Logistic and Nonlogistic Density Functions in Binary Regression with Nonstochastic Covariates

A binary random variable depends on nonstochastic covariates through a density function. The equations that determine the maximum likelihood estimators of the parameters are intractable and difficult to solve iteratively. We develop modified maximum likelihood estimators for both logistic and nonlo-gistic densities. These estimators are explicit functions of sample observations and are, therefore, easy to compute. They are asymptotically fully efficient and, for small samples, are almost fully efficient. The appropriateness of the logistic density function is also discussed.     

Binary Regression Analysis with Pooled Exposure Measurements: A Regression Calibration Approach

Summary It has become increasingly common in epidemiological studies to pool specimens across subjects to achieve accurate quantitation of biomarkers and certain environmental chemicals. In this article, we consider the problem of fitting a binary regression model when an important exposure is subject to pooling. We take a regression calibration approach and derive several methods, including plug‐in methods that use a pooled measurement and other covariate information to predict the exposure level of an individual subject, and normality‐based methods that make further adjustments by assuming normality of calibration errors. Within each class we propose two ways to perform the calibration (covariate augmentation and imputation). These methods are shown in simulation experiments to effectively reduce the bias associated with the naive method that simply substitutes a pooled measurement for all individual measurements in the pool. In particular, the normality‐based imputation method performs reasonably well in a variety of settings, even under skewed distributions of calibration errors. The methods are illustrated using data from the Collaborative Perinatal Project.     

Misclassification in Logistic Regression with Discrete Covariates

We study the effect of misclassification of a binary covariate on the parameters of a logistic regression model. In particular we consider 2 × 2 × 2 tables. We assume that a binary covariate is subject to misclassification that may depend on the observed outcome. This type of misclassification is known as (outcome dependent) differential misclassification. We examine the resulting asymptotic bias on the parameters of the model and derive formulas for the biases and their approximations as a function of the odds and misclassification probabilities. Conditions for unbiased estimation are also discussed. The implications are illustrated numerically using a case control study. For completeness we briefly examine the effect of covariate dependent misclassification of exposures and of outcomes.     

Tests for Trend in Binary Response

Tests for trend are important in analyzing data where the binary response in ordered categories is of interest. An example is in toxicology where the response in various dose groups is observed. For testing an association between the dose and the response the approach from Cochran and Armitage is widely used. However the result of this test is highly dependent on the scores assigned to the dose groups. Various dose assignments can lead to different outcomes. As an alternative the isotonic regression, a nonparametric method, is proposed. The outcome of this approach is independent of the quantification of the dose. Both methods (Cochran‐Armitage test and isotonic regression) are compared within a simulation study to an isotonic version of the Pearson's Chi‐squared test and the Wilcoxon rank sum test.     

基于分位数回归模型的卫生总费用影响因素研究

目的:利用分位数回归模型对近十年来陕西省卫生总费用增长的影响因素进行研究,从而为卫生行政部门配置卫生总费用以及制定卫生政策提供依据。方法:首先根据已往文献研究以及陕西地区实际情况,挑选出2003-2014年间可能影响陕西省卫生总费用的因素,然后利用逐步回归法检验自变量间的共线性,并对解释变量进行筛选,最后利用R软件对陕西省卫生总费用及其影响因素建立分位数回归模型,确定影响卫生总费用的因素。结果:陕西省国内生产总值(GDP)在10%-90%分位点上的系数检验结果均有统计学意义,且所有分位点的回归系数均为正值。结论:国内生产总值是影响陕西省卫生总费用的主要因素,其与卫生总费用的变化呈正相关,国内生产总值的增长促进了陕西省卫生总费用的增长。     

Binary Responses and the Three-period Cross-over

Problems with carry-over effects in the simple two-period cross-over have lead to interest in more complex cross-over designs. A method for analysing the optimum two-treatment three-period design with binary response variables is given by making a simple extension to Gart's logistic model. The method gives independent tests for, and estimates of the difference in treatment and first-order carry-over effects. An example of the analysis is given, using the loglinear models facility in GLIM.     

Measures of Stability (Trait) and Mutability (State) of Binary Responses in Pre-post-treatment Fourfold Tables

For the discussion of binary responses in pre-post-treatment we define new, simple measures for the stability (Trait) and mutability (State) of the responses, which have very nice and simple properties. We show the important fact that under certain conditions these two measures are uncorrelated. Because of the simplicity of the measures we derive the exact and limit distributions for testing the one respectively the two sample case.     

Binary regression: Total gain in positive and negative predictive values

Models that predict disease incidence or disease recurrence are attractive for clinicians as well as for patients. The usefulness of a risk prediction model is linked to the two questions whether the observed outcome is confirmed by the prediction and whether the risk prediction is accurate in predicting the future outcome, respectively. The first phrasing of the question is linked to considering sensitivity and specificity and the latter to the positive and negative predictive values. We present the measures of standardized total gain in positive and negative predictive values dealing with the performance or accuracy of the prediction model for a binary outcome. Both measures provide a useful tool for assessing the performance or accuracy of a set of predictor variables for the prediction of a binary outcome. This concept is a tool for evaluating the optimal prediction model in future research.     

Longitudinal Studies of Binary Response Data Following Case–Control and Stratified Case–Control Sampling: Design and Analysis

Summary We discuss design and analysis of longitudinal studies after case–control sampling, wherein interest is in the relationship between a longitudinal binary response that is related to the sampling (case–control) variable, and a set of covariates. We propose a semiparametric modeling framework based on a marginal longitudinal binary response model and an ancillary model for subjects' case–control status. In this approach, the analyst must posit the population prevalence of being a case, which is then used to compute an offset term in the ancillary model. Parameter estimates from this model are used to compute offsets for the longitudinal response model. Examining the impact of population prevalence and ancillary model misspecification, we show that time‐invariant covariate parameter estimates, other than the intercept, are reasonably robust, but intercept and time‐varying covariate parameter estimates can be sensitive to such misspecification. We study design and analysis issues impacting study efficiency, namely: choice of sampling variable and the strength of its relationship to the response, sample stratification, choice of working covariance weighting, and degree of flexibility of the ancillary model. The research is motivated by a longitudinal study following case–control sampling of the time course of attention deficit hyperactivity disorder (ADHD) symptoms.     

Assessing the amount of heterogeneity in random-effects meta-analysis

In a random-effects meta-analysis, a new confidence interval for the heterogeneity parameter is proposed. With this interval, the amount of heterogeneity in a meta-analysis can be assessed so that it can be judged whether the pooling of the estimates is meaningful. Through suitable corrections of the lower bound, based on the treatment effect measure of interest, the resulting interval yields satisfactory results with respect to the predefined confidence coefficient. Lower and upper bound of the interval can be used for one-sided hypothesis testing on the amount of the underlying between-trial variability.     

Binary regression for risks in excess of subject-specific thresholds

We describe models for binary valued data to be used to explain the incidence of disease given the level of a known risk factor. Every individual has an unobservable tolerance of the risk. Risk levels below the individual tolerance do not increase the disease incidence above the background, unexposed rate. We estimate parameters from both the tolerance distribution and the risk function for a large group of mice exposed to very low levels of a known carcinogen.     

Regression modeling of competing crude failure probabilities

In a randomized trial of tamoxifen therapy for breast cancer, women can experience tumor recurrence or die from competing causes. One goal of analysis is to describe the effect of tamoxifen on the probabilities of recurrence or death from other causes. To this end, we propose a semi-parametric transformation model for the crude failure probabilities of a competing risk, conditional on covariates. The model is developed as an extension of the standard approach to survival data with independent right censoring. Estimation of the regression coefficients is achieved with a rank-based least squares criterion. Simulations show that the procedure works well with practical sample sizes. A separate estimating function is developed for the baseline parameter. Prediction of covariate-adjusted failure probabilities is considered. The methodology is motivated and illustrated with data from the tamoxifen trial.     

重症医学病房中早产儿死亡危险因素的单变量logistic 回归 分析研究

目的:探讨重症医学病房内早产儿的相关性危险因素对其死亡的影响.方法:回顾性收集我重症医学病房从2008年6月1日至2011年8月31日收治的早产患儿共45例,分组后,对相关死亡危险因素进行logistics回归分析研究.结果:45例早产儿死亡的相关危险因素为出生体重(OR=4.157),体重越低,死亡率越高.结论:加强孕期保健,优化围产期管理,促进胎儿成熟,加强对低出生体重儿的管理,可提高早产儿的存活率和存活质量.     

外科病房医院感染相关危险因素的Logistic 回归分析

目的:探讨外科病房医院感染的相关危险因素,为临床的外科病房进行医院感染的防控提供理论支持。方法:选取本院外科病房住院进行手术治疗的8046例患者作为本研究的研究对象,其中发生医院感染253例,采用目标监测的调查研究方法,对患者进行医院感染相关危险因素的问卷调查,对外科病房医院感染相关危险因素进行单因素和多因素非条件Logistic回归分析。结果:单因素Logistic回归分析发现年龄、治疗专科(心胸外科)、治疗专科(神经外科)、入住ICU病房、急诊手术、住院治疗天数、气管插管全麻醉、切口类型(污染切口)、切口长度、侵袭性操作、侵袭性操作时间、抗菌药物治疗、术前抗菌药物治疗、术前抗菌药物治疗时间、术后抗菌药物治疗、术后抗菌药物治疗时间是医院感染的相关危险因素(P0.05)。多因素Logistic回归分析发现年龄、治疗专科(心胸外科)、治疗专科(神经外科)、入住ICU病房、急诊手术、住院治疗天数、切口类型(污染切口)、切口长度、侵袭性操作、侵袭性操作时间、抗菌药物治疗均是医院感染的相关危险因素(P0.05)。结论:外科病房医院感染是多种因素共同作用的结果,要针对外科病房医院感染相关危险因素制订相应的防治对策,对于降低医院感染率、防控外科病房医院感染的发生具有重要的意义。     

生长曲线参数估计的一种新方法-优化回归组合法

在现有文献研究的基础上,对生长曲线参数估计问题又作了进一步研究,给出了生长曲线参数估计的一种新方法优化回归组合法,该方法创造性地将最优化方法与回归方法结合在一起,利用最优化理论中的区间搜索和一维搜索,可以得到一系列c^＊值,利用回归方法可求得与其相对应的一系列a和b的值．当c取最优值c时,a和b便得到最优值a^＊和b^＊经示例计算表明,这种参数估计法具有较高的精度,     

The Treatment of Missing Values in Logistic Regression

The efficiencies of the estimators in the linear logistic regression model are examined using simulations under six missing value treatments. These treatments use either the maximum likelihood or the discriminant function approach in the estimation of the regression coefficients. Missing values are assumed to occur at random. The cases of multivariate normal and dichotomous independent variables are both considered. We found that in general, there is no uniformly best method. However, mean substitution and discriminant function estimation using existing pairs of values for correlations turn out to be favourable for the cases considered.     

高龄患者下肢深静脉血栓超声诊断的Logistic回归分析

目的：应用Logistic回归筛选高龄患者下肢深静脉血栓灰阶及彩色多普勒超声诊断特征。方法：对我院150例主动要求下肢深静脉血栓灰阶及彩色多普勒超声检查的高龄患者,应用超声检查观察血管管径、管腔内回声及血流动力学等特征,进行Logistic回归分析,筛选超声诊断特征,对Logistic回归模型预测诊断绘制受试者工作曲线图（ROC）,评估模型效果。结果：150例超声检查高龄患者,发生下肢深静脉栓塞129例,占86.00%。Logistic回归筛选,血管管径、管腔内回声、管壁内壁、血流信号改变4个变量进入回归模型,Logistic回归模型预测超声检出的ROC曲线下面积为0.903,灵敏度为90.3%,特异度为93.8%。结论：以高龄患者下肢深静脉血栓超声特征建立的Logistic回归模型对该病具有较好的预测诊断价值。