*2.2. Mortality Calculations*

Household weighting values in the EHS were used to estimate the mean and distribution of occupant temperature exposures across the West Midlands housing stock. As there is no spatial information for the EHS, we assume the modelled households have equal distributions of UHI temperature exposures. From this, a dwelling-specific indoor temperature anomaly relative to the regional population-weighted mean was calculated:

$$T\_{\text{max},k,d}^{\*} = T\_{\text{max},\text{out},d} + T\_{\text{Indoor} \atop \text{Anomaly},k,d} \tag{1}$$

where *Tmax*,*out*,*<sup>d</sup>* is the two-day rolling mean maximum outdoor temperature for day *d*; *TIndoor Anomaly*,*k*,*<sup>d</sup>* is a positive or negative temperature anomaly representing the deviation in estimated two-day rolling mean maximum indoor temperature for dwelling *k* from the population-mean rolling maximum indoor temperature on day *d* for the West Midlands; and *T*∗ *max*,*k*,*<sup>d</sup>* is the temperature to which occupants are exposed on day *d* in household *k*. For adaptation scenarios, anomalies were calculated relative to the mean of the unadapted stock.

Calculations of heat-related mortality were based on applying region-specific temperaturemortality functions for the West Midlands to the EHS occupant age data and corresponding estimated dwelling indoor temperatures. Heat-associated mortality is described in terms of Relative Risk (RR), or the ratio of the probability of mortality occurring in a heat-exposed group to the probability of mortality in an unexposed group. The all-age heat-mortality RR for the West Midlands was derived from Armstrong et al. [38] from which age-specific (0–64, 65–74, 75–84, 85+) temperature-mortality slopes were derived using the age-specific RRs for England and Wales published by Gasparrini et al. [1]. The underlying age-specific all-cause mortality rates by season were obtained from the Office for National Statistics (ONS); here we adjust these to reflect summer rates. Dwelling-specific heat mortality was then calculated as:

$$D\_{k,d} = \sum\_{i} \left[ occumpants\_{i,k} \times deathrate\_i \times \left( RR\_{heat,i}^{\ \ (T\_{max,k,d}^\* - 23 \ ^\circ \mathbb{C})} - 1 \right) \right] \tag{2}$$

where *occupantsi*,*<sup>k</sup>* is the number of individuals of age-group *i* in dwelling *k*; *deathratei* is the summertime daily mortality rate per person for age-group *i*; *RRheat*,*<sup>i</sup>* is the relative risk (RR) of mortality due to temperature for age group *i*; and 23 ◦C is the estimated regional heat mortality threshold for the West Midlands [38]. Readers are referred to Taylor et al. [25] for a detailed description of mortality calculations.
