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  1. Abstract Public health intervention to contain the ongoing COVID-19 pandemic significantly differed by country since the SARS-CoV-2 spread varied regionally in time and in scale. Since vaccinations were not available until the end of 2020 non-pharmaceutical interventions (NPIs) remained the only strategies to mitigate the pandemic spread at that time. Belarus in Europe is one of a few countries with a high Human Development Index where no lockdowns have ever been implemented and only limited NPIs have taken place for a period of time. Therefore, the Belarusian case was evaluated and compared in terms of the mortality burden. Since the COVID-19 mortality was low, the excess overall mortality was studied for Belarus. Since no overall mortality data have been reported past June 2020 the analysis was complemented by the study of Google Trends funeral-related search queries up until August 2021. Depending on the model, the Belarusian mortality for June of 2020 was 29 to 39% higher than otherwise expected with the corresponding estimated excess death was from 2953 to 3690 while the reported COVID-19 mortality for June 2020 was only 157 cases. The Belarusian excess mortality for June 2020 was higher than for all neighboring countries with an excess of 5% for Poland, 5% for Ukraine, 8% for Russia, 11% for Lithuania and 11% for Latvia. The relationship between Google Trends and mortality time series was studied using Granger’s test and the results were statistically significant. The results for Google Trends searches did vary by key phrase with the largest excess of 138% for April 2020 and 148% for September 2020 was observed for a key phrase “coffin”, while the largest excess of 218% for January 2021 was observed for “funeral services”. In summary, there are indications of the excess overall mortality in Belarus, which is larger than the reported COVID-19-related mortality. 
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  2. Motivated by an investigation of the effect of surface water temperature on the presence ofVibrio choleraein water samples collected from different fixed surface water monitoring sites in Haiti in different months, we investigated methods to adjust for unmeasured confounding due to either of the two crossed factors site and month. In the process, we extended previous methods that adjust for unmeasured confounding due to one nesting factor (such as site, which nests the water samples from different months) to the case of two crossed factors. First, we developed a conditional pseudolikelihood estimator that eliminates fixed effects for the levels of each of the crossed factors from the estimating equation. Using the theory of U‐Statistics for independent but non‐identically distributed vectors, we show that our estimator is consistent and asymptotically normal, but that its variance depends on the nuisance parameters and thus cannot be easily estimated. Consequently, we apply our estimator in conjunction with a permutation test, and we investigate use of the pigeonhole bootstrap and the jackknife for constructing confidence intervals. We also incorporate our estimator into a diagnostic test for a logistic mixed model with crossed random effects and no unmeasured confounding. For comparison, we investigate between‐within models extended to two crossed factors. These generalized linear mixed models include covariate means for each level of each factor in order to adjust for the unmeasured confounding. We conduct simulation studies, and we apply the methods to the Haitian data. Copyright © 2016 John Wiley & Sons, Ltd.

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