Excess deaths, baselines, Z-scores, P-scores and peaks

Abstract: The recent Covid-19 epidemic has lead to comparisons of the countries suffering from it. These are based on the number of excess deaths attributed either directly or indirectly to the epidemic. Unfortunately the data on which such comparisons rely are often incomplete and unreliable. This article discusses problems of interpretation of data even when the data is largely accurate and delayed by at most two to three weeks. This applies to the Office of National Statistics in the UK, the Statistisches Bundesamt in Germany and the Belgian statistical office Statbel. The data in the article is taken from these three sources. The number of excess deaths is defined as the number of deaths minus the baseline, the definition of which varies from country to country. In the UK it is the average number of deaths over the last five years, in Germany it is over the last four years and in Belgium over the last 11 years. This means that in all cases the individual baselines depend strongly on the timing and intensity of adverse factors such as past influenza epidemics and heat waves. This makes cross-country comparisons difficult. A baseline defined as the number the number of deaths in the absence of adverse factors can be operationalized by taking say the 10\% quantile of the number of deaths. This varies little over time and European countries within given age groups. It therefore enables more robust and accurate comparisons of different countries. The article criticizes the use of Z-scores which distort the comparison between countries. Finally the problem of describing past epidemics by their timing, that is start and finish and time of the maximum, and by their effect, the height of the maximum and the total number of deaths, is considered.