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Association of Extreme Heat With All-Cause Mortality in the Contiguous US, 2008-2017

Key Points Question Is there an association between extreme heat and all-cause mortality in the US? Findings In this cross-sectional study using a longitudinal analysis of county-level monthly all-cause mortality rates from all counties in the contiguous US from 2008 to 2017, each additional extreme heat day in a month was associated with 0.07 additional death per 100 000 adults. Meaning These findings suggest that from 2008 to 2017 in the contiguous US, extreme heat was associated with higher adult all-cause mortality rates.


eAppendix 1: Spatial Empirical Bayes Smoothing
Mortality rate estimates from areas with small populations are prone to instability with potentially large changes seen in the mortality rate due to a small change in the absolute number of deaths. This may not provide an accurate assessment of the risk of mortality in these areas. To account for this instability, we used spatial empirical Bayes smoothing of the mortality rates. Empirical Bayes smoothing combines the raw mortality rate with a reference mortality rate and calculates a weighted average of the two with weights that are directly proportional to the population at risk. Therefore, counties with small populations will have their rates adjusted to a greater degree than counties with a larger population. As in other Bayesian frameworks, a prior distribution is specified, and after observing data, a posterior distribution is obtained.
The standard approach for Bayesian estimation of rates is to specify a Poisson distribution for the observed counts (deaths in this case) and a Gamma distribution prior. In an Empirical Bayes approach, parameters for the prior Gamma distribution are estimated from the actual data. The estimated prior rate can be considered the reference rate.
The empirical Bayes smoothed rate for a given county i is estimated using the following equation: where ω is a weight parameter calculated as follows: where σ 2 and μ represent the variance and mean of the prior distribution and Populationi refers to the population of county i.
μ is the reference mortality rate and is calculated as follows: and the σ 2 as follows: where n refers to the number of counties in the reference sample.
In spatial empirical Bayes, the mean and variance of the prior are estimated from a localized group of observations rather than the global sample (i.e. all counties in the US). In our analysis, we used all neighboring counties as the reference group for each county.

eAppendix 3: CDC Social Vulnerability Index
The CDC Social Vulnerability Index (SVI) is a measure of an area's vulnerability to public health hazards. 1 The SVI has been associated with health outcomes in previous studies. [2][3][4] The SVI consists of 15 variables grouped into 4 categories: 1) socioeconomic, 2) household composition and disability, 3) minority status and language, and 4) housing and transportation. Each area is ranked on a scale of 0 to 1 on each factor, and the SVI is the unweighted mean of these ranks. A higher value indicates greater vulnerability. All variables are derived from US Census Bureau estimates. The 2014 version of the SVI was used for this analysis.

Proportion of residents with income below poverty level
Proportion of residents unemployed

Median household income
Proportion of residents without high school diploma

Household Composition and Disability Index
Proportion of residents who are 65 years of age or older Proportion of residents who are 17 years of age or younger Proportion of civilian residents with a disability Proportion of households that are single-parent households

Minority Status and Language Index
Proportion of residents who are not Non-Hispanic White Proportion of residents who are speaks English "Less than Well"

eAppendix 4: Fixed-Effects Model
The fixed effects, or within, estimator is an econometric technique to analyze longitudinal or panel data. This method examines the association between change in the outcome with change in the predictor variable within each subject. The inclusion of subject fixed effects (counties in this analysis) controls for both observed and un-observed time-invariant confounders. The inclusion of time fixed effects accounts for secular time trends that are common for all subjects.
The following linear fixed effects model was used: Where is the mortality for county i, in month m (May, June, July, August, September), in year t (2008 to 2017), is a vector of time-varying independent variables, is the county fixed effect, is the month fixed effect, is the year fixed effect, and is the error term.