A Review of the Logistic Regression Model with Emphasis on Medical Research

This study explored and reviewed the logistic regression (LR) model, a multivariable method for modeling the relationship between multiple independent variables and a categorical dependent variable, with emphasis on medical research. Thirty seven research articles published between 2000 and 2018 which employed logistic regression as the main statistical tool as well as six text books on logistic regression were reviewed. Logistic regression concepts such as odds, odds ratio, logit transformation, logistic curve, assumption, selecting dependent and independent variables, model fitting, reporting and interpreting were presented. Upon perusing the literature, considerable deficiencies were found in both the use and reporting of LR. For many studies, the ratio of the number of outcome events to predictor variables (events per variable) was sufficiently small to call into question the accuracy of the regression model. Also, most studies did not report on validation analysis, regression diagnostics or goodness-of-fit measures;measures which authenticate the robustness of the LR model. Here, we demonstrate a good example of the application of the LR model using data obtained on a cohort of pregnant women and the factors that influence their decision to opt for caesarean delivery or vaginal birth. It is recommended that researchers should be more rigorous and pay greater attention to guidelines concerning the use and reporting of LR models.

Incorporating the Multinomial Logistic Regression in Vehicle Crash Severity Modeling: A Detailed Overview

Multinomial logistic regression (MNL) is an attractive statistical approach in modeling the vehicle crash severity as it does not require the assumption of normality, linearity, or homoscedasticity compared to other approaches, such as the discriminant analysis which requires these assumptions to be met. Moreover, it produces sound estimates by changing the probability range between 0.0 and 1.0 to log odds ranging from negative infinity to positive infinity, as it applies transformation of the dependent variable to a continuous variable. The estimates are asymptotically consistent with the requirements of the nonlinear regression process. The results of MNL can be interpreted by both the regression coefficient estimates and/or the odd ratios (the exponentiated coefficients) as well. In addition, the MNL can be used to improve the fitted model by comparing the full model that includes all predictors to a chosen restricted model by excluding the non-significant predictors. As such, this paper presents a detailed step by step overview of incorporating the MNL in crash severity modeling, using vehicle crash data of the Interstate I70 in the State of Missouri, USA for the years (2013-2015).

Cumulative logit model in the analysis of endometrial cancer under a matched pair case-control design

Background: Binary as well as polytomous logistic models are widely used for estimating odds ratios when the exposure of prime interest assumes unordered multiple levels under matched pairs case-control design. In our previous studies, we have shown that the use of a polytomous logistic model for estimating cumulative odds ratios when the outcome (response) variable is ordinal (in addition to being polytomous) under matched pairs case-control design. The cumulative odds ratios were estimated based on separate fitting of the model at each of the cutpoint level as compared to less than equal to that level. In this paper we propose an alternative method of estimating the cumulative odds ratios and reanalyze the Los Angeles Endometrial Cancer data in the context of dose levels of conjugated oestrogen exposure and development of endometrial cancer under the matched pair case-control design. Methods: In the present study, the cumulative logit model is fitted using a single multinomial logit model for the data. For this, the full maximum likelihood estimation procedure is adopted. A test for equality of the cumulative odds ratios across the exposure levels is proposed. Results: The analysis revealed that there is a strong evidence of risk for developing endometrial cancer due to oestrogen exposure above each of the three dose level as compared to less than equal to that level. The estimated values at the three cutpoint levels were found to be 6.17, 3.60 and 5.16 respectively. Conclusions: The odds of developing endometrial cancer are very high for the users of any amount of oestrogen, even if it is the least dose, as compared to the non-users.

Statistical Analysis of Variables Influencing Type of Birth in Sri Lanka: A Logistic Regression Approach

Caesarean is a major surgical procedure undertaken in obstetrics and its rate is increasing in Sri Lanka as well as in the world. In Sri Lanka, health statistics show an increase in caesarean rates from 13.3% in 1998 to 30.6% by 2007. Due to its potential serious risks and the burden on the health system, many authorities have recommended reducing the caesarean rate for many years. This motivated us to study the most influential variables on the type of birth in Sri Lanka. In this study, based on the Anuradhapura Teaching Hospital records, entire 805 new born babies’ birth information was considered during the month of May, 2015. The variable “Type of Birth” (Normal/Caesarean) was considered as a binary response variable and age, height, weight of mother and sex, weight, length, shoulder length, head circumference of the baby were treated as explanatory variables. Logistic regression was used to model the data and using stepwise regression;mother’s age, height and weight were identified as the most influential variables on the type of birth. Further, it was observed that the odds of having normal birth is 80% higher for woman who belongs to the age group less than or equal to 30 years compared to woman who belongs to the age group greater than 30 years. Moreover, the Hosmer-Lemeshow goodness of fit test was used to check the adequacy of the fitted model. Results from this study revealed that in future, the type of birth may be predicted by considering these identified influential variables.

Log-Link Regression Models for Ordinal Responses

The adjacent-categories, continuation-ratio and proportional odds logit-link regression models provide useful extensions of the multinomial logistic model to ordinal response data. We propose fitting these models with a logarithmic link to allow estimation of different forms of the risk ratio. Each of the resulting ordinal response log-link models is a constrained version of the log multinomial model, the log-link counterpart of the multinomial logistic model. These models can be estimated using software that allows the user to specify the log likelihood as the objective function to be maximized and to impose constraints on the parameter estimates. In example data with a dichotomous covariate, the unconstrained models produced valid coefficient estimates and standard errors, and the constrained models produced plausible results. Models with a single continuous covariate performed well in data simulations, with low bias and mean squared error on average and appropriate confidence interval coverage in admissible solutions. In an application to real data, practical aspects of the fitting of the models are investigated. We conclude that it is feasible to obtain adjusted estimates of the risk ratio for ordinal outcome data.

Logistic Regression for Prediction and Diagnosis of Bacterial Regrowth in Water Distribution System

This paper focuses on the quantitative expression of bacterial regrowth in water distribution system. Considering public health risks of bacterial regrowth,the experiment was performed on a distribution system of selected area.Physical,chemical,and microbiological parameters such as turbidity,temperature,residual chlorine and pH were measured over a three-month period and correlation analysis was carried out.Combined with principal components analysis(PCA) ,a logistic regression model is developed to predict and diagnose bacterial regrowth and locate the zones with high risks of microbiology in the distribution system.The model gives the probability of bacterial regrowth with the number of heterotrophic plate counts as the binary response variable and three new principal components variables as the explanatory variables.The veracity of the logistic regression model was 90%,which meets the precision requirement of the model.

多分类有序反应变量Logistic回归及其应用

对近年发展起来的多分类有序反应变量Logistic回归进行了补充和完善 ,设计出对样本数据的应用条件做 χ2 检验的方法 ,证明了比数比在分析自变量作用中的实际意义 .随机抽取 2 0 0 2年国家执业医师资格临床实践技能考试 30岁以下本科毕业考生 5 0 0 0人 ,以考生的考试成绩 (3分类有序变量 )为反应变量 ,以考生的性别、工作单位级别、考试评分方法、考官回避制度、考题重复次数、考试合格率控制措施等 9个影响因素为自变量 ,进行多分类有序反应变量逐步Logistic回归分析 .研究结果已为卫生部改革和完善国家医师资格考试方法。

累积比数Logistic回归模型及其应用

在临床医学中评价某种疾病的不同治疗方案效果,进行影响因素分析,可以优化治疗方案,也为制定医疗保障补偿方案提供科学依据.应用累积比数Logistic回归模型,以1 117例急性心肌梗塞(AMI)患者的治疗效果为因变量,以其影响因素为自变量,进行回归分析,找出对治疗效果影响显著的因素.结果表明应用该模型拟合有序多分类变量数据是有效的.

基于累积比数logistic回归的新农合满意度影响因素分析

[目的]针对新农合工作现状进行满意度影响因素分析,寻求科学决策参考。[方法]量表设计及问卷调查后建立累积比数logis-tic回归模型进行满意度影响因素分析,借助SPSS17.0和SAS工具进行数据处理。[结果]需求满足程度、制度可靠性、疾病报销种类和服务态度为新农合满意度主要影响因素,并建立累积比数logistic回归方程。[结论]满足主体需求、完善制度、提高服务效率和便捷化手续流程是提高满意度的主要方面;该模型方法具有科学实效性。

基于Logistic模型的城市慢行交通出行者特性研究

为了防治机动车污染,提升慢行交通系统使用率与服务水平,针对慢行交通出行者特性开展研究。以铜川市居民出行调查数据为基础,将其分为家庭属性、个人属性与出行特征属性3个类别,借助SPSS软件构建二元Logistic模型,以优势比(OR)为主要评判标准,从多种属性变量中辨识影响慢行交通使用的主要变量,阐述出行者特征。研究结果表明:步行出行距离一般小于3km,自行车出行距离小于5km,各种属性变量对慢行交通的选择有不同程度的影响,步行与自行车出行的影响变量也存在差异;女性更倾向于步行,而男性使用自行车的几率更高;非通勤出行以步行为主;交通工具保有量的提升会降低步行出行率,而对自行车出行基本不产生影响;家庭收入与是否选择慢行交通出行不存在显著关系。

用有序Logistic模型分析恒牙患龋程度与若干暴露因素的关系

目的 :进一步分析恒牙患龋程度与若干暴露因素的关系 ;方法 :采用有序Logistic回归进行分析 ;结果 :年龄是患龋的最大危险因素 ,随着年龄的增长患龋的牙数有增多的趋势 ,同样 ,性别、城市、职业、教育和水氟度也是患龋的重要影响因素 ;结论 :可以将暴露因素对恒牙患龋的影响程度的大小和方向定量化 ,测定各因素对恒牙患龋程度的综合作用及趋势 ,利用预测概率公式可以预测任何给定条件下个体平均恒牙患龋牙数的概率 ,根据模型可适当改变某些暴露因素的水平预防恒牙患龋。

累积比数logistic回归在医学研究中的应用

目的 :探讨医学研究中有序分类结果资料的回归分析手段。方法 :提出累积比数 logistic回归的数学模型 ,并进行了实例分析 ,以阐明其应用。结果 :医学研究中存在着大量的结果变量呈多分类且有序的等级资料 (可将此类结果变量分为 1,2 ,… ,k类 ) ,显然不适合用普通二分类 logistic回归处理之 ;文中所述的累积比数 logistic回归却既可用于多分类又可用于二分类结果资料 ,并能对各因素的作用强弱作出定量分析 ,且同时具有普通 logistic回归的特性。结论 :累积比数

影响判断肺部孤立性小结节良恶性因素的logistic回归分析

目的 探讨影响判断肺部孤立性小结节(solitary pulmonary nodule,SPN)良恶性的因素。方法 对本院近10年来150例肺部孤立性小结节进行研究。选择18个可能影响临床医生判断的因素,应用SPSS10.0程序进行二维logistic回归分析。结果 150例肺部孤立性小结节中恶性78例(52％),良性72例(48％),判断其良恶性的主要因素是:年龄,吸烟量,SPN有无毛刺、分叶,密度是否均匀。结论 病人的年龄,吸烟量,影像学特征(SPN有无毛刺、分叶、密度是否均匀)对判断SPN良恶性有重要意义。

Multinomial Logistic模型在区域高等教育资源结构优化中的应用

在区域确定的前提下,将各高等教育资源数据进行整理,建立Multinomial Logistic模型,分析各结构的相对发生比率以及各结构的最佳分布。分析该回归分析的多维发生比率,由此确定各种离散等级状态之间的调整方向及调整程度。对黑龙江省的各高等教育区域进行实证分析,结果表明,黑龙江省高等教育资源结构以教学型、教学研究型、研究教学型、研究型的比例来判断,高等教育效用有待于进一步挖掘。多维发生比率以及自变量对多维发生比率的变化影响这两个参数对区域高等教育资源结构优化起着关键作用。

个人信用评估中的LOGISTIC模型

通过对以信贷申请书为基础的风险程度进行定量分析,使信贷决策合理化,从而降低个人信用风险。LOGISTIC回归模型提供给我们一个用来评估个人信用的非常有用的工具。本文利用美国花旗银行某分支机构1999年部分客户贷款量数据,应用LOGISTIC回归模型进行了实证分析。

原发性肝癌危险因素研究的条件Logistic回归分析──以人群为基础的配对病例对照研究

对广东省中山市１９９０年全人群的原发性肝癌１２３例进行了１：ｌ配对病例对照研究。结果表明：乙肝病史、肝吸虫病史、家庭肝炎史、吃霉变食物和饮陋是中山市原发性肝癌发病的主要危险因素，而饮用深井水是保护因素。文中描述了单因素、多因素以及交互作用分析的结果，计算了人群归因危险度和不同条件下的相对危险度。

1∶r配对设计二值资料一水平多重Logistic回归分析

本文的目的是介绍“1∶1”“1∶2”和“1∶r”配对设计二值资料一水平多重Logistic回归分析方法。统计分析的前提条件是资料值得分析,而确保配对设计二值资料值得分析的重要基础是“配对设计”科学合理。为此,本文从六个方面阐述“配对设计的要领”,不仅介绍了构建“1∶1”“1∶2”和“1∶r”配对设计二值资料一水平多重Logistic回归模型的方法,还通过三个实例,介绍了采用SAS软件实现统计分析及结果解释的详细步骤。

二项分类logistic回归的基本原理和关键问题

二项分类logistic回归是医学研究中常用的方法，优势比及其95％可信区间是logistic回归分析最重要的参数值，直接反映了自变量作用的大小和方向。而样本含量、自变量筛选、变量赋值和结果解释则是进行logistic回归分析的关键问题，决定了回归分析是否能得到相对最佳的回归模型而准确反映自变量的影响作用，作者将就上述问题进行阐述。