Models for the statistical analysis of infectious disease data

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.