eAppendix
Information on daily deaths in the city of Moscow between 1 January 2000 and 31 December
2012 was based on Russian State official statistics. Average daily temperatures were obtained
from the Meteorological Observatory of the Moscow State University. Setting the heat wave
threshold at the 98th percentile of the “historic” (1980-2009) distribution of the mean temperature
on the referent and the previous day, two episodes were identified in 2010: 22 – 28 June and 3
July 3 – 19 August. Because elevated mortality was observed during all these days and the
bridging 4 days between them, we consider the 59 days between 22 June and 19 August as a
single heat wave period in the subsequent assessment of the mortality displacement.
We derived a model for prediction of baseline mortality from non-accidental causes that could
have been expected in the absence of the 2010 heat wave. We estimated the temporal trend from
the data observed during the pre-heat wave period. To estimate mortality displacement, we
selected the predictive model based on its ability to predict cumulative number of deaths during
the pre-heat-wave (learning) period. The pre-heat-wave period was split in two: training period
and test period. The regression model coefficients were estimated from the training period and
then applied to predict mortality during the test period. The prediction error ε(L) was defined as
the cumulative sum of errors between day 1 and L of the test period:
̂𝑖 )
𝜀(𝐿) = ∑𝐿1(𝑀𝑖 − 𝑀
̂𝑖 are the observed and predicted number of deaths, respectively, on day i. We
where 𝑀𝑖 and 𝑀
estimated the mean squared error (MSE) of forward and backward predictions
𝜀𝑓2 (𝐿) + 𝜀𝑏2 (𝐿)
2
The model which minimized the MSE value was the preferred predictive model. Once the
predictive model was chosen, it was applied to the whole learning period to estimate the new set
of regression coefficients, which were used to predict mortality during the projection period. We
assumed that, if no systematic changes occur, the variance of the cumulative excess mortality
(CEM) during the projection period could be approximated by MSE during the test period, for
periods of the same length.
𝑀𝑆𝐸(𝐿) =
The choice of long-term trend was also based on a comparison of annual standardized death rates
between Moscow and Saint Petersburg. The latter city was much less affected by the 2010 heat
wave. Annual mortality increased until 2003 and decreased since then in both cities (eFigure 1).
The predictive model with linear secular trend based on data since 2003 had the smallest MSE
value. Annual mortality data from St Petersburg for 2003 – 2012 were also better described by a
linear secular trend. For this reason, we defined the following periods for predictive modeling:
Learning period: Jan 2003 - May 2010
Projection period: June 2010 - Dec 2012
Training period, forward: Jan 2003 - Oct 2007; test period, forward: Nov 2007 - May 2010
Training period, backward: July 2006 - May 2010; test period, backward: June 2003 - Jan 2006
1
Seasonality during 2003-2012 was modeled with sinusoidal functions of time. Four alternative
models with varying numbers of degrees of freedom per year were tested: (1) a basic model with
annual periodicity only; (2) a model with 12- and 6-month periodicity; (3) a model with 12-, 6and 4-month periodicity, and (4) a model with 12-, 6-, 4- and 3-month periodicity. The basic
model had the smallest prediction error. The distribution of the dependent variable was close to
normal because of large daily counts of deaths (about 300). An additive model with robust
variance calculation had smaller prediction error than a Poisson model, and we used the NewtonWest error estimator to account for serial correlation among the residuals. Thus, the preferred
additive model for the expected count of daily deaths E(Mi) was the following:
2𝜋(𝑖 − 𝜃)
𝐸(𝑀𝑖 ) = 𝐶𝑜𝑛𝑠𝑡 + 𝛽𝑙𝑖𝑛 𝑖 + {𝐷𝑂𝑊} + 𝛽𝑐𝑜𝑠
365.25
where the regression coefficients 𝛽𝑙𝑖𝑛 , 𝛽, the phase 𝜃, and day-of-week indicator variables
{DOW} were estimated from the learning period. eFigure 2 shows CEM estimated from this
model:
𝐿
𝐶𝐸𝑀(𝐿) =
∑
̂𝑖 )
(𝑀𝑖 − 𝑀
𝑖=01.𝐽𝑎𝑛.09
Stratified analysis was done in two steps. Firstly, linear regression was applied to check if there
was any long-term trend in the mortality ratios during pre-heat wave period 2003-2009. The age𝑀(60+)
stratified ratio of daily non-accidental mortality counts 𝑀(0−59) showed a significant upward
linear trend (p<0.001), while mortality from all cardiovascular causes to that from all other
𝑀(𝐶𝑉𝐷)
natural causes 𝑀(𝑛𝑜𝑛𝐶𝑉𝐷) did not have any trend.
Secondly, a conditional fixed-effects Poisson model was used to study the dynamics of mortality
rate ratios during and after the heat wave. The age-stratified model contained the main effect of
the binary variable age and the set of age/time interaction terms, where the binary variables
periodj marked n successive and non-overlapping periods (less the referent period 2003-2009):
𝑛
𝑙𝑛𝐸(𝑀) = 𝐶𝑜𝑛𝑠𝑡 + 𝛽 × 𝑎𝑔𝑒 + ∑ 𝛽𝑗 × 𝑎𝑔𝑒 × 𝑝𝑒𝑟𝑖𝑜𝑑𝑗
𝑗=1
Before fitting this model, the time series of daily mortality counts for both age groups were
corrected for the linear long-term trends, estimated from the referent period and assumed to
continue until the end of 2012 in the absence of the heat wave. This provided the basis for
comparison of observed vs. expected rate ratios after the heat wave (eFigure 3). Stratification by
cause of death was studied similarly, but it was not necessary to consider trends in this case.
𝑀(60+)
During the heat wave period, the observed ratio 𝑀(0−59) was 30% (26-34; p<0.001) higher than
𝑀(𝐶𝑉𝐷)
expected, and the ratio 𝑀(𝑛𝑜𝑛𝐶𝑉𝐷) was 43% (40-47; p<0.001) higher than expected. However,
2
during the follow-up period until the end of 2012 these ratios behaved differently. The average
𝑀(60+)
value of 𝑀(0−59) ratio during this period stayed 2.4% (1.4-3.4; p<0.001) higher than expected,
𝑀(𝐶𝑉𝐷)
while the ratio 𝑀(𝑛𝑜𝑛𝐶𝑉𝐷) was 5.9% (5.1-6.8; p<0.001) lower than its pre-heat wave value.
eFigure 1. Age-standardized death rates in Moscow and St Petersburg 2002 – 2013.
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
Moscow_Males
StPetersburg_Males
Moscow_Females
StPetersburg_Females
2011
2012
3
eFigure 2. Cumulative excess mortality from non-accidental causes in Moscow 2009-2012 with
95% confidence bands. Red lines mark the heatwave period.
16000
14000
12000
10000
8000
6000
4000
23/Dec/12
24/Aug/12
25/Apr/12
26/Dec/11
27/Aug/11
28/Apr/11
28/Dec/10
29/Aug/10
30/Apr/10
30/Dec/09
31/Aug/09
-2000
2/May/09
0
1/Jan/09
2000
4
eFigure. 3. Daily mortality rate ratios in Moscow 2008-2012, stratified by age and cause of death
(cardiovascular vs non-cardiovascular causes). Red lines mark the heat wave period.
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
20/Dec/12
21/Aug/12
22/Apr/12
23/Dec/11
baseline
24/Aug/11
25/Apr/11
25/Dec/10
26/Aug/10
M(CVD)/M(nonCVD)
27/Apr/10
27/Dec/09
trend
28/Aug/09
29/Apr/09
29/Dec/08
30/Aug/08
1/May/08
0.0
1/Jan/08
M(60+)/M(0-59)
5