key: cord-0961071-h0l6my56
authors: Nakagawa, K.; Kanatani, T.
title: Monday effect on confirmed cases of COVID-19 in Japan
date: 2021-07-22
journal: nan
DOI: 10.1101/2021.07.20.21260858
sha: 3933cde03bc5295f354d2fa05b92aed4b7e986b9
doc_id: 961071
cord_uid: h0l6my56

We examined the phenomenon of fewer new confirmed cases on Monday in Japan, which we refer to as the Monday effect. In Japan, prefectures aggregate and announce the number of daily confirmed cases. We analyzed the impact of this effect in each prefecture. The effect is mainly found in prefectures with populations of 2 million or more. This effect is also constantly observed in the three major metropolitan areas in Japan. However, the magnitude of the observed effect is uncorrelated with both the number of positives per 1,000 people and the population size. Our results suggest that the reporting delay occurs in prefectures above a specific size, but the magnitude of the delay differs among prefectures. We consider two possible explanations for this effect: 1) delays caused by the administrative system. 2) fewer tests are conducted on the previous day. Our results indicate that delays are caused by the administrative system in some prefectures and that some prefectures with larger populations are less likely to conduct screenings on holidays.

We examined cases of COVID-19 that occurred on Mondays over the 500 days since the first cases were reported in Japan. The number of positive cases of COVID-19 is said to be lower on Monday compared to other days of the week. For example, in October 2020, the Asahi Shimbun [1] reported only one case in Tokyo 1 .

We refer to this phenomenon as the Monday effect. By observing the sample means of daily cases throughout the period, we can determine how the number of new confirmed cases actually varies by day of the week, see Table 1 . We use the daily data on the number of new positive cases by prefecture obtained from the NHK(Nippon Hoso Kyokai) website [2] . The duration of the data is 517 days from January 16, 2020, to June 15, 2021, t = 1, 2, ..., 517. The last column presents the difference between the mean of daily cases for the whole period and the mean for the day of the week. As shown in Table 1 , the Monday effect is observed on a nationwide scale. Differences in means of each weekday seem to be recognized as a nationwide phenomenon. Previously, news channels reported the raw number of daily cases, but they now add a one-week moving average or a comparison with the same day of the previous week.

We determined that the number of confirmed cases was lower on Mondays. As shown in Table 1 , the number of reported positive cases is lower in the first three days of the week and higher in the remaining. There are two possible explanations for this phenomenon: the first is that fewer tests on the previous day if the previous day's situation is immediately reflected on the next day. The second is the delay caused by the administrative system. The latter may be due to the way government employees work. Administrative officials usually do not work on Sunday, which is a holiday as defined by their employment regulations. We examined the effect of the days of the week, focusing on holidays and their following days, that is, Sunday and Monday. We also added two more days before and after Monday and Sunday. We examined the effect of Saturday, Sunday, Monday, and Tuesday.

Furthermore, we analyzed how this effect differs in each administrative geographic unit, mainly because the distribution of the population is skewed within the nation. In other words, we analyzed the data for the regional unit that is practically responsible for the effective management of public health administration. In Japan, public health management is carried out by the 47 prefectures, which are local governments. The central government has delegated counting of confirmed cases to these local governments. We examined the Monday effect using the daily data of the number of new confirmed cases in each prefecture.

On the effects within the week, Li (2020) [3] examined time series data on new confirmed cases of COVID-19 and discussed the weekly recurrence. The author analyzed countries around the world using country-level data and identified an autocorrelation with a 7-day lag.

The rest of this paper is organized as follows. In section 2, we discuss the data and methods used in the subsequent sections. In section 3, we first demonstrate the Monday effect in the national scale data and then present the analysis results for each prefecture. In section 4, we discuss the implications of the results.

We use the data outlined in the previous section.

It is well known that biological count data have a tendency of over-dispersion; see Zuur et al. (2010) [9]. To handle such over-dispersion, we assume that the new confirmed positive cases of the tth day Y t follow the negative binomial distribution. 2 In our model, the probability function of Y t is defined as

where µ t is a time-varying deterministic parameter and θ > 0.

Since the random variable Y t has the conditional mean and variance

it is clear that θ > 0 is the condition of over-dispersion and θ −1 is referred to as the over-dispersion parameter. If θ goes to infinity, the distribution converges to the Poisson distribution.

To evaluate the effect of the weekdays, we define the dummy variable

TUE t , SAT t , and SUN t are similarly defined. We assume that the natural logarithm of µ t is a linear combination of weekday dummies and a time trend t,

Note that φ represents a compound daily growth rate of the conditional mean µ t . 3 Since the prefectural data series of daily new cases contain a certain amount of zeros in some prefectures, we modify our model to handle such data.

The probability function of zero-inflated negative binomial regression (ZINB) is defined as 4

where

Note that the probability π t is a time-varying deterministic parameter. We estimate all 12 parameters in (5) and (7) and θ using the maximum likelihood method, 5 then select the variables in (5) and (7) via a stepwise approach based on Akaike's information criterion (AIC). In our approach, we select and delete the same variables in both (5) and (7) to limit computational complexity.

As mentioned in the previous section, we choose a model by AIC in a stepwise algorithm to keep on minimizing the step-AIC value. Based on the selected model, we examined whether the conditional mean of confirmed cases was significantly less on Monday. We define the Monday effect if the coefficient of the Monday dummy variable is negative and the p-value is less than 0.01 (p < 0.01).

We first demonstrate the Monday effect in the national scale data. The result indicates that the number of confirmed cases was significantly lower on Monday, see Table 2 . The column named "count" reports the estimates of coefficients in (5) and θ. The column "zero" also presents estimates of the coefficients in (7). As shown in Table 2 , we obtain the selected model that contained the following variables: constant term, Monday dummy, and time trend.

We identified the Monday effect in 19 prefectures. On the contrary, we did not find the effect in 22 prefectures. Table 3 reports the prefectures that were negative and significant at the 1% level in the Zero-Inflated Negative Binomial regression model. Note that six prefectures (Iwate, Tochigi, Yamanashi, Shiga, Nara, and Okayama) had Monday effects that were significant at the 5% level. We also identified an outlier case, Shimane. The number of confirmed cases in Shimane was significantly higher on Sunday and lower on Monday. This tendency is only observed in Shimane. For more detailed results for all prefectures, see Table 4 -11 in the Appendix.

The Monday effect was identified in 19 prefectures. The total populations of these prefectures covers more than 65% of the total population in Japan. A map 4 See Benlagha (2020)[6] for an example application of ZINB. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 22, 2021. ; 

of the Monday effects for each prefecture is presented in Figure 1 shows. The darker the shade of red, the greater the Monday effect. This map shows that regions with a significant Monday effect include the three largest metropolitan areas in Japan, that is, Tokyo, Osaka, and Nagoya. It is clear that the Monday effect is related with areas where the population is concentrated.

We perform a brief analysis of the prefectures where the Monday effect was obtained, see Moreover, Figure 2 shows that, in prefectures with four or fewer new positive cases per 1,000 population, the existence of such an effect is independent of the spread of infection, see the white dots without a name in Figure 2 -4. This also implies that the Monday effect would be related to the system of public health administration.

In general, the Monday effect seems to be correlated with the number of cases per 1,000 people. Figure 3 illustrates the relationship between the total population and the magnitude of the Monday effect. Figure 4 shows the relationship between the number of new positive cases per 1,000 population and the magnitude of the Monday effect. The magnitude appears to be almost uncorrelated with population size and the number of new confirmed cases per 1,000 population.

Our results indicate that the increase in the number of infected people in populated areas delays release of the actual number of confirmed cases. This 5 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 22, 2021. ; https://doi.org/10.1101/2021.07.20.21260858 doi: medRxiv preprint -0.521*** Significance: * * * ≡ p < 0.001; * * ≡ p < 0.01 is consistent with the general conjecture that the Monday effect seems to be a phenomenon that can be observed in urban areas with large population sizes where the spread of infection is more serious. On the other hands, our results also indicate that the degree of delay in release of confirmed cases was not correlated with the scale of the outbreak.

We examined the Monday effect, which is the phenomenon of fewer new confirmed cases of COVID-19 on Monday. We identified the Monday effect in 19 prefectures. We consider two possible explanations for this effect: 1) delays caused by the administrative system. 2) fewer tests are conducted on holidays. We identified delays caused by the administrative system in some prefectures. Our results also indicate that some prefectures with larger populations are less likely to conduct screenings on holidays. In terms of policy implications, it is important to consider whether the difference is due to some kind of difference in health administration among prefectures.

6 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 22, 2021. 7 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 22, 2021. ; https://doi.org/10.1101/2021.07.20.21260858 doi: medRxiv preprint CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 22, 2021. ; https://doi.org/10.1101/2021.07.20.21260858 doi: medRxiv preprint Significance: * * * ≡ p < 0.001; * * ≡ p < 0.01; * ≡ p < 0.05 13 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 22, 2021. ; https://doi.org/10.1101/2021.07.20.21260858 doi: medRxiv preprint CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 22, 2021. ; https://doi.org/10.1101/2021.07.20.21260858 doi: medRxiv preprint Significance: * * * ≡ p < 0.001; * * ≡ p < 0.01; * ≡ p < 0.05 16 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted July 22, 2021. ; https://doi.org/10.1101/2021.07.20.21260858 doi: medRxiv preprint Significance: * * * ≡ p < 0.001; * * ≡ p < 0.01; * ≡ p < 0.05 17 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted July 22, 2021. ; https://doi.org/10.1101/2021.07.20.21260858 doi: medRxiv preprint Significance: * * * ≡ p < 0.001; * * ≡ p < 0.01; * ≡ p < 0.05 18 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted July 22, 2021. ; https://doi.org/10.1101/2021.07.20.21260858 doi: medRxiv preprint 

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Significance: * * * ≡ p < 0