以對數線性二分類迴歸模型估算病原體感染之不顯性感染率

Abstract

不顯性感染率在公共衛生上是一個重要的指標，是計算感染病原體的個案中，未發生症狀的個案比例。然而，被某種病原體感染的個案所產生的症狀不全然發自於該病原體。此外，當個案同時感染多重病原體時，我們也不易分辨導致症狀的真正因素。因此，對同時感染多重病原體的個案，我們很難估計出每一個病原體真正的不顯性感染率。 本研究以對數線性二分類迴歸模型為模型套式，其中自變數為研究病原體感染情形，依變數為個案是否發出可觀察症狀（令發出症狀為0，未發出症狀為1）。我們使用現成的套裝軟體SAS中的PROC GENMOD，求出各自變數的迴歸係數。迴歸係數取自然指數，即為個案感染該種病原體卻不因此發生症狀的機率。我們稱之為該種病原體的病原體特定不顯性感染率。截距項取自然指數後，即為未感染病原體者維持無症狀的機率，我們稱之為背景不顯性感染率。 我們自林[1]研究的1104名學童中，隨機抽出600人為例。我們發現在估計不顯性感染率情況下，對數線性二分類迴歸模型較一般處理二分類依變數的羅吉斯迴歸模型來得直接且有效，並能清楚分辨出背景因素及病原體因素的影響。在比較以上兩迴歸模型對此研究資料的模型適合度上，兩種模型皆能符合未感染及各種感染情況下有無症狀之實際人數，但對數線性二分類迴歸模型較羅吉斯迴歸模型更能符合觀察數值。

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.