key: cord-280437-6u3kepat authors: Kalippurayil Moozhipurath, R.; Kraft, L.; Skiera, B. title: Evidence of Protective Role of Ultraviolet-B (UVB) Radiation in Reducing COVID-19 Deaths date: 2020-05-12 journal: nan DOI: 10.1101/2020.05.06.20093419 sha: doc_id: 280437 cord_uid: 6u3kepat Background: Research is ongoing to identify an effective way to prevent or treat COVID-19, but thus far these efforts have not yet identified a possible solution. Prior studies indicate the protective role of Ultraviolet-B (UVB) radiation in human health, mediated by vitamin D synthesis. In this study, we empirically outline a negative association of UVB radiation as measured by the ultraviolet index (UVI) with the number of deaths attributed to COVID-19 (COVID-19 deaths). Methods: We carry out an observational study, applying a fixed-effect log-linear regression model to a panel dataset of 64 countries over a period of 78 days (n=4992). We use the cumulative number of COVID-19 deaths and case-fatality rate (CFR) as the main dependent variables to test our hypothesis and isolate UVI effect from potential confounding factors such as underlying time trends, country-specific time-constant and time-varying factors such as weather. Findings: After controlling for time-constant and time-varying factors, we find that a permanent unit increase in UVI is associated with a 2.2 percentage points decline in daily growth rates of cumulative COVID-19 deaths [p < 0.01], as well as a 1.9 percentage points, decline in the daily growth rates of CFR [p < 0.05]. These results represent a significant percentage reduction in terms of the daily growth rates of cumulative COVID-19 deaths (-22.92%) and CFR (-73.08%). Our results are consistent across different model specifications. Interpretation: We find a significant negative association between UVI and COVID-19 deaths, indicating evidence of the protective role of UVB in mitigating COVID-19 deaths. If confirmed via clinical studies, then the possibility of mitigating COVID-19 deaths via sensible sunlight exposure or vitamin D intervention will be very attractive because it is cost-effective and widely available. COVID-19 is causing significant economic, healthcare and social disruption globally. However, it is not yet known how to prevent or treat Prior studies indicate the protective role of Ultraviolet-B (UVB) radiation in human health. UVB radiation exposure is a major source of vitamin D, which increases immunity and reduces the likelihood of severe infections and mortality. A recent COVID-19 study indicates abnormally high case-fatality-rate (CFR) of 33.7% among nursing home residents 1 , which is consistent with the studies indicating higher prevalence of vitamin D deficiency among them, due to lower mobility 2, 3 . Increasingly, studies establish a link between vitamin D deficiency and comorbidities such as cardiovascular disease 4 , hypertension 5 , obesity 2,6 , type 1, and type 2 diabetes 7 . This evidence is consistent with the clinical studies in China and Italy that indicate comorbidities such as hypertension, diabetes and cardiovascular diseases could be important risk factors for critical COVID-19 cases 8-10 . Epidemiology of COVID-19 provides evidence that vitamin D might be helpful in reducing risk associated with COVID-19 deaths 11, 12 . If such a link is true, then it will be cost-effective to mitigate COVID-19 via sensible exposure to sunlight or via vitamin D nutritional intervention. Yet, to the best of our knowledge, so far, no empirical study has used data across many countries to explore the association between UVB radiation as measured by ultraviolet index (UVI) and the number of deaths attributed to (COVID-19 deaths). The aim of this study is therefore to examine the relation of UVB radiation, as measured by ultraviolet index (UVI), with the number of COVID-19-deaths. The results of our study demonstrate that a one-unit increase in UVI is associated with a 2.2 percentage points decline in daily growth rates of cumulative COVID-19 deaths. The robustness checks show similar Other weather factors such as cloud cover, precipitation and temperature influence the likelihood of exposure to UVB radiation and thereby vitamin D deficiency due to reduced skin synthesis. For example, clouds not only reduce the amount of UVB radiation but also the likelihood of UVB radiation exposure as people are more likely to undertake outdoor activities on less cloudy days. Lifestyle and mobility also influences the likelihood of UVB radiation exposure 3,23,24 . Similarly, the likelihood of vitamin D deficiency also increases with age 21 , skin pigmentation 25 and obesity due to reduced skin synthesis 26 . In Figure 1 , we summarize these different factors explaining the potential protective role of UVB radiation in reducing COVID-19 deaths, mediated by vitamin D synthesis and deficiency. Since UVB radiation exposure is a major source of vitamin D, an increase in the All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint likelihood of skin exposure to UVB radiation increases vitamin D synthesis, thereby reducing the likelihood of vitamin D deficiency. Therefore, different time varying and time-constant factors influencing the UVB radiation variation and exposure also influence the likelihood of vitamin D synthesis and thereby deficiency. Prior studies indicate that vitamin D deficiency increases the likelihood of weakened immune response 18, 27, 28 , infectious diseases in the upper respiratory tract 21,29,30 and the severity as well as mortality in critically ill patients 31 . Therefore, we expect that an increased skin synthesis of vitamin D due to increased UVB radiation increases the likelihood of immunity and reduces the likelihood of severe infections, thereby reducing the critical COVID-19 cases. Thus, we anticipate that an increase in UVB radiation as measured by ultraviolet index (UVI) relates to a reduction of the number of COVID-19 deaths. In order to identify the relation of UVB radiation and COVID-19 deaths, we constructed the dataset outlined in Table 1 . We collected data covering 78 days from 22 January 2020 until 8 April 2020 across 186 countries of which 147 reported COVID-19 deaths prior to 8 April 2020 and of which 64 reported more than 20 COVID-19 deaths prior to 8 April 2020. We focus on those 64 countries to ensure that the results are not biased by countries that are at a very early stage of COVID-19 outbreak, which would limit data points with respect to COVID-19 deaths. The corresponding country level data consist of the cumulative daily COVID-19 deaths and infections, the daily ultraviolet index (UVI), which is closely connected to the daily UVB radiation, and a set of control variables such as daily weather parameters such as precipitation index, cloud index, ozone level, humidity level, as well as minimum and maximum temperature. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The graph on the top of Figure 2 shows the cumulative COVID-19 deaths and the associated daily growth rates for Italy from 22 February 2020 until 8 April 2020. As time progresses, the cumulative COVID-19 deaths increase but at a slower rate. Initially, the growth rate is high at 69.31% (growth rate from 21 February to 22 February) and it gradually slows to 3.11% (growth rate from 7 April to 8 April). The graph on the bottom of Figure 2 shows the daily growth rates and daily UVI for Italy as well as the UVI values lagged by one, two, and three weeks respectively. It is important to consider the lagged effect of UVI because synthesized vitamin D is cumulative and can be stored in body fat to be used later 21 . Therefore, it seems more plausible that an increase of UVI today will continue to support an individual's immunity later i.e., twoand three-weeks' (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint time. Furthermore, the likelihood of skin synthesis is low in severely infected people, while they are hospitalized, indicating the importance of lagged UVI values. It is evident that the growth rates slow down over time, as counter-measures imposed by governments take effect, which results in lower infection rates and lower mortality rates. At the same time, the UVI is increasing due to seasonal changes in the northern hemisphere countries. In order to approximate the association of UVI, we need to isolate it from the underlying time-trends, which are potentially affecting both UVI as well as the growth rates of cumulative COVID-19 deaths. We estimate the effect of UVI on the cumulative COVID-19 deaths by using log-linear fixed-effects regression. The effect of UVI is isolated from time-constant country-specific factors (see Figure 1 ) by using a within-transformation of the transformed structural model as The key finding is the significant negative long-run association of UVI on cumulative COVID-19 deaths. As we outline in the Identification of UVI Effect section in Supplementary Appendix, the estimate is likely to identify an upper bound of the relation, indicating that the association could be even stronger. Our results presented in Table 3 suggest that a permanent unit increase of UVI is associated with a decline of 2.2 percentage points in daily growth rates of cumulative COVID-19 deaths [p < 0.01]. Relative to the average daily growth rate of cumulative COVID-19 deaths as of April 8 (9.6%), this decline translates into a significant All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint percentage change of -22.92% (=-2.2%/9.6%). We further find that a permanent unit increase of UVI is associated with a decline of 1.9 percentage points in the daily CFR growth rate [p < 0.05]. Compared with the average daily growth rate of CFR as of April 8 (2.6%), this decline translates into a significant percentage change of -73.08% (=-1.9%/2.6%). Results indicate no significant association from an increase of UVI on cumulative COVID-19 deaths on the same day or a week ahead. This insignificant finding is consistent with the fact that severely infected people are more likely to be hospitalized and therefore less likely to be exposed to UVB radiation during their hospital stay. We further recognize that UVB radiation may not make a real difference, when someone is already severely infected and developed severe complications. The results also show that UVI has a stronger relation to COVID-19 deaths than CFR. We anticipate that the weaker association with CFR is plausible as UVI helps in vitamin D synthesis, making the infection less severe due to increased immunity, thereby prompting fewer people to take the test. The results of the robustness checks presented in Table 2 and Table S3 deaths as outlined in Figure 3 . In order to simulate the long-run effects, we take the average number of cumulative COVID-19 deaths across all 64 countries as of April 8, 2020, i.e., 1,373 as cumulative COVID-19 deaths at day 0 as shown in Figure 3 . A scenario with a All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint permanent unit increase of UVI over the baseline scenario of average UVI of 5.31 across countries is associated with 1,225 or 24.72% fewer deaths in 14 days. In this study, we find evidence of the protective role of UVB radiation in reducing COVID-19 deaths. Specifically, we find that a permanent unit increase in ultraviolet index (UVI) is associated with a 2.2 percentage points decline in daily growth rates of COVID-19 deaths [p < 0.01] as well as a 1.9 percentage points decline in the daily growth rates of CFR [p < 0.05]. These results translate into a significant percentage reduction in terms of the daily growth rates of cumulative COVID-19 deaths (-22.92%) and CFR (-73.08%). Our results are consistent across different model specifications. We acknowledge that we may not be able to isolate the association of UVI with cumulative COVID-19 deaths from all confounding factors. Still, we anticipate that an increased (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint likelihood of immunity and a reduced likelihood of infections mediated by an increased likelihood of vitamin D synthesis may plausibly explain this finding. We also acknowledge that we may not be able to rule out the possibility of mediation by other UVB induced mediatorssuch as cis-urocanic acid, nitric oxide 13, 32 . Therefore, further clinical studiesobservational or randomized controlled trials -are required to establish the casual relationship of vitamin D deficiency and COVID-19 deaths, potentially leading to a cost-effective policy intervention for the prevention or as a therapy for COVID-19. The possibility of mitigating COVID-19 via sensible exposure to sunlight or via vitamin D intervention seem to be very attractive from a policy maker's perspective because of its low cost and side effects. Various countries are implementing lockdown as a preventive measure to mitigate COVID-19 impact on healthcare system. Unfortunately, confinement at home also leads to limited UVB exposure, possibly increasing the risk of COVID-19 deaths. While sensible exposure to sunlight helps in synthesizing vitamin D, disproportionate exposure may also increase the risk of sunburn and skin cancer 21 . Countries could create awareness among the population regarding the importance of sensible exposure to sunlight, whilst continuing other measures such as social distancing as well as cautioning against disproportionate exposure. If confirmed via additional clinical studies, then countries could adopt a cost-effective vitamin D intervention programespecially among vulnerable populations with increased risk of vitamin D deficiency, e.g., elderly populations living in nursing homes, people with high body mass index, dark skinned people residing in higher latitudes, people with indoor lifestyle, or vegetarians. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint All authors have completed the ICMJE uniform disclosure form at www.icmje.org/coi_disclosure.pdf and declare: no support from any organisation for the submitted work. RKM is a PhD student at Goethe University, Frankfurt. He also is a full-time employee of a multinational chemical company involved in vitamin D business and holds the shares of the company. BS also holds shares of the company. All other authors declare no competing interests. The views expressed in the paper are those of the authors and do not represent that of any organization. No other relationships or activities that could appear to have influenced the submitted work. We would like to acknowledge Sharath Mandya Krishna, and Rukhshan Ur Rehman for their immense contribution to this paper -for providing inputs and assisting with data collection, data transformation and data engineering. We thank Matthew Little for his assistance in review. We would also like to acknowledge Michael Niekamp, Magdalena Ceklarz and Daniel Gutknecht for their valuable contributions to our paper and the discussions about COVID-19. RKM conceptualized the research idea, conducted literature research, designed theoretical framework and collected the data. LK designed empirical methods and analyzed the data. RKM and LK interpreted the results and wrote the article. BS provided critical inputs, edited and revised the article. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint This study is not sponsored by any organization. The corresponding author had full access to all the data and had final responsibility for the submission decision. Correspondence and requests for materials should be addressed to Rahul Kalippurayil Moozhipurath (rahulkm85@gmail.com). We will make dataset used in this study available for any future research. Interested researchers can contact one of the authors via email to get access to the data. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint We apply a fixed-effect log-linear regression model to estimate the effect of UVI on the number of COVID-19 deaths that builds upon in the specific country. Importantly, this factor would partial out any linear change of growth rates over time that is similar across countries. Therefore, the model isolates the effect of UVI from an exponential-shaped curve which is often observed in the cumulative COVID-19 deaths over time or in the growth rates of Figure 2 in Manuscript. The model also isolates the effect of UVI from factors which can influence UVI or individuals' absorption of UVB such as precipitation index, cloud index, ozone level, humidity level, and temperature. Because an increase of UVB today plausibly affects individuals two and three weeks later we include in our model three weekly lags of UVI and of the control variables. Thus, we use the following model to explain the number of COVID-19 deaths: All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. 1) represents the daily growth rate of COVID-19 deaths from , −1 to , that is independent of the factors presented in Figure 1 in Manuscript. covers virus-specific attributes like its basic reproductive rate R0 combined with its lethality. , − represents the for a country at day lagged by weeks. , reflects the effect of lagged by weeks. 3) , − stands for the set of control variables. This set consists of precipitation index, cloud index, ozone level, humidity level, as well as minimum and maximum temperature for a country at day lagged by weeks. The vector , identifies the effect of these control variables lagged by weeks. , stands for the time passed by since the first reported COVID-19 infection for a country at day and identifies the associated effect. represents time-constant country-specific factors influencing the growth rate of cumulative COVID-19 deaths (e.g., diet related effects, population parameters about their activities and demographic composition). 6) , consists of all the remaining factors that are not identified but also have an effect on the cumulative COVID-19 deaths (i.e., all non-linear differences of growth rates with respect to time and country-specific linear differences of growth rates with respect to time. They could be caused by a decreasing number of people who could All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint potentially become infected or contagious, lockdowns in a country over time, mutation of the virus in a country over time, systematic false-reports of the dependent variable). An appropriate transformation (see Section 13.6 for the Derivation of Equation (2)) results in the estimable equation (2). and do not appear in the equation anymore and a linear regression can identify all other coefficients. Equation (2) observations of 64 countries in Table 2 and the 1,824 observations of 64 countries in Table 3 in Manuscript. We present an overview of how many observations of which country we use in our analysis in Table S8 . The interpretation of the coefficients of equation (2) is percentage wise and the effect of lagged variables can be separated into a short-and a long-run effect. For example, a one-unit increase of at time s affects the cumulative COVID-19 deaths = via ,0 in the short-run. After one week, the increase of affects = +1 firstly via = and secondly via ,1 because = +1 = = ,1 (partialling out the daily growth rate and keeping the control variables constant). Consequently, if the model consists of 3 lags, the long-run effect will be reached after 3 weeks (see Table S1 ). Therefore, an increase of by one-unit increases the cumulative COVID-19 deaths approximately by ( ,0 + ,1 + ,2 + ,3 ) × 100% percent in the long-run (the exact number is ( ( ,0 + ,1 + ,2 + ,3 ) − 1) × 100%). In comparison, a permanent increase of by one-unit increases the All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. The key assumption that is required to identify a causal effect of UVI on the cumulative COVID-19 deaths is that , − is uncorrelated to , at all points in time. This means that 1) past or future unexplained parts of , must not affect , . These unexplained parts would appear in , and be correlated with , − for some . The key assumption requires further, that 2) there is no factor affecting , which also influences , in addition to country-specific time-constant factors or those variables which we include in the analysis. , but would not be biased due to the behavioral change. The second assumption could be violated by changes in the growth rates of the cumulative COVID-19 deaths with respect to countries over time. Such changes could be growth rates which are 1) country-specific and time-constant, 2) linearly time-varying but similar across All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint countries, 3) non-linearly time-varying but similar across countries, and 4) linearly or nonlinearly time-varying and country-specific. Such changes in the growth rates threaten a causal identification of the effect of UVI because UVI increases over time as summer is coming closer (in the countries on the Northern hemisphere). Our main model specification isolates the effect of UVI from changes in the growth rates of type 1) and type 2) by partialling out any country-specific time-constant differences of growth rates and linear changes of growth rates with respect to time that are similar across countries. In our robustness checks we increase flexibility of the model to also capture country-specific linear differences of growth rates with respect to time as well as some non-linear differences of growth rates with respect to time, which are either similar across countries or even country-specific. Cloud or precipitation index could also violate condition 2). On the one hand, a high cloud coverage and precipitation today decrease the future number of infections because individuals are less likely to go outside and get infected today and die in future. On the other hand, both indices decrease UVI, because they absorb the radiation. Therefore, these two relationships could create an upward bias in the estimate of UVI which we confirm in our analysis (the effect changes by 10% from -0.020 (Model A1.4) to -0.022 (Model A2.4)). Consequently, controlling for the cloud and precipitation index mitigates the bias and makes a causal identification more plausible. The air quality could violate condition 2). The decrease in traffic over time leads to an improvement of the air quality and air quality is likely to reduce the cumulative COVID-19 deaths 2 . Because UVI increases over time, the air quality could be positively correlated with UVI. These relationships could cause an upwards bias in the estimate of UVI meaning that the true effect of UVI is lower that the estimate. Therefore, negative estimates can be considered conservative. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint A country-specific mutation of the virus over time could also violate assumption 2. If a mutation increased the cumulative COVID-19 deaths, then it could positively correlate with UVI due to time.This relationship would create an upward bias. Therefore, negative estimates of the effect of UVI can be considered conservative. Another threat to our identification is a potential systematic false reporting about the cumulative COVID-19 deaths. In the beginning of the crisis it seems likely that not all deaths have been tested for COVID-19 (so that the reported number of COVID-19 deaths is smaller than the true value) while nowadays all deaths which are tested positively for COVID-19 are reported as a COVID-19 death, even though not entirely caused by it (i.e., reported COVID-19 deaths is higher than true value). This positive correlation of measurement error with time would generate an upward bias of the estimate of the effect of UVI. Therefore, negative estimates can be considered conservative. We estimate equation (2) up to a lag of 8 weeks and decided to choose models with 3 lags and all control variables as presented in Table S2 . On the one hand, we did not find major changes with respect to the size and statistical significance of the estimate of UVI. On the other hand, including more lags increases the number of estimates which decreases their accuracy such that a more parsimonious model is favorable. To examine the robustness of our results we change the dependent variable into the casefatality-rate (CFR). CFR is defined as the cumulative COVID-19 deaths divided by the cumulative COVID-19 infections. Therefore, CFR of country day is calculated as CFR , = , , , where , stands for the cumulative COVID-19 infections. It is a common measure to assess the severity of diseases because a high CFR leads to a high number of cumulative All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint COVID-19 deaths. Its advantage to the cumulative COVID-19 deaths is that it relates the cumulative number of deaths to the cumulative number of infections for a disease. Therefore, it helps to isolate the effect of UVI on cumulative COVID-19 deaths from its effect on cumulative COVID-19 infections. Provided that the cumulative COVID-19 infections follow the same model structure as outlined in equation (2), we can express , via an exponential growth model: The interpretation of the coefficients and variables is essentially the same as in equation (2) After applying the same transformation on equation (4) to derive equation (2) Every coefficient of equation (5) we expect UVI to decrease the cumulative COVID-19 infections. The reason is not that fewer people get infected but rather that the infections are less severe which makes it less likely that people get themselves tested. One concern when using the observed case fatality rate All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint that is obtained during an epidemic, is that it likely understates the true case fatality rate . Note, however, that the model is robust to a miss-reported value of as long as the error is multiplicative and time-constant. Suppose the observed case fatality rate (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint or will be positive and , as well as , will first be negative and later (i.e., with larger values for ) become positive. Despite those two forms of measurement-error outlined in equations (7) and (8), our statistical analysis is able to identify the effect of UVI on CFR. The four aforementioned changes in growth rates of cumulative COVID-19 deaths with respect to time threaten a causal identification of the effect of UVI. Therefore, in addition to controlling for time-constant country-specific changes of growth rates as well as linear changes of growth rates that are similar across countries, we increase the flexibility of our main model specification. The more flexible model isolates the effect of UVI from time trends by allowing time to affect the growth rates of all countries linearly or non-linearly in the same or different way. Essentially, in addition to , we also include ( , ) 2 and , into the model, and we interact each of the variables , , ( , ) 2 and , with 64 dummy variables, one for each country, to allow for country-specific linear and non-linear time effects. Start from equation (1). Taking the natural logarithm leads to equation (1. Deducting ln ( , −1 ) leads to equation (1.2) All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. Instead of demeaning equation (1) we can assume that is uncorrelated to all explanatory variables such that a random effects model can be estimated. Under these more restrictive assumptions, is identified. The results are provided in Table S4 . The daily growth rate is estimated to increase COVID-19 deaths by 13.2% [ 0.124 -1]. A robust Hausman test to assess the plausibility of the additional assumptions required to identify is not rejected. Therefore, a random effects model can be used. Table S5 , S6, and S7 outline the estimation results of our main model up to 8 weeks lagged for different sets of control variables. The estimates do not change substantially after we include three or more lags of UVI or the control variables. We find that the model with three lags is favorable and we use this model in our main analysis. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint Tables Table S1: Short- Weeks Passed by Change of + 0 ,0 × 100% 3 or more ( ,0 + ,1 + ,2 + ,3 ) × 100% All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. Time Note: +: p < 0.10, *: p < 0.05, **: p < 0.01. t-statistics based on robust standard errors in parentheses. F-statistic for long-run coefficient in parentheses. L0.UVI stands for the effect of UVI at time t on the cumulative number of COVID-19 deaths at the same time, whereas L1.UVI, L2.UVI and L3.UVI stand for the effect of UVI lagged by one, two, or three weeks respectively. FE stands for country fixed-effects, TCSE stands for time country-specific effects. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint (which was not certified by peer review) 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 May 12, 2020. Note: +: p < 0.10, *: p < 0.05, **: p < 0.01. t-statistics based on robust standard errors in parentheses. L0.UVI stands for the effect of UVI at time t on the cumulative number of COVID-19 deaths at the same time, whereas L1.UVI, L2.UVI and L3.UVI (etc.) stand for the effect of UVI lagged by one, two, or three (etc.) weeks respectively. The same is true for the other variables. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. All rights reserved. No reuse allowed without permission. (which was not certified by peer review) 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 May 12, 2020. . https://doi.org/10.1101/2020.05.06.20093419 doi: medRxiv preprint Evidence that Vitamin D Supplementation Could Reduce Risk of Influenza and COVID-19 Infections and Deaths Preventing a covid-19 pandemic Modulation of the immune system by UV radiation: more than just the effects of vitamin D? Prostate cancer risk and exposure to ultraviolet radiation: further support for the protective effect of sunlight An estimate of premature cancer mortality in the US due to inadequate doses of solar ultraviolet-B radiation An ecologic study of the role of solar UV-B radiation in reducing the risk of cancer using cancer mortality data, dietary supply data, and latitude for European countries Ultraviolet light may contribute to geographic and racial blood pressure differences Skeletal and extraskeletal actions of vitamin D: current evidence and outstanding questions Geographical differences in vitamin D status, with particular reference to European countries Vitamin intakes from supplements and fortified food in German children and adolescents: results from the DONALD study Causal inference using potential outcomes: Design, modeling, decisions Can atmospheric pollution be considered a co-factor in extremely high level of SARS-CoV-2 lethality in Northern Italy? No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity