Estimating Asymptomatic Ratio of Pathogen Infection by Log-Linear Binomial Regression Model

Asymptomatic ratio, which is the relation of cases with no symptoms in proportion to cases infected with pathogens, is an important indicator in public health. However, symptoms of infected cases are not altogether caused by the pathogens. What is more, it is difficult to find out the real factor that leads to the symptoms of the case that is infected with multi-pathogen infection at the same time. As a result, we may have trouble estimating asymptomatic ratio of each pathogen in such a case. In this study, we use log-linear binomial regression model, in which independent variables are set as the situations of pathogen infection of the cases and dependent variable is set as whether the cases have symptoms that can be observed symptoms (symptom coding with 0, non-symptom coding with 1), for model fitting. We derive the regression coefficients of each independence variable from PROC GENMOD in SAS. Regression coefficient taking exponential is the probability of infected cases without symptoms caused by the pathogen. We call that probability pathogen-specific asymptomatic ratio. Intercept taking exponential is the probability of non-infected cases in asymptomatic state. We call that probability background asymptomatic ratio. We random sample 600 from Lin’s [1] study of 1104 children as an example. We find that while estimating asymptomatic ratio, log-linear binomial regression model is more direct and effective than logistic regression model, which is generally used in dealing with binary dependant variables. Moreover, log-linear binomial regression model is more clearly discriminate between the effects of background factors and those of pathogens. In terms of goodness-of-fit of two regression models to the data, they are both consistent with the observed data on the numbers of non-infected cases and infected cases in various situations. However, log-linear binomial regression model is more accurate than logistic regression model in fitting the observed numbers.