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.     

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.     

α-内收蛋白Gly460Trp、AGT Met235Thr基因多态性与环境因素的交互作用研究

目的探讨α-内收蛋白(α-adducin)Gly460Trp、AGT Met235Thr基因多态性与环境因素之间的交互作用。方法运用logistic回归模型及叉生分析方法,分析α-adducin Gly460Trp、AGTMet235Thr基因多态性与环境因素(体质指数、腰臀比、吸烟、饮酒)之间的交互作用,评价交互作用在原发性高血压发生中的作用。结果α-adducin Gly460Trp基因型与体质指数、腰臀比、饮酒之间呈次相乘模型交互作用,α-adducin Gly460Trp基因型与吸烟之间呈超相乘模型交互作用;而AGTMet235Thr基因型与吸烟之间呈次相乘模型交互作用,AGT Met235Thr基因型与体质指数、腰臀比、饮酒之间交互作用不存在相乘模型,进一步分析其有无相加模型交互作用,结果显示AGTMet235Thr基因型与体质指数、饮酒之间存在负相加模型交互作用,AGT Met235Thr基因型与腰臀比之间存在正相加模型交互作用。结论α-adducin Gly460Trp和AGT Met235Thr基因多态性与环境因素之间存在明显的交互作用。     

环境低浓度石棉暴露与肺癌危险性的巢式病例对照研究

目的探讨云南省大姚县环境低浓度青石棉暴露与肺癌之间的关联以及肺癌高发的主要危险因素，为当地的肺癌防制提供依据。方法采用巢式病例对照研究方法，从队列中获得53例肺癌病例，按1：3的比例分别匹配以性别相同、年龄相当的对照。结果单因素条件logistic回归分析发现石棉环境污染、吸烟、饮酒、喝茶与肺癌有统计学关联，石棉环境污染的各种形式中，只有使用石棉炉对肺癌发生有显著性意义。用多因素条件logistic回归进一步分析，使用石棉炉和吸烟与肺癌有统计学关联，OR值分别是3．38(95％CI1．43～7．95)和2．62(95％CI1．08～6．56)．其他各因素对肺癌的影响未发现有显著性意义。对吸烟与使用石棉炉的交互作用进行相乘模型的拟合，未发现两因素存在相乘模型的交互作用(P=0．310)。相加模型交互作用分析结果显示，吸烟和使用石棉炉对肺癌发病的影响可能存在着相加模型的交互作用。结论吸烟和使用石棉炉是当地肺癌高发的主要危险因素，且两者存在着相加模型的交互作用。     

Assessing interaction in case-control studies: type I errors when using both additive and multiplicative scales

Epidemiologic researchers often explore effect modification in case-control studies on more than one statistical scale, an approach that one expects would increase the rate of false-positive findings of interaction. For example, researchers have measured effect modification by using both a multiplicative interaction coefficient (M) in a logistic regression model and a measure of interaction on the additive scale such as the interaction coefficient from an additive relative risk regression model (A). We performed computer simulations to investigate the degree to which type I error may be inflated when statistical interactions are evaluated by using both M and A. The overall type I error rate was often greater than 5% when both tests were performed together. These results provide empiric evidence of the limited validity of a common approach to assessing etiologic effect modification. When the scale has not been specified before analysis, interaction hypothesis tests of effect modification should be interpreted particularly cautiously. Researchers are not justified in choosing the interaction test with the lowest P value.     

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.     

Regression analysis with multiplicative and time-varying additive regression coefficients with examples from breast and colon cancer

Regression analysis may be used to simplify the representation of mortality rates when there are many significant prognostic covariates or to adjust for confounding effects. The principal request of the regression model in this range of use is to have unbiased parameter estimates. A model with constant multiplicative and time-varying additive regression coefficients is discussed. The model allows some covariate effects to be multiplicative while allowing others to have a time-varying additive effect. Thus, it is a mix of classical Cox regression and Aalen's additive risk model. A major characteristic of cancer mortality rates, in contrast to general mortality rates, is that hazard rates, after a potentially initial increase, decrease, although not always tending to zero. Cancer diseases, like breast and colon cancer, have significantly increased cause-specific mortality rates even 20 years after diagnosis. Another major feature in cancer survival analysis is that many covariate effects are time-varying. Some covariate effects, like age at diagnosis, may only be significant for a limited time after diagnosis. Furthermore, some treatment procedures may initially decrease the mortality, while the long-term effect may be opposite. A third issue is that average covariate effects are very often not multiplicative. Estimation is carried out iteratively; the cumulative additive regression functions are estimated non-parametrically using a least-squares method and the multiplicative parameters are estimated from the partial likelihood. The method is applied on 3201 female breast cancer and 1372 male colon cancer patients.     

A weighting approach to causal effects and additive interaction in case-control studies: marginal structural linear odds models

Estimates of additive interaction from case-control data are often obtained by logistic regression; such models can also be used to adjust for covariates. This approach to estimating additive interaction has come under some criticism because of possible misspecification of the logistic model: If the underlying model is linear, the logistic model will be misspecified. The authors propose an inverse probability of treatment weighting approach to causal effects and additive interaction in case-control studies. Under the assumption of no unmeasured confounding, the approach amounts to fitting a marginal structural linear odds model. The approach allows for the estimation of measures of additive interaction between dichotomous exposures, such as the relative excess risk due to interaction, using case-control data without having to rely on modeling assumptions for the outcome conditional on the exposures and covariates. Rather than using conditional models for the outcome, models are instead specified for the exposures conditional on the covariates. The approach is illustrated by assessing additive interaction between genetic and environmental factors using data from a case-control study.     

叉生分析在复杂疾病基因-基因、基因-环境交互作用研究中的应用

目的 探讨叉生分析在复杂疾病基因-基因、基因-环境交互作用研究中的应用及其意义.方法 应用叉生分析对病例对照研究的糖尿病数据进行基因-基因、基因-环境交互作用分析结果 交互作用的分析依赖于对相加或相乘模型的选择.本文中相加模型与相乘模型的交互作用结果均具有统计学意义,根据交互作用模型选择原则,本文结果适合应用相加模型进行解释.基于相加模型的ENPP1基因K121Q（rs1044498）与饮酒交互作用具有统计学意义（OR=4.01,S=17.22,AP=0.71,P〈0.05）,与家族史交互作用也具有统计学意义（OR=5.14,S=7.43,AP=0.69,P〈0.05）;174G/C与572C/G两基因交互作用具有统计学意义（OR=5.12,S=5.40,AP=0.65,P〈0.05）结论 叉生分析不仅可以分析基因-环境的交互作用,同样可以分析基因-基因的交互作用.而且叉生分析结果简单明了,通过SAS、R等统计软件都可实现叉生分析的分析过程和假设检验过程.并且可以非常直观地呈现绝大部分的流行病学中基本单元的信息,可为我们判断交互作用提供基本的理论依据因此叉生分析在复杂疾病的基因-基因、基因-环境交互作用研究中具有广阔的应用前景.     

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.     

糖尿病与脂肪肝对绝经女性胆石症患病的交互作用

目的 探讨糖尿病与脂肪肝的交互作用对绝经女性胆石症患病的影响。方法 研究采用多阶段分层整群抽样方法抽取苗族、侗族绝经女性作为研究对象，纳入符合条件的研究对象共3 938人。采用SPSS25.0软件进行Mann - Whitney U检验、χ2检验、单因素和多因素logistic回归分析；同时运用相乘模型和相加模型探讨糖尿病与脂肪肝的交互作用对绝经女性胆石症患病的影响。结果 本次3 938名绝经女性中，平均年龄为59.51岁，胆石症检出率为17.01%，糖尿病检出率为9.09%，脂肪肝检出率为19.86%，糖尿病合并脂肪肝检出率为4.06%。多因素logistic回归结果显示，糖尿病(OR = 1.715, 95%CI:1.325～2.220)和脂肪肝(OR = 1.438, 95%CI:1.162～1.780)均与绝经女性胆石症的患病风险有关。交互作用分析结果显示，糖尿病与脂肪肝对绝经女性胆石症的患病不存在相乘交互作用(OR = 1.605,95%CI:0.951～2.707)，结果无统计学意义；但糖尿病与脂肪肝对绝经女性胆石症的患病存在相加交互作用，糖尿病合并脂肪肝者的患病风险高于无糖尿病且无脂肪肝者(OR = 2.905,95%CI:2.040～4.138)，其相加交互作用评价指标RERI(95%CI)、AP(95%CI)和SI(95%CI)分别为1.216(0.115～2.316)、0.418(0.148～0.688)和2.760(1.043～7.305)，结果有统计学意义。结论 在绝经女性中，糖尿病和脂肪肝均与胆石症存在关联，二者对增加胆石症患病风险可能存在协同作用。