## 1. Data sources

Age-standardised mortality rates are calculated for vaccination status groups using the Public Health Data Asset (PHDA) dataset. The PHDA is a linked dataset combining the 2011 Census, the General Practice Extraction Service (GPES) data for pandemic planning and research, and the Hospital Episode Statistics (HES). We linked vaccination data from the National Immunisation Management Service (NIMS) to the PHDA based on NHS number, and linked data on positive coronavirus (COVID-19) Polymerase Chain Reaction (PCR) tests from Test and Trace to the PHDA, also based on NHS number.

The PHDA dataset contains a subset of the population and allows for analyses to be carried out that require a known living population with known characteristics. These characteristics include age-standardised mortality rates (ASMRs) by vaccination status and the use of variables such as health conditions and census characteristics.

Nôl i'r tabl cynnwys## 2. Definitions

### Deaths involving COVID-19

For this analysis we define a death as involving coronavirus (COVID-19) if either of the ICD10 codes, U07.1 (COVID-19, virus identified) or U07.2 (COVID-19, virus not identified), are mentioned on the death certificate. In contrast to the definition used in the weekly deaths released, deaths where the ICD10 code U09.9 (Post-COVID-19 condition, where the acute COVID-19 had ended before the condition immediately causing death occurred) is mentioned on the death certificate and neither of the other two COVID-19 codes mentioned are not included, they are likely to be the result of an infection caught a long time previously. Therefore, they are not linked to the vaccination status of the person at date of death. Deaths involving U10.9 (Multisystem inflammatory syndrome associated with COVID-19) where U07.1 or U07.2 are mentioned are also excluded. This is a rare complication affecting children and there are no such deaths in our dataset for the data released in "Deaths involving COVID-19 by vaccination status and vaccine manufacturer, England: deaths occurring between 1 Jan and 2 July 2021".

### Vaccination status and age

COVID-19 vaccination status is determined on the date of death occurrence if a death has occurred, and on the last day of each week if not. Possible values are:

unvaccinated

vaccinated with the first dose only, date of death/last day of week is within 21 days of vaccination

vaccinated with the first dose only, date of death/last day of week is 21 days or more after vaccination

vaccinated with both the first and second dose, date of death/last day of week is date of second vaccination or later

Age is age in years on date of death if a death has occurred, or the age on the last day of each week if not. Children aged 10 years and under are not included when calculating the aged-standardised mortality rate (ASMR), as numbers are very small because of the linkage to the 2011 census.

Nôl i'r tabl cynnwys## 4. Age-standardised mortality rates

Age-standardised mortality rates (ASMRs) are used to allow for comparisons to be made between populations that may contain different overall population sizes and proportions of people of different ages. The 2013 European Standard Population is used to standardise age-specific rates to a consistent population. The formula used to calculate the weekly age-standardised mortality rates per 100,000 for week w is:

where:

*w*is the week number for which we calculate the ASMR*i*is the age group*ESP*is the standard population for age group_{i}*i**D*is the number of deaths for age group_{i,w}*i*occurring in week*w**P*is the population for age group_{i,w}*i*alive at the beginning of the week*w*

To calculate the ASMRs by vaccination status, those aged under 10 years were not used, as the associated dataset includes only those aged nine years and over because it is linked to the 2011 census.

### Confidence limits

95% confidence limits are calculated for the age-standardised mortality rates (ASMRs). You can find out more about confidence limits in this Population Health Metrics publication. For ASMRs where the total count of deaths is less than 100, Dobson's method is used, and where the total count of deaths is at least 100, the normal approximation is used.

With Dobson's method:

Σ__{i} D_{i,w}_ is the total count of deaths across all age/sex groups. *0 _{upper}* and

*0*are the upper and lower 95% confidence limits for the total count of deaths based on the Poisson distribution.

_{lower}*σ(ASMR _{w})* is the variance of the age-standardised mortality rate

with the normal approximation:

where *σ(ASMR _{w})* is the standard error of the ASMR, which is equal to the square root of the variance of the ASMR.