Impact of High Temperatures on Mortality: Is There an Added Heat Wave Effect? : Epidemiology

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Impact of High Temperatures on Mortality

Is There an Added Heat Wave Effect?

Hajat, Shakoor*; Armstrong, Ben*; Baccini, Michela; Biggeri, Annibale; Bisanti, Luigi; Russo, Antonio; Paldy, Anna§; Menne, Bettina; Kosatsky, Tom

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Epidemiology 17(6):p 632-638, November 2006. | DOI: 10.1097/01.ede.0000239688.70829.63
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The 2003 heat wave of western Europe was a dramatic illustration of the dangers of exposure to hot weather. A total estimated burden of well over 25,000 excess deaths was attributed to this one event alone,1–3 and many governments across Europe are now recognizing the need for health warning systems to minimize the impact of future heat waves, especially with an increasingly warm and less stable climate.4

Interventions to reduce the effects of heat on mortality requires an understanding of the temperature-mortality relationship. The focus of interventions on “heat waves” (sustained exceptionally high temperatures) raises questions on which there has been little research. In particular, do heat waves carry mortality risks not predicted by models for smooth increases in risk by daily temperature? How important are heat waves in comparison to more moderate and unsustained heat not occurring during heat waves?

Epidemiologic studies assessing the effects of high ambient temperature on population-level mortality traditionally incorporate either heat episode analyses or time-series regression analyses.5 Heat episode analyses describe mortality during specific heat wave events and generally find substantial excesses in mortality during the heat episode.6–11 Alternatively, regression models of time-series data are used to quantify the heat-related mortality observed throughout the summer; these have shown that, in countries with a temperate climate, mortality rises with temperature in a general linear or smooth fashion once temperatures reach certain threshold levels.12–16 The overlap between the health effects observed in these 2 types of studies has been little studied.

By analyzing extended time-series data sets of daily mortality counts, and specifically modeling heat wave periods defined using a variety of specifications, we explored whether the effects of hot days are increased when they occur over a period of sustained, exceptionally high temperatures. We also estimated what fraction of all deaths due to heat occurred during these specific heat wave periods.



Daily counts of all-cause mortality in all ages excluding violent deaths (International Classification of Diseases Ninth Revision [ICD-9]) were obtained for 3 major European cities of differing climatic conditions: London (England), Budapest (Hungary), and Milan (Italy). For each city, counts were also obtained for the following separate broad cause-of-death categories: cardiovascular (ICD-9: 390–459), respiratory (ICD-9: 460–519), and other nonviolent deaths. The time-series of daily death data available for analysis in each city covered long time periods: 28 years in the case of London (1976–2003), 31 years for Budapest (1970–2000), and 18 years for Milan (1985–2002).

For the same periods, daily maximum and minimum temperature (plus mean temperature for Milan) and relative humidity were obtained for each location. For each city, the monitoring station was situated near an airport. For London and Budapest, daily average temperatures were computed as the mean of the daily maximum and minimum value. In addition, mean apparent temperature (a measure of perceived exposure) was derived using the following formula17–19

where Ta is air temperature and Td is dew point temperature (derived from relative humidity).

To investigate sensitivity of results to inclusion of air pollution data, we also obtained daily mean concentrations of black smoke (μg/m3) and ozone (parts per billion) for London from the U.K. National Air Quality Archive. A single series was derived from 3 monitoring stations across London with missing values being replaced by the mean level of the remaining stations using the APHEA algorithm.20 Pollution measures were not available for the time periods in Milan or Budapest.

Statistical Methods

We examined daily mortality in relation to hot weather using a generalized estimating equations (GEE) approach.21 For each series, only the summer months (June to September) were considered to minimize confounding by cold temperature. We modeled the marginal relationship between daily mortality count and temperature, adjusted for confounders, assuming independence among summers and treating serial dependence of daily number of deaths within each summer as a nuisance parameter. We specified a first-order autoregressive structure within summer and assumed a Poisson distribution for the outcome variable. Any long-term trends in the series were modeled using natural cubic splines of time allowing one degree of freedom (df) for every 5 years of data. To allow for within-summer seasonal variation not explained by temperature, we fit natural cubic splines of day-in-year (4 df) constrained to be the same over all years. Relative humidity was also controlled for using natural cubic splines (3 df). Humidity was not modeled separately when apparent temperature was the main exposure. As a sensitivity analysis, we reran models without constraining the within-year seasonal variability to be the same for each year. We also reduced model complexity by adjusting for time-related confounding by means of indicator variables for calendar year and month and by modeling humidity using linear and quadratic terms.

The smooth heat effect was modeled using a variety of specifications ranging from simple to more complex models:

  1. Simple linear threshold models, ie, models that assume a log-linear increase in risk above a heat threshold. The maximum likelihood estimate for the threshold and a corresponding profile confidence interval was obtained separately for each city by calculating model likelihoods over a grid of threshold values at all possible values of temperature in increments of 0.1°C;
  2. Natural cubic splines of temperature on 3 df to model moderate nonlinearity of the temperature effect on mortality; and
  3. Natural cubic splines of temperature on 6 df to model greater nonlinearity.

Temperature splines were created using the whole range of temperature. (In sensitivity analysis, restricting splines to values above the identified threshold changed results little.) Interior knots for temperature splines were at equally spaced intervals (rather than using quantiles) of the temperature variable.

Finally, we incorporated a separate indicator term to model “heat wave” periods. The coefficient from this indicator term was used to estimate any “heat wave” effects in excess of those identified by the smooth heat effect standard in time-series models.

No standard definition of a heat wave exists for most European countries. We used a combination of intensity and duration to model heat wave periods. Sensitivity of results to different specifications of both intensity and duration was considered:

  • Intensity: 98th percentile, 99th percentile, or 99.5th percentile of daily temperatures in whole data set (ie, over all of the year).
  • Duration: a minimum of 2 or 4 consecutive days with temperature above the intensity criterion.

We estimated both heat wave and general heat effects using daily minimum, daily maximum, daily mean, or daily apparent temperature. In addition, each measure was considered as temperature on the same day as the day of death (lag 0) and also as an average value up to 2 days before death (lags 0–2) to capture any delayed effects of heat on mortality.

The percentage of all annual deaths attributable to heat was calculated for both the heat wave and general temperature terms by averaging over all days the fraction attributable to heat ([RR-1]/RR) weighting the average by the number of deaths on each day.22 All analyses were conducted in Stata 8.2 (Stata Corp., College Station, TX).


Table 1 summarizes the health and meteorological variables in the 3 cities. Milan had the highest mean temperature and London the lowest. In all cities, a high proportion of summertime deaths was from cardiovascular causes.

City Characteristics

Figure 1 shows the relationship between mean temperature and the relative risk of death in London as estimated under 3 smooth model specifications: linear slope above threshold, 3 df cubic spline, and 6 df cubic spline. The splines suggest some degree of nonlinearity in the heat-mortality relationship with a steeper slope at higher temperatures.

Relationship between mean temperature and relative risk of mortality (righthand axis) in London estimated using 3 model specifications. Dots represent individual observations of daily mortality (lefthand axis).

Table 2 shows estimated smooth heat and heat wave effects based on the above models with heat waves defined as exceeding the 99th percentile temperature on at least 2 days. (Details on the number of identified heat wave periods and the number of days making up these periods are provided in the footnote to Table 2.) The top half of the table presents the effects on mortality of heat on the same day, and the bottom half presents the cumulative effects of temperature on the day itself and the 2 previous days as identified by the mean of that period. For lag 0, the temperature at which heat-related mortality effects are observed was highest in Milan (23.4°C) and lowest in Budapest (19.6°C) despite the fact that Budapest's average summertime temperature was higher than London's.

Heat Effects: Smooth Model Slopes and Heat Wave Increments (all Nonaccidental Deaths)

In the models without specific terms for heat waves, a strong heat effect was observed in all 3 cities. Mortality in London increased 5.1% for every degree increase in temperature above the identified threshold (95% confidence interval [CI] = 4.6 to 5.6). This estimate was slightly higher for Milan and much lower for Budapest (although the estimated slope will, to some extent, be dependent on the threshold value).

When heat wave terms were explicitly modeled, the heat effect was reduced slightly while an additional “heat wave” effect was observed (Table 2). This additional effect was estimated to be a 5.5% increase on heat wave days in the case of London (95% CI = 2.2 to 8.9), 9.3% for Budapest (5.8 to 13.0), and 15.2% for Milan (5.7 to 22.5). These heat wave effects reduced slightly when the linear assumption of the heat slope was relaxed by using either 3 df or 6 df cubic splines instead, except in the case of the 6 df model in London where the heat wave effect was larger than that estimated in the linear model.

Regarding the bottom half of the table, the heat slopes associated with cumulative mortality were increased compared with the same-day estimates, suggesting that temperature exposure on a given day has some additional impact on mortality on the next 2 days. The wave effects were considerably diminished in these models.

Figure 2 shows estimates of the “heat wave” increment from the linear-slope models when varying percentiles are used in the definition of the heat wave term. In general, “heat wave effect” estimates increased as the percentile of temperature was increased, except in the case of the 99.5th percentile in Milan when it was much reduced.

Heat wave effects estimated from linear slope models with varying percentiles of temperature used in the heat wave definition.

Figure 3 shows heat wave effects by cause of death based on linear-slope models with heat waves defined at the 99th percentile. In Milan and London, heat wave effect estimates were biggest for respiratory deaths and cardiovascular deaths. In Budapest, no heat wave effect was observed for respiratory deaths.

Heat wave effects estimated from linear slope models by cause of death. Heat wave defined using 99th percentile.

The patterns of heat wave effects were little changed if minimum temperature, maximum temperature, or apparent temperature (mean, minimum, or maximum) was used in place of mean temperature. Mean temperature gave consistently and substantially a better fit to mortality than did other indicators (judged by model deviance). When humidity was excluded from the model, mean (or minimum or maximum) apparent temperature remained a poorer predictor of mortality in Milan and London, whereas in Budapest, mean and maximum apparent temperature provided the better fit.

Repeating analyses with heat waves defined as 4 consecutive days above the intensity criterion also left patterns of heat wave effects largely unchanged. Also, all results were similar when within-year variability was allowed to vary across years. For example, in Milan, the wave increment from the linear slope and wave model in Table 2 changed from 15.2% (5.7 to 22.5) to 14.7% (5.4 to 24.9). Furthermore, simplification of the regression models by using indicators for month and year to control for season and trend, and linear and quadratic terms to model the humidity effect, resulted in very little change to the estimates—the wave increment from the same model changed to 15.9% (6.4 to 26.3).

The heat and heat wave estimates in London were largely unchanged when daily levels of same-day black smoke were added to the model. However, the heat wave estimates associated with deaths from respiratory disease were reduced slightly when daily same-day ozone measures were controlled for (not shown).

Table 3 shows the percentage of all annual deaths attributable to heat, first including heat-related deaths on all summer days and then just during heat waves. In London, 0.39% of all deaths could be attributed in the linear threshold model (first row) to heat with slightly less than half of this fraction occurring during the time of the heat wave periods (0.15% as defined by the 99th percentile). Similar fractions were obtained when terms for heat waves were explicitly modeled in addition to the heat slope (second row). In Milan and Budapest, the fraction of deaths attributable to heat was higher than for London, but less than one third of these could be attributed to heat wave episodes defined by the 98th percentile (less than one fifth if waves were defined at the 99th percentile).

Percentage of Total (Year-long) Deaths Attributable to Heat (Overall and Only During Heat Waves)


In each of the 3 cities studied, we observed an effect of heat waves on mortality that was in addition to the general linear heat-mortality relationship. The heat wave effect was largest in Milan, which is also the hottest city and smallest in London, which is the coolest.

Heat wave effects were smaller in models allowing curvature, suggesting that the heat wave effect is driven partly by nonlinearity. A previous study23 from London reported that days occurring only during very extreme heat episodes such as the 1976 event may explain such nonlinearity. This may be due to the long duration or the extreme heat of these episodes.

We also observed that heat wave effects largely disappeared when we modeled the heat terms using an average measure of lags 0 to 2. This is perhaps unsurprising, because some of the duration aspects of the heat wave term—the accumulation of excess deaths due to effects of high temperatures delayed by up to 3 days—are already captured by the heat slope. The lag 0–2 model nevertheless cannot incorporate added risk due to consecutive days of heat, whereas the heat wave effect term can. The weak evidence for heat wave effects under the lag 0–2 models, therefore, suggests that the heat wave effect evident in the lag 0 models is due more to the heat wave term capturing delayed as well as immediate effects rather than additional risk if heat is experienced on consecutive days.

The negative heat wave coefficient obtained in the case of London suggests there may be some degree of short-term mortality displacement (“harvesting”). In heat waves, excess deaths due to recent hot days (lags 0–2) may be offset by deficits due to deaths accelerated a few days by previous hot days. This also provides some evidence that short-term displacement, found for heat deaths by some other analyses,24,25 occurs in heat waves as well as with heat more generally. However, we have not investigated whether heat-related deaths in heat waves are on average displaced less than other heat-related deaths. One study estimated that harvesting accounted for approximately 50% of deaths during the 1994 heat waves in the Czech Republic,26 whereas a recent study found no evidence of short-term harvesting associated with the extreme 2003 heat wave in France.27

How do our analyses of heat waves compare with conventional episode analyses? For example, the heat wave of 2003 was reportedly associated with a 42% rise in deaths in London during the 10-day period of August 4–13 by comparison with the same period in the previous 5 years.28 The 4 London models on the top of Table 2 predict excesses of 29%, 31%, 36%, and 39% for the same period, suggesting that the models picked up most, but not all, of the heat effect in this long heat wave. In general, it seems likely that the greater comprehensiveness of the general time-series approach is at the expense of ability of episode analyses to pick up effects specific to a particular wave.

Time-series analyses with indicators specific to each major wave offer a compromise approach.23 When our regression model included a “heat wave” indicator specifically for the 2003 heat wave, the total heat excess was estimated at 56% (linear-threshold model). This is higher than the estimate from the episode analysis, probably reflecting the use of August days in previous years as baseline in the episode analysis—days that would also have experienced some heat-related deaths.

It is noteworthy that, in all cities, daily mean temperature was a better predictor of mortality than daily maximum or minimum temperature. It has been suggested that high nighttime temperatures (ie, daily minimum) may contribute to heat-related deaths by allowing no cooling-down period. However, high daytime temperatures are also of obvious importance, and so mean temperature may better reflect complete exposure compared with either daily maximum or minimum temperatures. Apparent temperature provided a better predictor of mortality than mean temperature in only one of our 3 cities and a worse predictor in the others. However, our formulation of apparent temperature was based on daily measures of mean temperature rather than on hourly measurements, and this may have had some bearing on estimates (PHEWE Study Group, personal communication, 2006).

In basic models, heat effects were found to be strongest for cardiovascular deaths in Milan and Budapest and for respiratory deaths in London (not shown). Specific heat wave effects were strongest on respiratory deaths in both Milan and London but not in Budapest. This may be explained by differences in coding of respiratory deaths in Budapest, in which some deaths that would have been considered respiratory in London were instead coded as cardiovascular. This is consistent with the low proportion of respiratory deaths in Budapest (Table 1). It was also demonstrated for London that ozone may contribute to some of the respiratory deaths during heat waves.

The heat wave effect coefficients in this study were for all identified heat wave periods. It is likely that heat waves may have different effects on mortality depending on their intensity, duration, timing during the season, and other characteristics. It has previously been suggested that heat waves early in the summer may have greater effects on mortality compared with later periods.23,29,30 Identifying heat wave periods by using month-specific percentiles provides an alternative criterion allowing for this pattern, but it seems unlikely that doing so would substantially alter the results we observed.

One of the major strengths of the current study was the availability of long time-series data sets. This provided us with enough power to identify and estimate heat wave effects with a large degree of accuracy. It is also possible that the heat thresholds, slopes, and heat wave effects may have changed over time due to factors such as population aging or, conversely, population adaptation (both behavioral and physiological), but this is beyond the scope of the present study.

We made an a priori decision to control for within-year variation in all models using cubic smoothing splines of day-in-year with 4 df and similarly controlled for longer trends using natural cubic splines with 1 df for every 5 years of data. Repeating the analyses after doubling the degrees of freedom changed patterns little. When, as a further sensitivity analysis, we used alternative methods of seasonal control, estimates were largely unchanged. This suggested our original choice of smoothing had adequately adjusted for seasonal trends. In addition, because a large number of years were available for analysis, a GEE approach was adopted, assuming correlation of observations within a summer but independence between summers. When an alternative method was used to incorporate a first-order autoregressive term in our models,31 we obtained very similar effect estimates as before with slightly smaller standard errors (not shown).

Deaths attributable to heat were approximately 1.5% of all deaths in Milan, slightly less in Budapest and much lower in cooler London. The biggest burden of heat deaths did not occur during heat waves but during isolated hot days or other periods when temperatures were perhaps more moderate but occurred with greater frequency. Although each of the 3 cities now has a heat health watch warning system in operation32–34 reducing the greater impact on mortality of general summertime heat would most likely require different types of interventions, for example, long-term changes in housing stock.

In conclusion, our results showed that heat waves were associated with excesses of mortality above those expected from linear increments with increasing daily temperature. However, these wave effects diminished when smooth nonlinear increments were allowed for and were largely absent when smooth increments of risk with 3-day mean temperature were allowed for. The attributable burden associated with these periods varied by city but was small when compared with the overall summertime heat burden. Preventive measures in addition to the plans already in place during heat waves should be considered.


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