数时间序列重建的一个重要方法,已经广泛应用于森林面积动态变化监测、农作物估产、遥感物候信息提取、生态系统碳循环研究等领域。基于秦岭样区多年MODIS EVI遥感数据及其质量控制数据,探讨并改进了时序EVI重建过程中噪声点优化和对原始高质量数据保真能力的评价方法;在此基础上,比较了常用的非对称性高斯函数拟合法(AG)、双Logistic函数拟合法(DL)和单Logistic函数拟合法(SL)。基于SL方法,调整了模型形式并重新定义d的参数意义,提出了最值优化单Logistic函数拟合法(MSL),并与其他3种方法进行对比。结果表明;在噪声点优化及保留原始高质量数据方面,AG方法和DL方法二者整体差别不大,而在部分像元的处理上AG方法表现出更好的拟合效果;MSL方法和SL方法相比于AG方法和DL方法其效果更为突出;在地形气候复杂,植被指数噪声较多的山区,MSL方法表现出更好的适用性。     

Exploratory data analysis of DNA microarrays by multivariate curve resolution

In this work, the application of a multivariate curve resolution procedure based on alternating least squares optimization (MCR-ALS) for the analysis of data from DNA microarrays is proposed. For this purpose, simulated and publicly available experimental data sets have been analyzed. Application of MCR-ALS, a method that operates without the use of any training set, has enabled the resolution of the relevant information about different cancer lines classification using a set of few components; each of these defined by a sample and a pure gene expression profile. From resolved sample profiles, a classification of samples according to their origin is proposed. From the resolved pure gene expression profiles, a set of over- or underexpressed genes that could be related to the development of cancer diseases has been selected. Advantages of the MCR-ALS procedure in relation to other previously proposed procedures such as principal component analysis are discussed.     

Plotting receiver operating characteristic and precision–recall curves from presence and background data

1. The receiver operating characteristic (ROC) and precision–recall (PR) plots have been widely used to evaluate the performance of species distribution models. Plotting the ROC/PR curves requires a traditional test set with both presence and absence data (namely PA approach), but species absence data are usually not available in reality. Plotting the ROC/PR curves from presence‐only data while treating background data as pseudo absence data (namely PO approach) may provide misleading results.
2. In this study, we propose a new approach to calibrate the ROC/PR curves from presence and background data with user‐provided information on a constant c, namely PB approach. Here, c defines the probability that species occurrence is detected (labeled), and an estimate of c can also be derived from the PB‐based ROC/PR plots given that a model with good ability of discrimination is available. We used five virtual species and a real aerial photography to test the effectiveness of the proposed PB‐based ROC/PR plots. Different models (or classifiers) were trained from presence and background data with various sample sizes. The ROC/PR curves plotted by PA approach were used to benchmark the curves plotted by PO and PB approaches.
3. Experimental results show that the curves and areas under curves by PB approach are more similar to that by PA approach as compared with PO approach. The PB‐based ROC/PR plots also provide highly accurate estimations of c in our experiment.
4. We conclude that the proposed PB‐based ROC/PR plots can provide valuable complements to the existing model assessment methods, and they also provide an additional way to estimate the constant c (or species prevalence) from presence and background data.

     

具有种群动力的时滞SI模型

对一类具有幼年和成年两个生理阶段结构和时滞的Logistic种群动力的SI传染病模型进行了分析,得到了传染病最终消除和成为地方病的阈值．