American Journal of Epidemiology
© The Author 2013. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of
Public Health. All rights reserved. For permissions, please e-mail: [email protected].
Vol. 179, No. 4
DOI: 10.1093/aje/kwt264
Advance Access publication:
November 20, 2013
Original Contribution
Mortality Displacement as a Function of Heat Event Strength in 7 US Cities
Michael V. Saha*, Robert E. Davis, and David M. Hondula
* Correspondence to Michael V. Saha, Department of Environmental Sciences, University of Virginia, 291 McCormick Road, Charlottesville,
VA 22904 (e-mail: [email protected]).
Initially submitted June 3, 2013; accepted for publication October 9, 2013.
Mortality rates increase immediately after periods of high air temperature. In the days and weeks after heat
events, time series may exhibit mortality displacement—periods of lower than expected mortality. We examined
all-cause mortality and meteorological data from 1980 to 2009 in the cities of Atlanta, Georgia; Boston, Massachusetts; Minneapolis–St. Paul, Minnesota; Philadelphia, Pennsylvania; Phoenix, Arizona; Seattle, Washington; and
St. Louis, Missouri. We modeled baseline mortality using a generalized additive model. Heat waves were defined as
periods of 3 or more consecutive days in which the apparent temperature exceeded a variable percentile. For each
heat wave, we calculated the sum of excess and deficit mortality. Mortality displacement, which is the ratio of grand
sum deficit to grand sum excess mortality, decreased as a function of event strength in all cities. Displacement was
close to 1.00 for the weakest events. At the highest temperatures, displacement varied from 0.35 (95% confidence
interval: 0.21, 0.55) to 0.75 (95% confidence interval: 0.54, 0.97). We found strong evidence of acclimatization
across cities. Without consideration of displacement effects, the net impacts of heat-wave mortality are likely to
be significant overestimations. A statistically significant positive relationship between the onset temperature of nondisplaced heat mortality and mean warm-season temperature (R 2 = 0.78, P < 0.01) suggests that heat mortality
thresholds may be predictable across cities.
apparent temperature; harvesting; temperature; heat; heat waves; human biometeorology; mortality displacement;
United States
Abbreviations: AT, apparent temperature; MAT, maximum afternoon apparent temperature; MDR, mortality displacement ratio.
(5–7). Generally, anomalously high mortality rates do not
last for more than 3 days (4). Lagged effects, in which the impact of a heat event influences subsequent mortality, can last
from 3 to 30 days after the high heat, and there is little consensus among researchers on the duration of the effect (4, 8).
Mortality displacement is the hypothesis that some excess
deaths that occur during and shortly after a heat wave are
deaths that would have occurred in the coming days or
weeks, regardless of whether there was stress-inducing
heat. Observed negative mortality anomalies in the period
after a heat event can be supportive of this hypothesis. The
displacement phenomenon largely affects a frail subset of
the population, such as those with chronic illness, and is expected to vary based on the overall health of a population and
the prevalence of certain demographic characteristics (9, 10).
A mortality displacement metric has been presented as a ratio
Periods of high heat are believed to have a considerable effect on human health. Daily mortality rates increase monotonically with temperature above a certain location-specific
temperature threshold in many midlatitude climates (1, 2).
Mortality often increases over prolonged periods of elevated
heat—the so-called “heat-wave effect” (3). Understanding
the mortality dynamics during and after periods of high
heat is useful in targeting especially dangerous heat waves
and forecasting the health burden of individual events. It remains difficult to quantify the net effect of a heat event in
these cases because of confounding variables (such as poor
air quality, seasonality in mortality, and occurrence of multiple heat waves) and the complexity of lagged responses (4).
A large number of heat-related deaths occur on the same
day as or 1 day after a day in which the atmospheric temperature is excessively high (hereafter referred to as high heat)
467
Am J Epidemiol. 2014;179(4):467–474
468 Saha et al.
of the sum of negative mortality departures from a baseline
divided by the sum of positive anomalies over some duration
that includes the heat wave and the period immediately after
(2). In the present study, we adapted this method of quantifying displacement to 7 major United States cities.
The displacement phenomenon is not limited to heat stress;
air pollution and cold spells may cause mortality displacement as well, on time scales that span multiple seasons
(11–14). Mortality displacement can mask thresholds in the
relationship between particulate matter air pollution and mortality; it is conceivable that mortality displacement related to
high heat may exhibit a similar tendency (10). There is limited evidence that mortality displacement varies regionally
and may be larger in milder climates, but the number of cities
examined remains small (2, 8, 15). In surveys of US cities, it
has been suggested that displacement is weaker in more extreme heat events (16) and could be affected by the duration
of the heat wave (17). It has been well-documented that there
is a higher number of deaths during heat waves that occur earlier in the season (18, 19), especially in northeastern US cities
(20), but this response is not consistent and the association of
seasonal timing with possible displacement is unclear (21).
For individual heat waves, estimates of displacement range
from 6% to 71% (2, 22). There is a similarly large range in
the overall estimates of heat-related mortality displacement
in temperate regions (19, 23).
Although mortality displacement is commonly mentioned
in the scope of larger studies on heat and human health, systematic comparisons of displacement in multiple locations
are rare (8). There is no conclusive evidence that mortality
displacement is a city-specific constant and that the number
of deficit deaths scales with excess deaths. Instead, displacement could vary with the severity of heat or vary randomly, as
is evidenced by the wide range in estimates (4). In light of this
knowledge gap, we aimed to quantify how excess and deficit
mortality during and after heat waves combine to alter mortality displacement as a function of event strength and location in selected US metropolitan areas.
METHODS
Weather data
Seven cities were chosen to represent the climatic variety
across the United States. Meteorological data were obtained
from the National Climatic Data Center for Atlanta, Georgia;
Boston, Massachusetts; Minneapolis–St. Paul, Minnesota;
Philadelphia, Pennsylvania; Phoenix, Arizona; Seattle,
Washington; and St. Louis, Missouri. Hourly values of apparent temperature (AT) were calculated using an adaptation
of the Steadman equation (24), as follows:
AT ¼ 2:653 þ ð0:994 × TÞ þ ð0:0153 × TD2 Þ þ C, ð1Þ
where AT is the apparent temperature (°C), T is the dry-bulb
temperature (°C), TD is the dew-point temperature (°C), and C
is a wind correction factor. AT combines the effects of temperature and humidity—it serves as the basis of the National
Weather Service Heat Index and has been commonly used in
heat-mortality research (1). It has been shown that AT is preferable to dry-bulb temperature for approximating the biological stress on the human body (24). The constants were
calculated from temperature and wind speed in a table also
devised by Steadman and were linearly interpolated when
necessary (24). The daily maximum afternoon AT (MAT)
was used for all subsequent analyses.
Mortality data
Daily all-cause mortality counts were obtained from the respective state departments of health for each of the study cities. The periods of record differed for each city, with the
shortest record for Atlanta (14 years) and the longest for
St. Louis (30 years) (Table 1). The average length of record
was 21 years. The associations of mortality with MAT, longterm trend, and seasonality components were estimated using
a generalized additive model, as is common in epidemiologic
time-series studies (13, 18, 25, 26). We used a natural penalized spline with 5 degrees of freedom per year to model the
seasonal and long-term trends and a natural penalized spline
with 6 degrees of freedom to model the relationship with
MAT. The generalized additive model we used is given as:
Log½EðMÞ ¼ α þ sðMAT; df ¼ 6Þ
þ sðTime; df ¼ 5 × yÞ,
ð2Þ
where α is the model intercept, s represents a penalized
smoothing spline, df represents the number of degrees of
freedom for each smoothing term, Time is a counter indicating the number of observations in the time series, and y represents the number of years in each city’s period of record.
We then calculated the model-predicted values for each day
in the time series, holding MAT constant at the mean May–
September MAT. This “baseline mortality” time series represents expected mortality from season and long-term time
trends with any effect of MAT removed. The working unit
of daily mortality in all subsequent analyses was the residual
number of daily deaths from this baseline mortality time
series.
The mortality data utilized in this research consisted only
of frequency counts for large metropolitan areas and have
been de-identified. State governments archive these data for
the purposes of retrospective analysis. Because personal
identifiers have been redacted, consent is not required; as
such, this research is exempt from the institutional review
board according to Title 45, Part 46, Exemption Category 4.
Identifying heat events
Heat events were defined as 3 consecutive days in which
the MAT exceeded a variable temperature threshold (AT*).
Though metrics such as heat-wave duration can be used to
quantify the “strength” of an event, in this article the term
“event strength” refers to the temperature threshold used to
classify periods of high heat as “heat events.” We varied
the temperature threshold from the 80th percentile to the
100th percentile of MAT for the period of record to search
for heat events in each city. As the threshold was increased,
Am J Epidemiol. 2014;179(4):467–474
Mortality Displacement and Heat Event Strength 469
Table 1. Summary of Data and Results From 7 Cities, United States, 1980–2009
Years of Record
Mean MAT, °C
MDminTa
MDmaxTa
MDdiffb
ATsigc, °C
Percentiled
Atlanta, Georgia
1994–2007
20.98
0.92
0.48
0.44
31.28
80.58
Boston, Massachusetts
1986–2007
12.70
1.03
0.75
0.28
30.80
94.89
Minneapolis, Minnesota
1992–2008
10.57
1.02
0.66
0.36
27.03
89.52
Philadelphia, Pennsylvania
1983–2009
16.38
0.89
0.35
0.54
27.60e
79.95
Phoenix, Arizona
1989–2007
26.34
0.82
0.56
0.26
36.98e
79.94
Seattle, Washington
1988–2008
11.49
0.87
0.57
0.30
17.83e
80.11
St. Louis, Missouri
1980–2009
17.00
1.00
0.59
0.41
35.70
92.31
Location
Abbreviations: AT, apparent temperature; MAT, daily maximum apparent temperature; MD, mortality displacement.
a
MD at the lowest (minT) and highest (maxT) severity event thresholds.
b
Equal to MDminT − MDmaxT.
c
The lowest AT at which the confidence interval excludes unity.
d
The approximate percentile of daily MAT to which ATsig corresponds.
e
Denotes significance at the lowest temperature considered.
the number of heat events became rarer. To preserve statistical robustness, only thresholds that identified 10 or more independent events were included in further analyses. Because
of the discrete coding of the meteorological data, some increments in AT* identified the same events as belonging in another, minutely lower threshold. We only considered the most
severe of these “redundant” thresholds for further analysis,
resulting in a unique set of i thresholds and their corresponding lists of events, ni.
The length of each displacement period, li,n, was the duration of the heat event plus either 15 days or the number of
days before the next event, whichever value was less. Lagged
mortality effects have been observed on time-scales that
ranged from 2 days to months after the onset of environmental stress (4, 14). Though deaths that are displaced further forward in time contribute to more life-time lost, our specific
aim was to understand intraseasonal mortality. We formalized the definition of short-term mortality displacement to
mean the displacement that occurs within a maximum of
15 days after the end of high heat. A fixed definition of the
B)
Calculating mortality displacement
Mortality displacement is defined as the proportion of excess deaths displaced forward in time (Figure 1A). We find
this proportion by summing the negative anomalies in a temporal window after a heat event and dividing by the sum of
the positive anomalies. For each event at each threshold, 1
through ni, the sum of positive mortality residuals (Σ[+]i,n)
was calculated as the sum of mortality residuals from the
onset of the heat event to lag li,n (as defined above) only on
days with mortality exceeding the baseline mortality (as
C)
Residual deaths
A)
maximum value of l serves a dual purpose: 1) It allows us
to compare the short-term mortality response of different cities and events rather than using a city-specific or thresholdspecific lag, and 2) it limits the noise in the mortality
time-series that would be incorporated by examining aggregate deaths over a longer window. The sensitivity of our results to the choice of l is reported in the Web Appendix and
Web Figure 1, available at http://aje.oxfordjournals.org/.
Figure 1. A) An idealized heat-related mortality time-series with displacement. Solid lines represent the mortality time series. Dotted lines represent baseline mortality. Periods of excessive heat are indicated with shading. There is a sharp peak in mortality after the onset of high heat (I). If
mortality displacement is present, we observe negative mortality for a period after the initial peak (II) that lasts through lag l. Mortality displacement is
the proportion of deaths during the heat wave that may have occurred regardless of high heat but were instead displaced forward in time, equal
to area II divided by area I. B) The mortality signals of 2 proximal heat events overlaid. The distance, d, is the time between the onset of each
event. C) The additive effect of the mortality signals in B. The mortality displacement of individual events can be influenced by the history of the
system as well as future events. We tally the area under the curve from onset until lag l + d to find the overall mortality effect. Our total displacement is
given by (II + IV) / (I + III).
Am J Epidemiol. 2014;179(4):467–474
470 Saha et al.
defined by the fitted models, i.e., positive residuals). Conversely, Σ[−]i,n was calculated as the sum of negative mortality over the same period. The values Σ[+]i,n and Σ[−]i,n are
analogous to areas I and II in Figure 1A, respectively. Although these areas are idealized as being temporally contiguous (Figure 1), because of noise in the mortality time series,
they invariably are not. In cases in which 2 successive events,
ni,x and ni,x+1, occurred less than li,x days apart, the mortality
anomaly in the overlapping period was attributed to the later
event. Computationally, the specific heat event to which any
mortality anomalies are attributed does not influence the
results—every day within 15 days of a heat event and its corresponding mortality anomaly are included in the thresholdspecific displacement calculation but not more than once.
The conceptual model of mortality displacement anticipates a mortality peak temporally close to the heat event followed by a shallower, extended negative period (Figure 1A).
We did not make explicit the expected temporal segmentation
in our calculation of displacement (i.e., only summing aboveexpected mortality for the first 5 days and only summing
the below-expected mortality the last 10 days) because of the
lack of a consensus over the time frames involved and the
sensitivity of these estimates to varying definitions of heat
waves (4). Rather, our approach required no assumption of
a temporally coherent “displacement period.” This simplified
the calculation in the hypothetical case of 2 temporally proximate heat events and allowed the possibility of accounting
for a mortality rebound after the displacement period (13)
if one did occur.
In each event threshold, all Σ[−]i,n and Σ[+]i,n values were
summed to give ΣΣ[−]i and ΣΣ[+]i , respectively. ΣΣ[+]i
Atlanta
60
represents the total excess mortality during and a short time
after all events of a given event strength i, whereas ΣΣ[−]i
represents the total deficit mortality observed during these
events. The mortality displacement ratio (MDR) for each
event threshold was calculated as follows:
MDRi ¼
RESULTS
The average number of excess deaths increased as a function of threshold temperature in all cities (Figure 2, black line,
light shading). The shape of the trend in negative mortality
was less related to event strength (Figure 2, white line, dark
shading). We defined mortality displacement as the ratio of
the negative to positive accumulated departures at each
MAT interval (Figures 2 and 3). This is equal to the pointwise ratio of the white lines to the black lines in Figure 2
for each MAT threshold and is shown in Figure 3. The mortality displacement at lower event strengths approached unity
Boston
60
Minneapolis–St. Paul
40
60
Average Excess and Deficit Deaths
30
20
40
20
20
10
0
0
32
34
36
38
0
25
Phoenix
80
30
35
0
24 26 28 30 32 34
Seattle
60
60
Philadelphia
100
80
40
20
ð3Þ
Point-wise 95% confidence intervals were generated from
bootstrapped samples of heat events to illustrate the uncertainty in our estimate of the displacement ratio. Bootstrapped
95% confidence intervals were also constructed for the estimates of the excess and deficit deaths from repeated samples
of Σ[+]i,n and Σ[−]i,n, respectively. Linear regressions were
applied to the severity-displacement relationship to determine the MAT threshold at which heat began to contribute
to nondisplaced mortality.
50
40
ΣΣ½i
:
ΣΣ½þi
28 30 32 34 36 38
St. Louis
80
60
40
40
40
20
20
0
20
0
38
40
42
0
18
20
22
24
30
35
40
Apparent Temperature Threshold, °C
Figure 2. Average number of excess (black line and light shading) and deficit (light line and dark shading) deaths over the course of a heat event as
a function of 3-day heat wave apparent temperature with 95% point-wise confidence intervals for Atlanta, Georgia, in 1994–2007; Boston, Massachusetts, in 1986–2007; Minneapolis–St. Paul, Minnesota, in 1992–2008; Philadelphia, Pennsylvania, in 1983–2009; Phoenix, Arizona, in 1989–
2007; Seattle, Washington, in 1988–2008; and St. Louis, Missouri, in 1980–2009. The average net mortality effect for the heat event can be seen as
the difference between the excess and deficit curves. Triangles along the horizontal axis indicate the 90th, 95th, and 97th percentiles of daily maximum afternoon temperature for the whole period of record.
Am J Epidemiol. 2014;179(4):467–474
Mortality Displacement and Heat Event Strength 471
Atlanta
Mortality Displacement
1.2
Boston
1.2
1.2
Minneapolis–St. Paul
0.8
0.8
0.8
0.8
0.4
0.4
0.4
0.4
0.0
0.0
32
34
36
38
Phoenix
1.2
0.0
0.0
25
30
35
24 26 28 30
Seattle
1.2
32 34
0.8
0.8
0.4
0.4
0.4
0.0
38
40
42
28 30 32 34 36 38
St. Louis
1.2
0.8
0.0
Philadelphia
1.2
0.0
18
20
22
24
30
35
40
Apparent Temperature Threshold, °C
Figure 3. Mortality displacement as a function of 3-day heat wave apparent temperature threshold in Atlanta, Georgia, in 1994–2007; Boston,
Massachusetts, in 1986–2007; Minneapolis–St. Paul, Minnesota, in 1992–2008; Philadelphia, Pennsylvania, in 1983–2009; Phoenix, Arizona,
in 1989–2007; Seattle, Washington, in 1988–2008; and St. Louis, Missouri, in 1980–2009. Shading represents a point-wise 95% confidence interval. Triangles along the horizontal axis indicate the 90th, 95th, and 97th percentiles of daily maximum afternoon apparent temperature for the whole
period of record.
However, because these relationships were based on somewhat limited samples of events at very high apparent temperature thresholds, the exact functional relationship between
displacement and severity should be clarified in the future
with the occurrence of additional extreme events. Interestingly,
1.2
1.0
Mortality Displacement
for all cities, with only Philadelphia, Phoenix, and Seattle
showing significant departures at the lowest thresholds considered (equal to the 80th percentile of MAT for the whole
period of record (Figure 3)).
Displacement significantly decreased as a function of increasing threshold MAT. All 7 of the cities studied had at
least 1 incremental bootstrapped confidence interval that
did not include 1, indicating a statistically significant net association between mortality and heat once a high enough
threshold was reached. The AT percentiles at which this divergence occurred varied from approximately 80% in Philadelphia and Phoenix to 95% in Boston (Table 1). On the basis
of results from linear least-squares regression, we found a
statistically significant relationship between event strength
and displacement (P < 0.001) in every city (Figure 4). At
the highest MAT thresholds examined, the mortality displacement ranged from 0.35 (95% confidence interval:
0.21, 0.55) in Philadelphia to 0.75 (95% confidence interval:
0.54, 0.97) in Boston; the average displacement across all
cities at the highest MAT was 0.57. Thus, for the most severe
heat events, approximately one-half of heat-related deaths
were displaced.
0.8
0.6
Atlanta
Boston
Minneapolis−St. Paul
Philadelphia
Phoenix
Seattle
St. Louis
0.4
0.2
0.0
15
20
25
30
35
40
Apparent Temperature Threshold, °C
45
DISCUSSION
Our results indicate that mortality displacement varies with
both the severity of heat events and location. In accordance
with the thoroughly documented U-shaped temperaturemortality response (1, 27), we expected a nonlinear increase
in the mortality response with temperature. This qualitative
feature was only observed in Philadelphia and St. Louis.
Am J Epidemiol. 2014;179(4):467–474
Figure 4. Mortality displacement as a function of event strength in
Atlanta, Georgia, in 1994–2007; Boston, Massachusetts, in 1986–
2007; Minneapolis–St. Paul, Minnesota, in 1992–2008; Philadelphia,
Pennsylvania, in 1983–2009; Phoenix, Arizona, in 1989–2007; Seattle, Washington, in 1988–2008; and St. Louis, Missouri, in 1980–2009.
Colored points show observed displacements. A least-squares linear
regression is applied to each city. All regression slopes are statistically
significant (P < 0.001).
472 Saha et al.
A)
Departure Temperature, °C
40
35
PHX
STL
30
MSP
25
ATL
BOS
PHL
20
15
SEA
10
10
15
20
25
30
Average MAT, °C
B)
40
Departure Temperature, °C
the average number of deficit deaths in the displacement time
period was generally invariant with event strength (Figure 2,
light lines and dark shading). This may indicate that even at
the lowest event strengths considered (80th percentile of
MAT for 3 days in a row), a frail subset of the population experiences a short-term displacement of mortality. As the
event strength increases, there is a higher likelihood that
heat stress will impact the healthier cohort. When this occurs,
it is likely that the life-time lost will be greater than 15 days
(i.e., the lag we investigated) (8).
As defined herein, the mortality displacement of a purely
noisy signal would theoretically be equal to 1. We found substantial divergence from this value at high temperatures in
every city (Figure 3). The individual shapes of the displacement functions of event strength varied by city, but all
showed a negative relationship with AT (Figure 4). This
shows evidence that the number of displaced deaths does
not simply scale up with the observed positive mortality,
that is, displacement is not a city-specific constant. Rather,
mortality displacement varies with event strength in a predictable way. It is apparent that a substantial proportion of
deaths in each city are the result of short-term displaced mortality, even for the most severe events on record. Though
these cities span a large range of mean temperatures, the
ranges of mortality displacement observed across event
strengths do not vary markedly between cities (Table 1).
Our results indicate that investigators must account for the
phenomenon of mortality displacement to accurately assess
the health burden of high temperature. Simply averaging
anomalous deaths that occur the same day as or 1 day after
a heat event may overestimate the actual mortality rate by a
factor of 2 or more.
The most immediate aim of this displacement analysis was
to assess net mortality as a function of heat-wave intensity.
By determining when heat waves start to contribute to “excess” deaths (as opposed to simply displacing them) on an
average basis, heat–wave warning protocols can be developed to target heat events that minimize the number of nondisplaced deaths and, by extension, life-time lost (17, 28).
Research has shown that the particulate-mortality response
curves are altered by the presence of displacement in a
times series (10). It is conceivable that displacement could
affect the heat-mortality response curve as well. Many authors have characterized the threshold temperature above
which there is a significant health burden by examining
how temperature correlates to mortality at 0- to 2-day lags
(1). The presence of displacement may alter this threshold.
In the present study, we provide an alternate approach:
When mortality displacement falls below 1, heat begins to exhibit a net impact on mortality. By fitting a simple linear regression to the empirical displacement function of each city,
we can estimate where in predictor space the MDR departs
from 1. This “departure temperature” is the apparent temperature at which we expect mortality in excess of the deaths that
were simply displaced forward by a few weeks.
As expected, the onset of nondisplaced deaths occurs at
higher absolute temperatures in warmer cities (16) (Figure 5).
Acclimatization to heat events has been well documented,
with warmer cities showing less of a mortality response
for a given temperature (29). There is a strong relationship
35
PHX
STL
30
ATL
BOS
25
PHL
MSP
20
15
SEA
10
20
25
30
35
40
Average Summer Temperature, °C
Figure 5. A) The relationship between city mean daily maximum apparent temperature (MAT) and the value at which the mortality displacement ratio from city-specific linear regressions in Figure 4
equals 1 (“departure temperature”) from Atlanta, Georgia (ATL),
1994–2007; Boston, Massachusetts (BOS), 1986–2007; Minneapolis–
St. Paul, Minnesota (MSP), 1992–2008; Philadelphia, Pennsylvania
(PHL), 1983–2009; Phoenix, Arizona (PHX), 1989–2007; Seattle,
Washington (SEA), 1988–2008; and St. Louis, Missouri (STL),
1980–2009. The R 2 value of the fitted line is 0.64. B) The relationship
between mean summer dry bulb temperature and the departure temperature from Figure 4. The R 2 value of the log-transformed relationship is 0.78.
(R 2 = 0.64) between the departure AT and mean city AT (Figure 5A), showing that the onset of heat-related death is affected by adaptation to the long-term thermal environment
that the residents of each city experience.
The departure temperature can be related to climatological
variables that capture more saliently the level of a population’s exposure to elevated heat. We expect the mean summer
temperature (average temperature from May through September) to be strongly correlated with departure temperature. The
relationship appears to be nonlinear, with departure temperature showing a weakening monotonic increase with average
summer temperature (Figure 5B). A linear regression of logtransformed mean summer temperature accounts for almost
four fifths of the variance observed (R2log ¼ 0:78, P < 0.01).
Although there is strong evidence for acclimatization (i.e., the
slope of this relationship is always positive), the association
with acclimatization diminishes at higher temperatures. This
could be indicative of a thermal physiological limit, suggesting that a population’s susceptibility to elevated heat is a
combination of both absolute temperature (°C) and relative
temperature ( percentile of observed temperature).
Am J Epidemiol. 2014;179(4):467–474
Mortality Displacement and Heat Event Strength 473
If a universal relationship between mean temperature and
susceptibility to heat can be identified, this information could
profoundly impact heat-wave warning protocols by providing
systematic guidance for public health personnel on appropriate initial thresholds for intervention measures. In locations in
which mortality data and/or epidemiologic research are lacking with respect to a population’s sensitivity to heat, one
could predict the onset of significant heat-related mortality
by interpolating from the displacement temperature relationships to climate (Figure 5). However, our study used data
from only 7 cities, so much additional research is required
to test and validate this hypothesis before this approach
could be used in an operational setting.
The methods presented are useful in describing gross aggregate trends in mortality displacement, but they would be
less useful in examining individual heat events. Our approach
was effective because it aggregated single-event MDR
weighted by the total number of deaths instead of the highly
skewed displacement ratios developed from individual heat
events. A displacement ratio of 0 would indicate that all of
the deaths following any given heat event could be attributed
to elevated temperature, whereas a ratio of 1 would indicate
that the heat event did not result in the deaths of otherwise
healthy persons in the population. Mortality displacement ratios for individual heat events of the same severity criterion
ranged from 0 to 6 in some cities, and the arithmetic mean of
all of the single-event displacement ratios was considerably
larger than 1, a result that would indicate that heat waves actually have a protective effect. This is certainly not a hypothesis we forward, but it serves to highlight the usefulness of
the approach we used here in evaluating noisy time series.
Our analysis assumes a relationship between mortality and
high heat. Other collinear predictor variables may confound
our interpretation, and these should be considered in future
studies. Associations with fine particulate pollutants and
heat-wave duration are a few of factors that may affect
heat-related mortality and the mortality displacement metric
(4, 13, 17). In the case of particulates, numerous studies report little to no short-term displacement with respect to mortality attributed to high concentrations of particulate matter
(13, 30–32). If a portion of the deaths attributed to heat in
the present study were in fact related to high concentrations
of particulate matter, we underestimated the heat-related mortality displacement effect. As long-term continuous time series of particulate data become available, a more thorough
investigation of these potential confounding effects would
be useful. Alternate event classification metrics previously
associated with a stronger mortality response (20), such as
duration of high heat and within-season timing, exhibited a
similar negative relationship with displacement (Web Appendix and Web Figures 1 and 2). The removal of high mortality days from the analysis did not substantially change
observed displacement (Web Figure 3). We did not consider
temporal changes in heat-related mortality, which has the potential to impact our results (1, 5).
Although MDRs showed a marked decline with event severity, for most cities the severe events did not fall below 0.5.
Thus, more than half of the excess deaths observed within 15
days after heat events were accounted for by deficit mortality
during the same period, and in a number of cases, this ratio
Am J Epidemiol. 2014;179(4):467–474
was closer to 60%. Our results suggest that mortality displacement is an important consideration when examining
the net influence of heat events on mortality. Failing to account for this lagged phenomenon could result in substantial
overestimations of the association between heat and mortality. We show strong evidence for a relationship between the
onset of nondisplaced deaths and the long-term heat environment. Future studies should aim to incorporate additional cities to better understand the geographic patterns of mortality
displacement, as well as to improve our understanding of the
component of mortality displacement that may be universal
rather than location-specific.
ACKNOWLEDGMENTS
Author affiliations: Department of Environmental Sciences, University of Virginia, Charlottesville, Virginia
(Michael V. Saha, Robert E. Davis); and Center for Policy Informatics, School of Public Affairs, Arizona State University,
Phoenix, Arizona (David M. Hondula).
We thank the Georgia Department of Health, the Massachusetts Registry of Vital Records and Statistics, the Minnesota Department of Health, the Pennsylvania Department of
Health, the Arizona Department of Health Services, the
Washington State Department of Health, and the Missouri
Department of Health and Senior Services for providing
the mortality data used in this study.
The agencies that provided the data had no responsibility
for any of the analyses, interpretations, or conclusions contained herein.
Conflict of interest: none declared.
REFERENCES
1. Davis RE, Knappenberger PC, Michaels PJ, et al. Changing
heat-related mortality in the United States. Environ Health
Perspect. 2003;111(14):1712–1718.
2. Gosling SN, McGregor GR, Páldy A. Climate change and
heat-related mortality in six cities part 1: model construction
and validation. Int J Biometeorol. 2007;51(6):525–540.
3. Hajat S, Armstrong B, Baccini M, et al. Impact of high
temperatures on mortality: is there an added heat wave effect?
Epidemiology. 2006;17(6):632–638.
4. Gosling SN, Lowe JA, McGregor GR, et al. Associations
between elevated atmospheric temperature and human
mortality: a critical review of the literature. Clim Change. 2009;
92(3-4):299–341.
5. Davis RE, Knappenberger PC, Novicoff WM, et al. Decadal
changes in summer mortality in U.S. cities. Int J Biometeorol.
2003;47(3):166–175.
6. Anderson BG, Bell ML. Weather-related mortality: how heat,
cold, and heat waves affect mortality in the United States.
Epidemiology. 2009;20(2):205–213.
7. Hondula DM, Davis RE, Leisten MJ, et al. Fine-scale spatial
variability of heat-related mortality in Philadelphia County,
USA, from 1983–2008: a case-series analysis. Environ Health.
2012;11:16.
8. Hajat S, Armstrong BG, Gouveia N, et al. Mortality
displacement of heat-related deaths: a comparison of Delhi, São
Paulo, and London. Epidemiology. 2005;16(5):613–620.
474 Saha et al.
9. Kaiser R, Le Tertre A, Schwartz J, et al. The effect of the 1995
heat wave in Chicago on all-cause and cause-specific mortality.
Am J Public Health. 2007;97(suppl 1):S158–S162.
10. Roberts S. Can mortality displacement mask thresholds in the
concentration-response relation between particulate matter air
pollution and mortality? Atmos Environ. 2011;45(27):
4728–4734.
11. Zeger SL, Dominici F, Samet J. Harvesting-resistant estimates
of air pollution effects on mortality. Epidemiology. 1999;10(2):
171–175.
12. Huynen MM, Martens P, Schram D, et al. The impact of heat
waves and cold spells on mortality rates in the Dutch
population. Environ Health Perspect. 2001;109(5):463–470.
13. Zanobetti A, Schwartz J, Samoli E, et al. The temporal pattern
of mortality responses to air pollution: a multicity assessment of
mortality displacement. Epidemiology. 2002;13(1):87–93.
14. Rocklöv J, Forsberg B, Meister K. Winter mortality modifies
the heat-mortality association the following summer. Eur
Respir J. 2009;33(2):245–251.
15. Peng RD, Bobb JF, Tebaldi C, et al. Toward a quantitative
estimate of future heat wave mortality under global climate
change. Environ Health Perspect. 2011;119(5):701–706.
16. Medina-Ramón M, Schwartz J. Temperature, temperature
extremes, and mortality: a study of acclimatisation and effect
modification in 50 US cities. Occup Environ Med. 2007;64(12):
827–833.
17. Kinney PL, O’Neill MS, Bell ML, et al. Approaches for
estimating effects of climate change on heat-related deaths:
challenges and opportunities. Environ Sci Policy. 2008;11(1):
87–96.
18. Hajat S, Kovats RS, Atkinson RW, et al. Impact of hot
temperatures on death in London: a time series approach.
J Epidemiol Community Health. 2002;56(5):367–372.
19. Kyselý J. Mortality and displaced mortality during heat waves
in the Czech Republic. Int J Biometeorol. 2004;49(2):91–97.
20. Anderson BG, Bell ML. Heat waves in the United States:
mortality risk during heat waves and effect modification by heat
wave characteristics in 43 U.S. communities. Environ Health
Perspect. 2011;119(2):210–218.
21. Metzger KB, Ito K, Matte TF. Summer heat and mortality in
New York City: how hot is too hot? Environ Health Perspect.
2010;118(1):80–86.
22. Le Tertre A, Agnès L, Eilstein D, et al. Impact of the 2003
heatwave on all-cause mortality in 9 French cities.
Epidemiology. 2006;17(1):75–79.
23. Basu R, Malig B. High ambient temperature and mortality in
California: exploring the roles of age, disease, and mortality
displacement. Environ Res. 2011;111(8):1286–1292.
24. Steadman RG. A universal scale of apparent temperature.
J Clim Appl Meteorol. 1984;23:1674–1687.
25. Hastie TJ, Tibshirani RJ, eds. Generalized Additive Models.
Volume 43. Boca Raton, FL: Chapman and Hall, Publishers;
1990.
26. de’Donato FK, Stafoggia M, Rognoni M, et al. Airport and
city-centre temperatures in the evaluation of the association
between heat and mortality. Int J Biometeorol. 2008;52(4):
301–310.
27. Baccini M, Biggeri A, Accetta G. Heat effects on
mortality in 15 European cities. Epidemiology. 2008;19(5):
711–719.
28. Hajat S, Sheridan SC, Allen MJ, et al. Heat-health warning
systems: a comparison of the predictive capacity of different
approaches to identifying dangerously hot days. Am J Public
Health. 2010;100(6):1137–1144.
29. Kalkstein LS, Davis RE. Weather and human mortality:
an evaluation of demographic and interregional responses
in the United States. Ann Assoc Am Geogr. 1989;79(1):
44–64.
30. Schwartz J. Harvesting and long term exposure effects in the
relation between air pollution and mortality. Am J Epidemiol.
2000;151(5):440–448.
31. Dominici F, McDermott A, Zeger SL, et al. Airborne particulate
matter and mortality: timescale effects in four US cities. Am J
Epidemiol. 2003;157(12):1055–1065.
32. Brook RD, Rajagopalan S, Pope CA, et al. Particulate matter air
pollution and cardiovascular disease: an update to the scientific
statement from the American heart association. Circulation.
2010;121(21):2331–2378.
Am J Epidemiol. 2014;179(4):467–474