In the county that counts heat deaths best, a statistical model found 57% more of them

Every summer produces two kinds of heat death number. One comes from death certificates and medical examiners — cases where a human being looked at the circumstances and wrote heat down. The other comes from a statistical model that compares how many people died on hot days with how many would have been expected to die otherwise. The second number is almost always bigger, and readers are rarely told why.

A study published in April in the American Journal of Public Health is unusually useful because it runs both against the same population, in the one American county with the strongest claim to counting heat deaths properly.

The comparison

Researchers examined 126,854 deaths that occurred in Maricopa County, Arizona, during the 2019 to 2023 heat seasons, defined as April through October [s1]. They fitted a quasi-Poisson regression with distributed lag nonlinear models, estimating the cumulative relative risk of all-cause mortality against population-weighted daily mean temperature over a three-day lag, using 77°F as the reference [s1].

At 99°F — the 95th percentile of population-weighted daily mean temperature in that county — daily all-cause mortality was 11% higher than at 77°F, with a confidence interval of 7% to 16% [s1]. Summed across the five heat seasons, the model attributed 3,036 deaths to heat, with a 95% empirical confidence interval running from 968 to 4,887 [s1].

That is 57% more deaths than the county's epidemiological heat surveillance identified over the same period [s1].

Why the two numbers differ

The gap is not evidence that surveillance is failing. It is evidence that the two methods are answering different questions.

Case surveillance asks whether heat can be identified as a cause or contributing cause in an individual death. It produces a list of people. A distributed lag model asks whether the death rate on hot days exceeds the rate the same population produces on temperate days, and converts that excess into a count. It produces a population estimate with no names attached.

The authors state the implication directly: the effects of heat on mortality can be indirect and are incompletely captured by routine surveillance [s1]. A death from cardiac arrest during a heat wave is a cardiac arrest on the certificate. The model catches it; the certificate does not.

Note also what the confidence interval does. The central estimate is 3,036, but the interval spans 968 to 4,887 [s1]. A model that produces a bigger number than surveillance also produces a much less precise one. Reporting the point estimate without the interval overstates what the method delivers.

The method is not one method

The choices inside "a statistical model" turn out to be wide open. A scoping review published in March in JBI Evidence Synthesis analysed 197 studies of heat-related excess mortality and catalogued what they actually used [s2].

Almost all — 97% — used daily death data, and 77% used daily temperature data [s2]. Beyond that, consensus thins fast. Most studies used more than one temperature indicator: mean temperature appeared in 123 studies, daily maximum in 104, daily minimum in 79, diurnal temperature change in 8, and other indicators in 20 [s2]. Environmental parameters such as relative humidity, ozone, fine dust and wind were included in 58% of studies [s2].

The statistical machinery varied too. Distributed lag nonlinear models were used in 68 studies, generalised linear models in 52, and generalised additive models in 28, with some studies using more than one [s2]. Distributed lag models have gained popularity since 2010 [s2].

The review's conclusion is that the diversity in data sources, temperature indicators, environmental parameters and modelling approaches underscores the need for standardised, adaptable methods [s2]. Put less politely: two competent teams analysing the same heat wave can legitimately arrive at different totals, and the published literature does not currently let a reader tell how much of any difference is method rather than weather.

The reference point moves as well

Every excess mortality estimate needs a temperature at which mortality risk is lowest — the minimum mortality temperature. It is the baseline the excess is measured against, and it is usually treated as a single number for a whole population.

A multi-country study published in June in Environmental Research suggests that is a simplification with consequences. Analysing daily mean temperature and mortality across 667 communities in 39 countries from 1990 to 2019, the authors estimated minimum mortality temperature separately by cause of death and age group [s3].

It was highest for cardiovascular mortality, at 22.1°C (95% CI 20.9–23.4°C). Respiratory causes sat 0.87°C lower and non-cardiorespiratory causes 0.66°C lower [s3]. Expressed as a percentile of each community's own temperature distribution, the pattern held: 75% for cardiovascular mortality (95% CI 73–78%), five percentage points lower for respiratory and four lower for non-cardiorespiratory causes [s3].

Age shifted it further. Minimum mortality temperature rose with age for cardiovascular causes by 0.19°C per 10 years (95% CI 0.14–0.23) and for non-cardiorespiratory causes by 0.13°C per 10 years (95% CI 0.09–0.16) [s3]. The patterns were generally consistent across geographical regions [s3].

The authors' conclusion is that the optimal temperature varies across population subgroups [s3]. An estimate built on one population-wide baseline is therefore assuming away real variation between the causes and age groups it is aggregating.

What to take from it

None of this makes model-based heat mortality estimates unreliable. The Maricopa result is the opposite of a debunking — it is a well-instrumented county demonstrating that its own careful case counting misses a substantial share of the burden [s1].

What it does mean is that a heat death figure should be read as the output of a specified method rather than as a census. When two figures for the same summer disagree, the first question is not which is right but which question each was answering, over what lag, against what baseline, and with what interval around it.