CoVID-19流行軽減に学校閉鎖は無効だった ｰ ベイジアン推論を使用した時系列分析

3月に日本で突然始まった学校の休校だが、2月以前に中国からの報告では、5歳以上では患者自体が少なく、重症者も少ないことが分かっていました。

おそらく無意味な休校になるだろうと思っていましたが、やはりその通りでした。

老人を守るために、子どもたちは犠牲になりました。

専門家の意見も聞かずに、インフルエンザの状況と同様の措置を取った首相にはがっかりしました。

ガーゼマスクの配布と並ぶ失策です。

（※　管理者注　2020/08/19記載）

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COVID-19のパンデミックは、多くの国に重大な被害を与えています。

日本はそのリスクを軽減するために、2020年3月1日から全国のすべての小中学校を閉鎖するよう呼びかけました。しかし、病気の負担を減らす効果はまだ調査されていません。

方法

2020年3月31日まで、日本におけるCOVID-19とコロナウイルス感染率の日次データを使用しました。時系列分析は、ベイジアン法を使用して行われました。無症候性感染症を含む、COVID-19の新たに報告された症例数について、介入効果のある局所線形傾向モデルが構築されました。介入の効果は、学校閉鎖の9日後に現れ始めたと考えた。

結果

学校閉鎖の介入は、コロナウイルス感染の発生率を減少させるようには見えなかった。学校閉鎖の効果が3月9日に始まった場合、測定の効果の平均係数αは0.08（95％信頼区間-0.36〜0.65）と計算され、実際に報告された症例は予測を上回りましたが、広い信頼区間。異なる日付を使用した感度分析でも、学校閉鎖の有効性は示されませんでした。

討論

日本で実施された学校閉鎖は、新規コロナウイルス感染の伝染に対する緩和効果を示さなかった。

Was school closure effective in mitigating coronavirus disease 2019 (COVID-19)? Time series analysis using Bayesian inference

Kentaro Iwata , Asako Doi , Chisato , Miyakoshi.

International Journal of Infectious Diseases

Available online 31 July 2020

https://doi.org/10.1016/j.ijid.2020.07.052

https://www.sciencedirect.com/science/article/pii/S1201971220305981?fbclid=IwAR3Vc_jnx8sb03Rd0ylS05BTWWC3v3Wxq-j91M1QNJDLPorliarXhIk01EI

Abstract

Objectives

The Coronavirus disease 2019 (COVID-19) pandemic is causing significant damage to many nations. For mitigating its risk, Japan called on all elementary, junior high and high schools nationwide to close beginning March 1, 2020. However, its effectiveness in decreasing the disease burden has not been investigated.

Methods

We used daily data of the COVID-19 and coronavirus infection incidence in Japan until March 31, 2020. Time series analyses were conducted using the Bayesian method. Local linear trend models with interventional effect were constructed for the number of newly reported cases of COVID-19, including asymptomatic infections. We considered that the effects of the intervention started to appear 9 days after the school closure.

Results

The intervention of school closure did not appear to decrease the incidence of coronavirus infection. If the effectiveness of school closure began on March 9, the mean coefficient α for effectiveness of the measure was calculated to be 0.08 (95% confidence interval -0.36 to 0.65), and the actual reported cases were more than predicted, yet with a rather wide confidence interval. Sensitivity analyses using different dates also did not demonstrate the effectiveness of the school closure.

Discussion

School closure carried out in Japan did not show any mitigating effect on the transmission of novel coronavirus infection.

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Introduction

With the widespread incidence of coronavirus disease 2019 (COVID-19), many countries including Japan chose to restrict the movement of people. On February 27, 2020, Japan’s Prime Minister Shinzo Abe called on all elementary, junior high and high schools nationwide (from age 6 to 18-year-old) to close until the end of a spring break through early April for “children’s health and safety” [1]. Although it was a request, not an order, most followed the request, with a closure rate of 98.8 % among municipal elementary schools, and with closure of high schools at 46 out of 47 prefectures [2]. School closure occurred in other nations as well, such as in parts of China, Hong Kong, and Italy [3,4]. However, the measures taken in these countries were different from one taken in Japan. For example, Italy closed all universities in addition to other schools, since people in their twenties may spread the disease readily [5]. Most countries elected to have so-called “lockdown” at the same time, restricting the outings of most people other than school children. There is relatively little evidence on school closure for mitigating the spread of COVID-19. Therefore, we conducted a time series analysis with Bayesian statistics to infer the effectiveness of school closure for decreasing the incidence of coronavirus infection in Japan.

Methods

We used daily data on the report of COVID-19 and coronavirus infection incidence in Japan, provided by the Ministry of Health and Labor of Japan from inception until March 31, 2020 (https://www.mhlw.go.jp/stf/houdou/houdou_list_202003.html). Time series analyses were conducted using the Bayesian method. Local linear trend models with interventional effect were constructed for the number of newly reported cases of COVID-19, including asymptomatic infections.

We set the intervention as practically started on February 29, Saturday, since the Prime Minister called for the closure on the following Monday. With the estimated median incubation period of about 5 days, and consideration of Japan’s policy to test for COVID-19 only in those having symptoms for 4 days, or 2 days for the elderly, we considered that the effects of the intervention started to appear 9 days after the school closure; i.e., on March 9 [6], [7]. Predictions until the end of March were made. Because the reopening of schools occurred differently in each prefecture of Japan, and many re-opened fully on the week of this writing (June 15, 2020), we were not able to evaluate the effectiveness of reopening of schools.

The precise expressions of our model are as follows:

The numbers of newly reported patients, Y, are assumed to have a Poisson distribution with the intensity of exp(λ). At each time, λ is mainly determined by the previous state of λ, and the drift component δ. Z is a dichotomous variable which takes 0 before the effect of intervention is assumed to appear, and 1 afterwards. The coefficient α is the expected daily decrease of λ after the intervention isassumed to be effective. Therefore, we considered the intervention would have an effect of suppressing cases if α was negative. Estimations were calculated using data until March 17 for all analyses.

We set 4 separate sampling sequences, each consisting of 1000 random samples (including 500 samples discarded for convergence). The estimated numbers of newly reported patients, i.e., E(exp(λ)), were provided with 80% credible intervals (CrI). Sampling convergence was evaluated by Gelman-Rubin statistics and by visually inspecting a trace plot. We used the R software program, version 3.5.1 (R Foundation for Statistical Computing, Vienna, Austria) with a probabilistic programming language Stan (Stan development team) for all Bayesian analyses. Sensitivity analyses were also conducted daily for 2 days before and up to 7 days after March 9 (from March 7 to 16).

This study was exempted from approval by the ethics committee of Kobe University Graduate School of Medicine as the study used only data in the public domain.

Results

We found that the intervention of school closure did not appear to decrease the incidence of coronavirus infection. If the effectiveness of school closure began on March 9, the mean α was calculated to be 0.08 (95% confidence interval -0.36 to 0.65), which means the intervention was not effective and the number of newly reported infections continues to increase, although the predicted 80% confidence interval was wide (Fig. 1).

Fig. 2. Local linear trend model showing the number of predicted cases of coronavirus infection in Japan until March 31 (red line for predicted median with red area for 80%). The assumption is that the intervention began on February 29 (blue solid line), and the effectiveness started to appear on March 7. Black and white dots denote reported cases actually. Black dots are data until March 17 and used in our estimation.

Fig. 3. Local linear trend model showing the number of predicted cases of coronavirus infection in Japan until March 31 (red line for predicted median with red area for 80%). The assumption is that the intervention began on February 29 (blue solid line), and the effectiveness started to appear on March 16 (blue dotted line). Black and white dots denote reported cases actually. Black dots are data until March 17 and used in our estimation.

Table 1. Estimated α(coefficient for intervention effects)using our model with 95% credible intervals. Note if α is less than zero, the intervention is presumed to be effective in decreasing the number of newly reported cases, and if α is more than zero, the number continues to increase.

Discussion

Our analysis did not demonstrate the effectiveness of the school closure that occurred in Japan in mitigating the risk of coronavirus infection in the nation. Although the effectiveness could have occurred in some scenario on sensitivity analyses, most scenarios in our sensitivity analyses also did not demonstrate its effectiveness.

The effectiveness of school closure has been studied for other infections such as influenza, and these studies have suggested that school closure may be effective in reducing or delaying the epidemic peak. However, there were large heterogeneity in data and generalization of the findings remains difficult. Reopening of schools sometimes reversed the effects, and the optimal timing and duration of school closure, as well as the target age range and the ideal scale of closure remain unknown [8], [9], [10]. School children are liable to suffer from influenza every year, and the rationale for school closure to mitigate its epidemic appears sound. Decreasing influenza in children by vaccination could even decrease the disease burden among the elderly [11]. However, children are not a major population that suffers from COVID-19, and young children less than 20-year-old comprised only about 2% of all infected according to a large-scale epidemiological study in China [12]. A study using mathematical models suggested that school closure, including universities, is indeed effective in mitigating the impact of the COVID-19 outbreak, but only when combined with other measures [13]. While it is theoretically possible that school closure among children could reduce transmission among them and potentially to other generations, its impact is likely to be much less than the one conducted for influenza. Therefore, our findings that school closure in Japan did not demonstrate its effectiveness to mitigate the transmission of coronavirus infection are not surprising.

An epidemiological study on COVID-19 in children identified 2,143 pediatric patients in China, and it found that infants may be vulnerable to coronavirus infection. The proportion of severe and critical cases among those less than 1-year-old was 10.6% followed by 7.3% in those aged 1-5 years [14]. However, the school closure done in Japan was only for those aged 6-18, and those vulnerable were not likely to be protected by the measure. A cluster of outbreaks was found in Kyoto, Japan among college students [15], but again college/university students were not included in the school closure in Japan. When school closure was to be implemented to prevent the spread of COVID-19, those who are vulnerable to this disease and those who are likely to spread it also should be included.

Our study has several limitations. First, our local linear trend model might not be an appropriate model for the current epidemic of COVID-19 in Japan. One might argue that the school closure could have prevented rather stochastic clusters or outbreaks among school children, which could have not happened thanks to the measure. However, if we accept such theory of stochasticity in justifying the school closure, we will end up carrying on the measure until the coronavirus pandemic comes to an end, since we will never know when we can discontinue the measure while fearing unpredictable stochastic outbreaks occurring. Second, the estimated α value using data by the time of intervention effectiveness might not be accurately predicting the α value afterwards, i.e., the α value after March 18. Third, our estimations resulted in rather wide confidence intervals, and the results should be interpreted cautiously. Fourth, school closures in other forms might be effective in mitigating the epidemic, such as ones including infants and small children, or university students. Fifth, school closures combined with other measures such as traffic limitations or even city lock down might be effective. Therefore, we are not claiming that school closures overall are ineffective in mitigating the COVID-19 epidemic in a nation. However, we would like to suggest that the school closure carried out in Japan in March did not demonstrate meaningful effectiveness in controlling the COVID-19 epidemic. Further studies will be necessary to investigate the effectiveness of school closures in other forms at different settings.