四因素方差分析模型构建及癌症风险评估

Construction of Four Factor Analysis of Variance (ANOVA) Model and Cancer Risk Assessment

摘要: 在实际问题中，往往需要分析多重因素对实验结果的影响，方差分析是解决此类问题的一个重要工具。然而，对于方差分析的理论目前集中在单因素方差分析和两因素方差分析。为此，基于两因素方差分析模型给出带有交互效应的四因素方差分析模型的理论推导，并应用其来分析地域、性别、吸烟、离子辐射对癌症患病风险的影响。本文在两因素方差分析模型基础上给出了具有交互作用的四因素方差分析模型的理论推导，并将其应用到具体实例中。在应用多因素方差分析模型时，可以通过对数据做变换来达到正态性、方差齐性的要求。对癌症发病率数据的方差分析结果表明，吸烟时长和离子辐射剂量对癌症的患病风险具有显著性影响，地域和性别并没有显示对癌症风险具有显著性影响。

Abstract: In practical problems, it is often necessary to analyze the influence of multiple factors on the experimental results. Analysis of variance is an important tool to solve the problems. However, the theory of variance analysis (ANOVA) focuses on one-way analysis of variance and two-way analysis of variance (ANOVA). Therefore, based on the two factor analysis of variance (ANOVA) model, this paper gives the theoretical derivation of the four factor analysis of variance (ANOVA) model with interaction effect, and applies it to analyze the influence of region, gender, smoking and ion radiation on cancer risk. Based on the two factor analysis of variance model, this paper gives the theoretical derivation of the interactive four factor analysis of variance model and applies it to specific examples. When applying a multi-factor analysis of variance model, the data can be transformed to meet the requirements of normality and homogeneity of variance. The results of variance analysis of cancer incidence data show that smoking duration and ionizing radiation dose have a significant impact on the risk of cancer, region and gender do not show a significant impact on cancer risk.