Logistic回归模型中连续变量交互作用的分析

Rothman提出生物学交互作用的评价应该基于相加尺度即是否有相加交互作用,而logistic回归模型的乘积项反映的是相乘交互作用.目前国内外文献讨论logistic回归模型中两因素的相加交互作用以两分类变量为主,本文介绍两连续变量或连续变量与分类变量相加交互作用可信区间估计的Bootstrap方法,文中以香港男性肺癌病例对照研究资料为例,辅以免费软件R的实现程序,为研究人员分析交互作用提供参考.     

Logistic回归模型中连续变量交互作用的分析

Rothman提出生物学交互作用的评价应该基于相加尺度即是否有相加交互作用,而logistic回归模型的乘积项反映的是相乘交互作用.目前国内外文献讨论logistic回归模型中两因素的相加交互作用以两分类变量为主,本文介绍两连续变量或连续变量与分类变量相加交互作用可信区间估计的Bootstrap方法,文中以香港男性肺癌病例对照研究资料为例,辅以免费软件R的实现程序,为研究人员分析交互作用提供参考.     

logistic回归模型中交互作用的分析及评价

流行病学病因学研究常运用logistic回归模型分析影响因素的作用,并利用纳入乘积项的方法分析因素间交互作用,如有统计学意义表示两因素间存在相乘交互作用,但乘积项若无统计学意义并不表示两因素问相加交互作用或生物学交互作用的有无.文中介绍Rothman提出的针对logistic或Cox回归模型的三个评价相加交互作用的指标及其可信区间的计算,并以SPSS 15.0软件应用实例分析得出logistic回归模型的参数估计值和协方差矩阵,引入Andersson等编制的Excel计算表,计算相加交瓦作用指标及其可信区间,用于评价因素间的相加交互作用,为研究人员分析生物学交互作用提供依据.该方法方便快捷,且Excel计算表可在线免费下载.     

应用R软件进行logistic回归模型的交互作用分析

目的应用R软件进行logistic回归模型的交互作用分析,为探讨交互作用提供依据。方法使用R软件,编写程序实现logistic或Cox回归模型三个评价相加交互作用的指标及其可信区间的计算。结果生物学交互作用的评价应该基于是否有相加交互作用,而流行病学研究中常运用logistic回归模型,并纳入乘积项分析因素间交互作用,其是否有意义仅反映相乘交互作用,并不能反映两因素间相加或生物学交互作用的有无。本文通过实例分析,调用基于R软件编写的interact程序,可以直接计算出logistic或Cox回归模型的三个交互作用评价指标(RERI、AP、SI)及其可信区间;并将结果与运用Andersson编制的Excel计算结果相比较,验证了本程序的科学性和准确性。结论应用R软件编制程序,可实现logistic回归模型因素间交互作用和可信区间的计算,为流行病学研究人员分析生物学交互作用提供依据。     

队列研究资料相加交互作用可信区间的Bootstrap法估计

交互作用评估是流行病学数据分析的重要环节,病因学研究中得到广泛应用的指数模型如logistic回归或Cox比例风险模型,常将危险因素的乘积项纳入模型,其乘积项系数反映了因素间的相乘交互作用,而在公共卫生方面交互作用分析应基于加法模型才更合适.文中根据Rothman提出的评估相加交互作用的指标,通过一个队列研究实例拟合Cox比例风险模型,应用RR值计算两因素的相加交互作用指标,并利用内置Bootstrap功能的S-Plus软件,较为方便地得到Bootstrap法估计的可信区间,避免队列研究资料应用OR值计算导致的估值偏差,且有更高的估计精度.相加和相乘交互作用分析的组合模式相当复杂,当两者冲突时宜选择加法模型.     

队列研究资料相加交互作用可信区间的Bootstrap法估计

交互作用评估是流行病学数据分析的重要环节,病因学研究中得到广泛应用的指数模型如logistic回归或Cox比例风险模型,常将危险因素的乘积项纳入模型,其乘积项系数反映了因素间的相乘交互作用,而在公共卫生方面交互作用分析应基于加法模型才更合适.文中根据Rothman提出的评估相加交互作用的指标,通过一个队列研究实例拟合Cox比例风险模型,应用RR值计算两因素的相加交互作用指标,并利用内置Bootstrap功能的S-Plus软件,较为方便地得到Bootstrap法估计的可信区间,避免队列研究资料应用OR值计算导致的估值偏差,且有更高的估计精度.相加和相乘交互作用分析的组合模式相当复杂,当两者冲突时宜选择加法模型.     

队列研究资料相加交互作用可信区间的Bootstrap法估计

交互作用评估是流行病学数据分析的重要环节,病因学研究中得到广泛应用的指数模型如logistic回归或Cox比例风险模型,常将危险因素的乘积项纳入模型,其乘积项系数反映了因素间的相乘交互作用,而在公共卫生方面交互作用分析应基于加法模型才更合适.文中根据Rothman提出的评估相加交互作用的指标,通过一个队列研究实例拟合Cox比例风险模型,应用RR值计算两因素的相加交互作用指标,并利用内置Bootstrap功能的S-Plus软件,较为方便地得到Bootstrap法估计的可信区间,避免队列研究资料应用OR值计算导致的估值偏差,且有更高的估计精度.相加和相乘交互作用分析的组合模式相当复杂,当两者冲突时宜选择加法模型.     

SPSS中的分类树模型在分析伤害影响因素中的应用

目前,国内对于伤害影响因素的研究多采用logistic回归分析.虽然logistic回归模型的理论基础和建模方法都比较成熟,但仍有不足.例如,它对自变量的主效应分析充分,但对变量间的交互作用分析困难;注重自变量对结果影响的数量关系而轻视变量间的层次关系.分类树模型分析能较好的处理变量间的交互作用,并且可分析出各变量的具体影响人群,同时还可提示具有何种特征的人群更易发生伤害,从而可集中资源对伤害发生重点人群进行干预.     

实现logistic与Cox回归相乘相加交互作用的临床实践宏程序

病例对照研究常采用条件或非条件logistic分析,生存资料分析常采用Cox比例模型,但多数文献仅纳入主效应模型,然而广义线性模型不同于一般线性模型,其交互作用分为相乘交互与相加交互作用,前者只有统计学意义而后者更符合生物学意义。笔者以SAS 9.4软件编写宏,在计算logistic与Cox相乘交互项同时计算交互对比度、归因比、交互作用指数指标及利用Wald、Delta、PL(profile likelihood) 3种方法的可信区间评价相加交互作用,便于临床流行病学与遗传学大数据分析相乘相加交互作用时参考。     

核函数logistic回归模型在全基因组关联研究中的应用

[导读]探讨基于基因水平的核函数logistic回归模型及其在全基因组关联研究中的应用.以全基因组关联研究模拟数据为例,介绍核函数logistic回归模型在基因水平检测遗传变异与复杂性疾病之间关联的分析策略.模拟结果表明,在所有已知基因检验结果中致病位点所在基因假设检验的P值最小.结果提示基于基因水平的核函数logistic回归模型能够充分提取和综合基因中多个遗传突变位点信息,降低统计学检验的自由度,同时还能够控制多种协变量因素和交互作用,在检测致病基因与疾病关联时具有一定的效能.     

Estimating interaction on an additive scale between continuous determinants in a logistic regression model

BACKGROUND: To determine the presence of interaction in epidemiologic research, typically a product term is added to the regression model. In linear regression, the regression coefficient of the product term reflects interaction as departure from additivity. However, in logistic regression it refers to interaction as departure from multiplicativity. Rothman has argued that interaction estimated as departure from additivity better reflects biologic interaction. So far, literature on estimating interaction on an additive scale using logistic regression only focused on dichotomous determinants. The objective of the present study was to provide the methods to estimate interaction between continuous determinants and to illustrate these methods with a clinical example. METHODS: and results From the existing literature we derived the formulas to quantify interaction as departure from additivity between one continuous and one dichotomous determinant and between two continuous determinants using logistic regression. Bootstrapping was used to calculate the corresponding confidence intervals. To illustrate the theory with an empirical example, data from the Utrecht Health Project were used, with age and body mass index as risk factors for elevated diastolic blood pressure. CONCLUSIONS: The methods and formulas presented in this article are intended to assist epidemiologists to calculate interaction on an additive scale between two variables on a certain outcome. The proposed methods are included in a spreadsheet which is freely available at: http://www.juliuscenter.nl/additive-interaction.xls.     

Test for additive interaction in proportional hazards models

PURPOSE: We describe a method for testing and estimating a two-way additive interaction between two categorical variables, each of which has greater than or equal to two levels. METHODS: We test additive and multiplicative interactions in the same proportional hazards model and measure additivity by relative excess risk due to interaction (RERI), proportion of disease attributable to interaction (AP), and synergy index (S). A simulation study was used to compare the performance of these measures of additivity. Data from the Atherosclerosis Risk in Communities cohort study with a total of 15,792 subjects were used to exemplify the methods. RESULTS: The test and measures of departure from additivity depend neither on follow-up time nor on the covariates. The simulation study indicates that RERI is the best choice of measures of additivity using a proportional hazards model. The examples indicated that an interaction between two variables can be statistically significant on additive measure (RERI=1.14, p=0.04) but not on multiplicative measure (beta3=0.59, p=0.12) and that additive and multiplicative interactions can be in opposite directions (RERI=0.08, beta3=-0.08). CONCLUSIONS: The method has broader application for any regression models with a rate as the dependent variable. In the case that both additive and multiplicative interactions are statistically significant and in the opposite direction, the interpretation needs caution.     

Evaluation of removable statistical interaction for binary traits

This paper is concerned with evaluating whether an interaction between two sets of risk factors for a binary trait is removable and, when it is removable, fitting a parsimonious additive model using a suitable link function to estimate the disease odds (on the natural logarithm scale). Statisticians define the term ‘interaction’ as a departure from additivity in a linear model on a specific scale on which the data are measured. Certain interactions may be eliminated via a transformation of the outcome such that the relationship between the risk factors and the outcome is additive on the transformed scale. Such interactions are known as removable interactions. We develop a novel test statistic for detecting the presence of a removable interaction in case–control studies. We consider the Guerrero and Johnson family of transformations and show that this family constitutes an appropriate link function for fitting an additive model when an interaction is removable. We use simulation studies to examine the type I error and power of the proposed test and to show that, when an interaction is removable, an additive model based on the Guerrero and Johnson link function leads to more precise estimates of the disease odds parameters and a better fit. We illustrate the proposed test and use of the transformation by using case–control data from three published studies. Finally, we indicate how one can check that, after transformation, no further interaction is significant. Copyright © 2012 John Wiley & Sons, Ltd.     

Additive interaction in survival analysis: use of the additive hazards model

It is a widely held belief in public health and clinical decision-making that interventions or preventive strategies should be aimed at patients or population subgroups where most cases could potentially be prevented. To identify such subgroups, deviation from additivity of absolute effects is the relevant measure of interest. Multiplicative survival models, such as the Cox proportional hazards model, are often used to estimate the association between exposure and risk of disease in prospective studies. In Cox models, deviations from additivity have usually been assessed by surrogate measures of additive interaction derived from multiplicative models-an approach that is both counter-intuitive and sometimes invalid. This paper presents a straightforward and intuitive way of assessing deviation from additivity of effects in survival analysis by use of the additive hazards model. The model directly estimates the absolute size of the deviation from additivity and provides confidence intervals. In addition, the model can accommodate both continuous and categorical exposures and models both exposures and potential confounders on the same underlying scale. To illustrate the approach, we present an empirical example of interaction between education and smoking on risk of lung cancer. We argue that deviations from additivity of effects are important for public health interventions and clinical decision-making, and such estimations should be encouraged in prospective studies on health. A detailed implementation guide of the additive hazards model is provided in the appendix.