calculate_excess_time_series: Calculate excess mortality time series for a single...
In njhenry/covidemr: Tools for Mapping COVID Excess Mortality

Description Usage Arguments Details Value

Given draws of a baseline mortality rate, a starting population, and weekly deaths, calculate excess deaths, SMRs, and estimated population by draw and over the study time period. NOTE: This is a child function to estimate these quantities for a single sub-population, and should be called repeatedly to estimate excess mortality across different groups.

1	calculate_excess_time_series(baseline_mat, starting_pop, obs_deaths_vec)

`baseline_mat`	[numeric] A matrix of the baseline mortality rate by week, where each row corresponds to one week of the time series (in order) and each column corresponds to a predictive draw of the baseline mortality rate for that week.
`starting_pop`	[numeric] A scalar value giving the population size at the beginning of the excess mortality analysis.
`obs_deaths_vec`	[numeric] A vector of observed deaths for each week of the excess mortality analysis. This vector should be the same length as the number of rows in the 'baseline_mat'.

To calculate excess mortality in a time series, the effect of mortality changes on the population denominator must be considered. Without complete information about how many people are entering an age group by aging in or (for the youngest age group) through birth as opposed to the number of people aging out of an age group or dying each week, we make the assumption that at baseline mortality, the size of this population subgroup would have remained approximately stable. This is a reasonable assumption for most populations on the time scale of a few weeks. "Baseline mortality" here is estimated as the mean mortality *rate* calculated across all predictive draws for baseline mortality, multiplied by the population. The difference between the observed number of deaths and the expected baseline mortality will be subtracted from the population of future weeks. For example:

Starting population: 1,000 Mortality: week | mean_baseline_rate | observed_deaths —–+——————–+—————- 1 | 0.01 | 200 2 | 0.02 | 100 3 | 0.01 | 10

Week 1: * Estimated population size = starting population, 1,000 * Baseline deaths = 1,000 * 0.01 = 10 * Excess deaths = 200 - 10 = 190 Week 2: * Estimated population size = 1,000 - 190 = 810 * Baseline deaths = 810 * 0.02 = 16.2 * Excess deaths = 100 - 16.2 = 83.8 Week 3: * Estimated population size = 810 - 83.8 = 726.2 * Baseline deaths = 726.2 * 0.01 = 7.262 * Excess deaths = 10 - 7.262 = 2.738

Note that in the example, there are excess deaths measured in week 3. This would not be the case for a time series analysis where the population was not adjusted for previous excess deaths.

An excess mortality analysis is first run comparing against the mean baseline, to estimate population over the time series, and then comparing to baseline mortality by draw to calculate SMRs and excess deaths in a way that preserves uncertainty.

A list with three items: - 'pop': Vector of estimated adjusted population for each week of the time series. The first week population will always be equal to the value of 'starting_pop'. - 'baseline_deaths': A numeric matrix of size (num weeks) x (num draws) giving the estimated NUMBER of baseline deaths, a count, for each week and draw. - 'smrs': A numeric matrix of size (num weeks) x (num draws) giving the estimated standardized mortality ratio associated with each week and draw. - 'excess_deaths': A numeric matrix of size (num weeks) x (num draws) giving the estimated number of excess deaths, a count, for each week and draw.

njhenry/covidemr documentation built on Feb. 2, 2022, 2:31 a.m.