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:
M (¿ ¿i−^Mi) ε(L)=
∑
1 L
¿
where Mi and ^Mi are the observed and predicted number of deaths, respectively, on day i.
We estimated the mean squared error (MSE) of forward and backward predictions MSE(L)=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.
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 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-, 6- and 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 Newton- West 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:
E
(
Mi)
=Const+βlini+¿{DOW}+βcos2365.25π(i−θ)¿
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:
M (¿¿i−^Mi) CEM(L)=
∑
i=01.Jan.09 L
¿
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 age- stratified ratio of daily non-accidental mortality counts
60+¿
M¿¿
¿
showed a significant upward linear trend (p<0.001), while mortality from all cardiovascular causes to that from all other natural causes M(CVD)
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):
lnE(M)=Const+β × age+
∑
j=1 n
βj× age × periodj
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.
During the heat wave period, the observed ratio
60+¿
M¿¿
¿
was 30% (26-34; p<0.001) higher than expected, and the ratio M(CVD)
M(nonCVD) was 43% (40-47; p<0.001) higher than expected.
However, during the follow-up period until the end of 2012 these ratios behaved differently. The average value of
60+¿
M¿¿
¿
ratio during this period stayed 2.4% (1.4-3.4; p<0.001) higher than expected, while the ratio M(CVD)
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.
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Moscow_Males StPetersburg_Males Moscow_Females StPetersburg_Females
eFigure 2. Cumulative excess mortality from non-accidental causes in Moscow 2009-2012 with 95% confidence bands. Red lines mark the heatwave period.
1/Jan/09 2/May/09 31/Aug/09 30/Dec/09 30/Apr/10 29/Aug/10 28/Dec/10 28/Apr/11 27/Aug/11 26/Dec/11 25/Apr/12 24/Aug/12 23/Dec/12
-2000 0 2000 4000 6000 8000 10000 12000 14000 16000
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.
1/Jan/08 1/May/08 30/Aug/08 29/Dec/08 29/Apr/09 28/Aug/09 27/Dec/09 27/Apr/10 26/Aug/10 25/Dec/10 25/Apr/11 24/Aug/11 23/Dec/11 22/Apr/12 21/Aug/12 20/Dec/12
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
M(60+)/M(0-59) trend M(CVD)/M(nonCVD) baseline