Adjusting expected deaths for mortality displacement during the COVID-19 pandemic: a model based counterfactual approach at the level of individuals.

BACKGROUND: Near-real time surveillance of excess mortality has been an essential tool during the COVID-19 pandemic. It remains critical for monitoring mortality as the pandemic wanes, to detect fluctuations in the death rate associated both with the longer-term impact of the pandemic (e.g. infection, containment measures and reduced service provision by the health and other systems) and the responses that followed (e.g. curtailment of containment measures, vaccination and the response of health and other systems to backlogs). Following the relaxing of social distancing regimes and reduction in the availability of testing, across many countries, it becomes critical to measure the impact of COVID-19 infection. However, prolonged periods of mortality in excess of the expected across entire populations has raised doubts over the validity of using unadjusted historic estimates of mortality to calculate the expected numbers of deaths that form the baseline for computing numbers of excess deaths because many individuals died earlier than they would otherwise have done: i.e. their mortality was displaced earlier in time to occur during the pandemic rather than when historic rates predicted. This is also often termed "harvesting" in the literature. METHODS: We present a novel Cox-regression-based methodology using time-dependent covariates to estimate the profile of the increased risk of death across time in individuals who contracted COVID-19 among a population of hip fracture patients in England (N = 98,365). We use these hazards to simulate a distribution of survival times, in the presence of a COVID-19 positive test, and then calculate survival times based on hazard rates without a positive test and use the difference between the medians of these distributions to estimate the number of days a death has been displaced. This methodology is applied at the individual level, rather than the population level to provide a better understanding of the impact of a positive COVID-19 test on the mortality of groups with different vulnerabilities conferred by sociodemographic and health characteristics. Finally, we apply the mortality displacement estimates to adjust estimates of excess mortality using a "ball and urn" model. RESULTS: Among the exemplar population we present an end-to-end application of our methodology to estimate the extent of mortality displacement. A greater proportion of older, male and frailer individuals were subject to significant displacement while the magnitude of displacement was higher in younger females and in individuals with lower frailty: groups who, in the absence of COVID-19, should have had a substantial life expectancy. CONCLUSION: Our results indicate that calculating the expected number of deaths following the first wave of the pandemic in England based solely on historical trends results in an overestimate, and excess mortality will therefore be underestimated. Our findings, using this exemplar dataset are conditional on having experienced a hip fracture, which is not generalisable to the general population. Fractures that impede mobility in the weeks that follow the accident/surgery considerably shorten life expectancy and are in themselves markers of significant frailty. It is therefore important to apply these novel methods to the general population, among whom we anticipate strong patterns in mortality displacement - both in its length and prevalence - by age, sex, frailty and types of comorbidities. This counterfactual method may also be used to investigate a wider range of disruptive population health events. This has important implications for public health monitoring and the interpretation of public health data in England and globally.

Inequalities in excess premature mortality in England during the COVID-19 pandemic: a cross-sectional analysis of cumulative excess mortality by area deprivation and ethnicity.

OBJECTIVES: To examine magnitude of the impact of the COVID-19 pandemic on inequalities in premature mortality in England by deprivation and ethnicity. DESIGN: A statistical model to estimate increased mortality in population subgroups during the COVID-19 pandemic by comparing observed with expected mortality in each group based on trends over the previous 5 years. SETTING: Information on deaths registered in England since 2015 was used, including age, sex, area of residence and cause of death. Ethnicity was obtained from Hospital Episode Statistics records linked to death data. PARTICIPANTS: Population study of England, including all 569 824 deaths from all causes registered between 21 March 2020 and 26 February 2021. MAIN OUTCOME MEASURES: Excess mortality in each subgroup over and above the number expected based on trends in mortality in that group over the previous 5 years. RESULTS: The gradient in excess mortality by area deprivation was greater in the under 75s (the most deprived areas had 1.25 times as many deaths as expected, least deprived 1.14) than in all ages (most deprived had 1.24 times as many deaths as expected, least deprived 1.20). Among the black and Asian groups, all area deprivation quintiles had significantly larger excesses than white groups in the most deprived quintiles and there were no clear gradients across quintiles. Among the white group, only those in the most deprived quintile had more excess deaths than deaths directly involving COVID-19. CONCLUSION: The COVID-19 pandemic has widened inequalities in premature mortality by area deprivation. Among those under 75, the direct and indirect effects of the pandemic on deaths have disproportionately impacted ethnic minority groups irrespective of area deprivation, and the white group the most deprived areas. Statistics limited to deaths directly involving COVID-19 understate the pandemic's impact on inequalities by area deprivation and ethnic group at younger ages.

Evaluation of stability of directly standardized rates for sparse data using simulation methods.

BACKGROUND: Directly standardized rates (DSRs) adjust for different age distributions in different populations and enable, say, the rates of disease between the populations to be directly compared. They are routinely published but there is concern that a DSR is not valid when it is based on a "small" number of events. The aim of this study was to determine the value at which a DSR should not be published when analyzing real data in England. METHODS: Standard Monte Carlo simulation techniques were used assuming the number of events in 19 age groups (i.e., 0-4, 5-9, ... 90+ years) follow independent Poisson distributions. The total number of events, age specific risks, and the population sizes in each age group were varied. For each of 10,000 simulations the DSR (using the 2013 European Standard Population weights), together with the coverage of three different methods (normal approximation, Dobson, and Tiwari modified gamma) of estimating the 95% confidence intervals (CIs), were calculated. RESULTS: The normal approximation was, as expected, not suitable for use when fewer than 100 events occurred. The Tiwari method and the Dobson method of calculating confidence intervals produced similar estimates and either was suitable when the expected or observed numbers of events were 10 or greater. The accuracy of the CIs was not influenced by the distribution of the events across categories (i.e., the degree of clustering, the age distributions of the sampling populations, and the number of categories with no events occurring in them). CONCLUSIONS: DSRs should not be given when the total observed number of events is less than 10. The Dobson method might be considered the preferred method due to the formulae being simpler than that of the Tiwari method and the coverage being slightly more accurate.

A method for modelling GP practice level deprivation scores using GIS.

BACKGROUND: A measure of general practice level socioeconomic deprivation can be used to explore the association between deprivation and other practice characteristics. An area-based categorisation is commonly chosen as the basis for such a deprivation measure. Ideally a practice population-weighted area-based deprivation score would be calculated using individual level spatially referenced data. However, these data are often unavailable. One approach is to link the practice postcode to an area-based deprivation score, but this method has limitations. This study aimed to develop a Geographical Information Systems (GIS) based model that could better predict a practice population-weighted deprivation score in the absence of patient level data than simple practice postcode linkage. RESULTS: We calculated predicted practice level Index of Multiple Deprivation (IMD) 2004 deprivation scores using two methods that did not require patient level data. Firstly we linked the practice postcode to an IMD 2004 score, and secondly we used a GIS model derived using data from Rotherham, UK. We compared our two sets of predicted scores to "gold standard" practice population-weighted scores for practices in Doncaster, Havering and Warrington. Overall, the practice postcode linkage method overestimated "gold standard" IMD scores by 2.54 points (95% CI 0.94, 4.14), whereas our modelling method showed no such bias (mean difference 0.36, 95% CI -0.30, 1.02). The postcode-linked method systematically underestimated the gold standard score in less deprived areas, and overestimated it in more deprived areas. Our modelling method showed a small underestimation in scores at higher levels of deprivation in Havering, but showed no bias in Doncaster or Warrington. The postcode-linked method showed more variability when predicting scores than did the GIS modelling method. CONCLUSION: A GIS based model can be used to predict a practice population-weighted area-based deprivation measure in the absence of patient level data. Our modelled measure generally had better agreement with the population-weighted measure than did a postcode-linked measure. Our model may also avoid an underestimation of IMD scores in less deprived areas, and overestimation of scores in more deprived areas, seen when using postcode linked scores. The proposed method may be of use to researchers who do not have access to patient level spatially referenced data.