利用試題反應理論決定COVID-19疫情的拐點：以台灣疫情為例

Using item response theory to determine the inflection point of COVID0-19: Taiwan example

新冠肺炎疫情中常見的問題之一，是如何預測一個國家/地區中的疫情拐點。一些研究表認為，可以透過繪製每日確診病例來觀察疫情拐點。然而，除非觀察到日確診最高峰後的數天各確診數，否則無法預知其疫情拐點。本研究遂感興趣探討一項預測新冠肺炎疫情拐點的方法。從Github網站下載台灣確診病例的疫情資料，我們應用試題反應理論(IRT)建構一具預測疫情拐點的模型。自動調整洛基分數長度的適性方法，以其洛基分數長度(LR)從-5到S（小於5），LR的比率(=LL)係由公式（=（洛基-（-5））/ 10））計算而得。透過微軟試算表(Excel)中的規畫求解增益集來估計模型參數。利用肩形曲線的特徵，獲得模型的最佳參數，並將其用來決定肩形曲線上的疫情拐點。使用兩波觀察到的疫情峰點來驗證疫情拐點接近於洛基分數長度於0.5位置之效果，比較三種決定拐黠的方法。我們觀察到LL(=0.45)接近0.5時的第一波和第二波日期，分別為2020年3月26日和2020年8月5日，及陡坡圖法的判定拐點，值得推薦。建議利用IRT模式肩形曲線預測疫情拐點，而不只限於本研究的台灣疫情。

One of the frequently asked question in COVD-19 is how to predict the inflection point(IP) of pandemic confirmed cases in a country/region. Some studies suggested that the IP can be observed by plotting the daily confirmed cases. However, we cannot predict the IP unless observing the point after several days from the peak point. We are motivated to develop a way to predict the pandemic IP in COVID-19 for a country/region. Downloading Taiwan COVID-19 data of confirmed cases from the Github website, we applied the item response theory(IRT) to construct predictive models to predict the pandemic IP. An adaptive scheme of the data length in logit was automatically adjusted to tailor the logit range(=LR) along the pandemic transformed to logits from -5 to S less than 5. The ratio of LL was computed by the formula(=(logit-(-5))/10)). Model parameters were estimated by using the Solver add-in in Microsoft Excel. Through the characteristic of the ogive curve, the optimal parameters were obtained and used to determine the pandemic IP on the ogive curve and predict the number of infected cases in the nearest future. Two observed peak points were used to verify the effect of matching the infection point with LL approaching 0.5. Three methods were compared to determine the inflection point in COVID-19. We observed that the LLs (= 0.45) were dated on March 26 and Aug. 5, 2020, in the first and second waves, respectively, and the scree plot recommendable most among the three candidate methods. An adaptive scheme of model fitting the data can be used to predict cumulative confirmed cases in the future. The predictive model based on IRT is recommended to predict the pandemic IP and the infected cases, not just limited to Taiwan COVID-19 pandemic illustrated in this study.