Haber M, Longini I M, Cotsonis G A
Department of Statistics and Biometry, Emory University, Atlanta, Georgia 30322.
Biometrics. 1988 Mar;44(1):163-73.
The Longini-Koopman model (1982, Biometrics 38, 115-126) describes the process underlying the transmission of an infectious disease in terms of household and community level transmission probabilities. This model is generalized by allowing for different transmission probabilities that may correspond to various levels of risk factors on both the household and community levels. Two types of models are considered: (i) models for household data, where the numbers of susceptible and infected members in each household are known along with the values of household level risk factors; and (ii) models for individual data, where the infection status and risk factor level are known for each individual in the household. Although the type (i) models can be expressed as special cases of the type (ii) models, they deserve special attention as they can be represented and analyzed as log-linear models. Both types of models can be analyzed using maximum likelihood methods, while the type (i) models, when expressed as log-linear models, can also be analyzed by the weighted least squares method. Data from influenza epidemics in Tecumseh, Michigan and Seattle, Washington are used to illustrate these methods.
朗吉尼 - 库普曼模型（1982年，《生物统计学》第38卷，第115 - 126页）从家庭和社区层面的传播概率角度描述了传染病传播的潜在过程。通过考虑不同的传播概率对该模型进行了推广，这些概率可能对应家庭和社区层面各种风险因素水平。考虑了两种类型的模型：（i）家庭数据模型，其中每个家庭中易感成员和感染成员的数量以及家庭层面风险因素的值是已知的；（ii）个体数据模型，其中家庭中每个个体的感染状况和风险因素水平是已知的。尽管类型（i）模型可以表示为类型（ii）模型的特殊情况，但它们值得特别关注，因为它们可以表示为对数线性模型并进行分析。两种类型的模型都可以使用最大似然法进行分析，而类型（i）模型在表示为对数线性模型时，也可以通过加权最小二乘法进行分析。来自密歇根州特库姆塞和华盛顿州西雅图流感疫情的数据用于说明这些方法。
