logistic回归模型中交互作用的分析及评价

Study on the interaction under logistic regression modeling

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间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SPSS15．0a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，计算相加交互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。

When study on epidemiological causation is carried out, logistic regression has been commonly used to estimate the independent effects of risk factors, as wall as to examine possible interactions among individual risk factor by adding one or more product terms to the regression model. In logistic or Cox＇ s regression model, the regression coefficient of the product term estimates the interaction on a multiplicative scale while statistical significance indicates the departure from multiplicativity. Rothman argues that when biologic interaction is examined, we need to focus on interaction as departure from additivity rather than departure from multiplicativity. He presents three indices to measure interaction on an additive scale or departure from additivity, using logarithmic models such as logistic or Cox＇s regression model. In this paper, we use data from a case-control study of female lung cancer in Hong Kong to calculate the regression coefficients and covariance matrix of logistic model in SPSS. We then introduce an Excel spreadsheet set up by Tomas Andersson to calculate the indices of interaction on an additive scale and the corresponding confidence intervals. The results can be used as reference by epidemiologists to assess the biologic interaction between factors. The proposed method is convenient and the Excel spreadsheet is available online for free.