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Commentary: What measure of temperature is the best predictor of mortality?
Environmental Research 118 (2012) 149–151
Contents lists available at SciVerse ScienceDirect
Environmental Research journal homepage: www.elsevier.com/locate/envres
Commentary
Commentary: What measure of temperature is the best predictor of mortality? ˚ ¨ b A.G. Barnett a,n, C. Astr om a b
School of Public Health & Institute of Health and Biomedical Innovation, Queensland University of Technology, 60 Musk Avenue, Kelvin Grove, Australia Occupational and Environmental Medicine, Department of Public Health and Clinical Medicine, Ume˚ a University, Ume˚ a, Sweden
a r t i c l e i n f o Article history: Received 16 January 2012 Accepted 15 May 2012 Available online 30 July 2012 Keywords: Climate Mortality Weather Temperature Apparent temperature Humidex
1. Introduction Our previous paper aimed to examine what measure of temperature was the best predictor of mortality (Barnett et al., 2010). We wanted to find the temperature measure that best predicted the daily number of deaths, as knowing this would be useful for future studies. The best predictions were judged using cross-validation, with the aim of giving a realistic predictions for future studies. We used data from the National Morbidity and Mortality Air Pollution Study (NMMAPS) which covers a wide range of data for the years has daily data for the years 1987–2000 (Samet et al., 2000). An important measure was apparent temperature, which should be calculated using the equation (Zanobetti and Schwartz, 2008): Apparent temperature ð1CÞ ¼ 2:653 þ 0:994mean temperature ð1CÞ þ 0:0153 ½Dew-point temperature ð1CÞ2 :
ð1Þ
Maximum or minimum apparent temperature can be calculated using the same equation, with maximum or minimum temperature in place of mean temperature. Unfortunately our previous calculations wrongly used degrees Fahrenheit instead of degrees Celsius. This meant our estimates of apparent temperature were wrong, which meant we had not correctly estimated whether apparent temperature was a good predictor of mortality. n
Corresponding author. Fax: þ61 7 3138 6010. E-mail addresses: [email protected] (A.G. Barnett), ˚ ¨ [email protected] (C. Astr om). 0013-9351/$ - see front matter & 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.envres.2012.05.008
In this commentary we re-run our analysis of the best predictor of mortality using the correct estimates of apparent temperature, minimum apparent temperature and maximum apparent temperature. We compare these new results with the previous results in order to check whether apparent temperature is a better predictor of mortality than the other measures tested, such as mean temperature or the Humidex. 2. Methods We used the same statistical methods as before to estimate the predictive ability of each temperature measure (Barnett et al., 2010). We fitted Poisson regression models in each of the 107 cities with daily deaths as the dependent variable and the daily temperature measure as the key independent variable. We tried 13 different measures of temperature and also fitted a model without temperature as a baseline comparison. The temperature estimates were fitted using a distributed lagged nonlinear model to allow both a delayed and non-linear effect (Gasparrini et al., 2010). We assumed a delay of up to 25 days and modeled the shape of the delayed risk using a natural spline with 3, 4 or 5 degrees of freedom. We tried 4, 5 and 6 degrees of freedom for the temperature measures in order to capture the typically non-linear U-shaped risk. We also fitted a natural spline for time to control for trends and seasonal patterns in mortality, and tried 5, 6 and 7 degrees of freedom per year. Before fitting the model we randomly deleted 10% of the mortality data, and then compared the predicted daily mortality with the observed using the squared Pearson residual. We repeated this cross-validation 50 times in each city. The average of the squared residuals is then a useful statistic, as smaller values mean a better predictor of mortality. We compared these averages for the different degrees of freedom in order to find the best combination of degrees of freedom for season, lag and temperature. To find the temperature measure with the smallest residuals we used a regression model with a dependent variable of mean residual and independent variable of the temperature measure (n¼ 14 categories), city (n¼107) and cross-validation (n¼50). We plotted the modeled mean residuals for each
˚ om / Environmental Research 118 (2012) 149–151 A.G. Barnett, C. Astr¨
150
Table 1 Average Pearson correlations between the daily temperature measures and humidity for the 107 US Cities, 1987–2000. The correlations wrongly using degrees Fahrenheit for apparent temperature are in parenthesis.
Mean temperature (1C) Min temperature (1C) Max temperature (1C) AT (1C) Min AT (1C) Max AT (1C) Humidex (1C)
Min (1C)
Max (1C)
AT (1C)
Min AT (1C)
Max AT (1C)
Humidex (1C)
RH (%)
0.963
0.971 0.890
0.989 (0.955) 0.963 (0.953) 0.953 (0.906)
0.954 0.989 0.881 0.974
0.975 0.911 0.988 0.979 0.921
0.988 0.968 0.948 0.996 (0.989) 0.975 (0.973) 0.971 (0.988)
0.048 0.082 0.146 0.001 (0.154) 0.108 (0.213) 0.087 (0.102) 0.051
(0.933) (0.963) (0.865) (0.992)
(0.962) (0.937) (0.939) (0.993) (0.975)
Abbreviations: AT, apparent temperature; RH, relative humidity.
3. Results
New Previous
0.842
The Pearson correlations between the measures of temperature and humidity are shown in Table 1. The biggest changes after correctly using degrees Celsius for apparent temperature were generally smaller correlations between apparent temperature and relative humidity. The other correlations were similarly strong and positive. The mean cross-validated residuals for the 14 models by age group are in Fig. 1. There was very little difference in the predictive ability of apparent temperature when it was calculated using degrees Celsius or Fahrenheit. There was a small difference in the oldest age group, with the new apparent temperature doing worse than the previous, and the new minimum apparent temperature doing slightly better.
0.840 0.838 0.836 0.834
Mean residual
0.756 0.755
4. Discussion
0.754 0.753 0.752
0.955 0.954 0.953 0.952
in ea n A M pp ax A M pp in A H pp um M id ax ex + H M u in m1 M + ea Hu n m1 + H M ax um 1 + M Hu in m2 M +H ea n um 2 + H um 2
M
M
N
on e M ax
0.951
Fig. 1. Mean cross-validated residuals (and 95% credible intervals) for the 14 different models by age group: o 65 years (top row), 65–74 years (middle row), Z 75 years (bottom row). The smaller the residual, the better the model. App ¼apparent; Hum1 ¼ humidity with the same natural spline basis as temperature; Hum2 ¼ same day humidity using a natural spline with 3 degrees of freedom. The new results using degrees Celsius for apparent temperature are in black, and the previous results using degrees Fahrenheit are in gray.
temperature measure together with its 95% credible interval. We give the credible interval rather than the confidence interval as the model was fitted using a Bayesian paradigm. To summarize the correlations between the daily measures of temperature and humidity we calculated the Pearson correlations in each city and then averaged these correlations over the 107 cities.
Wrongly calculating apparent temperature made no difference to its ability to predict mortality. The mistake had a relatively minor impact because of the strong positive correlation between apparent temperatures calculated using either degrees Fahrenheit or Celsius (Eq. (1)). This strong correlation made for similar mortality predictions, and hence similar conclusions about apparent temperature’s ability to predict mortality. The main conclusion from our previous analysis holds: that there was no one temperature measure that was superior to the others. Future studies on the health effects of temperature should use a temperature measure that (i) has a good coverage across the study area from multiple monitoring sites, (ii) has few missing values, (iii) is easily understood by the public (e.g., mean temperature). This last point is particularly true for heat-warnings systems, as warnings on scales that people do not understand are often ignored (Bickerstaff, 2004). Bobb et al. (2011) recently aimed to find which of the 33 different combinations of maximum and dew-point temperature was the best predictor of mortality in heat waves, and they also used the NMMAPS data. Similar to our study, they found that no model was dominant, as there was a great variability in the best temperature model between cities. Other experts in the field have also recently commented on how estimates of mortality differ little for different temperature measures (Basu et al., 2008; Hajat and Kosatky, 2010). When estimating the health effects of temperature the choice of the temperature measure is of less importance compared with other model choices, such as the length of the longest exposure lag, and whether heat waves are modeled as additional effects.
Acknowledgments Thanks to the Department of Biostatistics at the Johns Hopkins Bloomberg School of Public Health and the Health Effects Institute
˚ om / Environmental Research 118 (2012) 149–151 A.G. Barnett, C. Astr¨
for making the National Morbidity and Mortality Air Pollution Study data publicly available. Computational resources and services used in this work were provided by the High Performance Computer and Research Support Unit, Queensland University of Technology, Brisbane, Australia. References Barnett, A., Tong, S., Clements, A., 2010. What measure of temperature is the best predictor of mortality? Environ. Res. 110 (6), 604–611. Basu, R., Feng, W.-Y., Ostro, B.D., 2008. Characterizing temperature and mortality in nine California counties. Epidemiology 19, 138–145.
151
Bickerstaff, K., 2004. Risk perception research: socio-cultural perspectives on the public experience of air pollution. Environ. Int. 30, 827–840. Bobb, J.F., Dominici, F., Peng, R.D., 2011. A Bayesian model averaging approach for estimating the relative risk of mortality associated with heat waves in 105 U.S. cities. Biometrics 67, 1605–1616. Gasparrini, A., Armstrong, B., Kenward, M.G., 2010. Distributed lag non-linear models. Stat. Med. 29 (21), 2224–2234. Hajat, S., Kosatky, T., 2010. Heat-related mortality: a review and exploration of heterogeneity. J. Epidemiol. Community Health 64 (9), 753–760. Samet, J.M., Dominici, F., Zeger, S.L., et al., 2000. National Morbidity, Mortality, and Air Pollution Study. Part I: Methods and Methodologic Issues. Technical Report, Health Effects Institute. Available from /http://pubs.healtheffects. org/view.php?id=118S. Zanobetti, A., Schwartz, J., 2008. Temperature and mortality in nine US cities. Epidemiology 19 (4), 563–570.
Contents lists available at SciVerse ScienceDirect
Environmental Research journal homepage: www.elsevier.com/locate/envres
Commentary
Commentary: What measure of temperature is the best predictor of mortality? ˚ ¨ b A.G. Barnett a,n, C. Astr om a b
School of Public Health & Institute of Health and Biomedical Innovation, Queensland University of Technology, 60 Musk Avenue, Kelvin Grove, Australia Occupational and Environmental Medicine, Department of Public Health and Clinical Medicine, Ume˚ a University, Ume˚ a, Sweden
a r t i c l e i n f o Article history: Received 16 January 2012 Accepted 15 May 2012 Available online 30 July 2012 Keywords: Climate Mortality Weather Temperature Apparent temperature Humidex
1. Introduction Our previous paper aimed to examine what measure of temperature was the best predictor of mortality (Barnett et al., 2010). We wanted to find the temperature measure that best predicted the daily number of deaths, as knowing this would be useful for future studies. The best predictions were judged using cross-validation, with the aim of giving a realistic predictions for future studies. We used data from the National Morbidity and Mortality Air Pollution Study (NMMAPS) which covers a wide range of data for the years has daily data for the years 1987–2000 (Samet et al., 2000). An important measure was apparent temperature, which should be calculated using the equation (Zanobetti and Schwartz, 2008): Apparent temperature ð1CÞ ¼ 2:653 þ 0:994mean temperature ð1CÞ þ 0:0153 ½Dew-point temperature ð1CÞ2 :
ð1Þ
Maximum or minimum apparent temperature can be calculated using the same equation, with maximum or minimum temperature in place of mean temperature. Unfortunately our previous calculations wrongly used degrees Fahrenheit instead of degrees Celsius. This meant our estimates of apparent temperature were wrong, which meant we had not correctly estimated whether apparent temperature was a good predictor of mortality. n
Corresponding author. Fax: þ61 7 3138 6010. E-mail addresses: [email protected] (A.G. Barnett), ˚ ¨ [email protected] (C. Astr om). 0013-9351/$ - see front matter & 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.envres.2012.05.008
In this commentary we re-run our analysis of the best predictor of mortality using the correct estimates of apparent temperature, minimum apparent temperature and maximum apparent temperature. We compare these new results with the previous results in order to check whether apparent temperature is a better predictor of mortality than the other measures tested, such as mean temperature or the Humidex. 2. Methods We used the same statistical methods as before to estimate the predictive ability of each temperature measure (Barnett et al., 2010). We fitted Poisson regression models in each of the 107 cities with daily deaths as the dependent variable and the daily temperature measure as the key independent variable. We tried 13 different measures of temperature and also fitted a model without temperature as a baseline comparison. The temperature estimates were fitted using a distributed lagged nonlinear model to allow both a delayed and non-linear effect (Gasparrini et al., 2010). We assumed a delay of up to 25 days and modeled the shape of the delayed risk using a natural spline with 3, 4 or 5 degrees of freedom. We tried 4, 5 and 6 degrees of freedom for the temperature measures in order to capture the typically non-linear U-shaped risk. We also fitted a natural spline for time to control for trends and seasonal patterns in mortality, and tried 5, 6 and 7 degrees of freedom per year. Before fitting the model we randomly deleted 10% of the mortality data, and then compared the predicted daily mortality with the observed using the squared Pearson residual. We repeated this cross-validation 50 times in each city. The average of the squared residuals is then a useful statistic, as smaller values mean a better predictor of mortality. We compared these averages for the different degrees of freedom in order to find the best combination of degrees of freedom for season, lag and temperature. To find the temperature measure with the smallest residuals we used a regression model with a dependent variable of mean residual and independent variable of the temperature measure (n¼ 14 categories), city (n¼107) and cross-validation (n¼50). We plotted the modeled mean residuals for each
˚ om / Environmental Research 118 (2012) 149–151 A.G. Barnett, C. Astr¨
150
Table 1 Average Pearson correlations between the daily temperature measures and humidity for the 107 US Cities, 1987–2000. The correlations wrongly using degrees Fahrenheit for apparent temperature are in parenthesis.
Mean temperature (1C) Min temperature (1C) Max temperature (1C) AT (1C) Min AT (1C) Max AT (1C) Humidex (1C)
Min (1C)
Max (1C)
AT (1C)
Min AT (1C)
Max AT (1C)
Humidex (1C)
RH (%)
0.963
0.971 0.890
0.989 (0.955) 0.963 (0.953) 0.953 (0.906)
0.954 0.989 0.881 0.974
0.975 0.911 0.988 0.979 0.921
0.988 0.968 0.948 0.996 (0.989) 0.975 (0.973) 0.971 (0.988)
0.048 0.082 0.146 0.001 (0.154) 0.108 (0.213) 0.087 (0.102) 0.051
(0.933) (0.963) (0.865) (0.992)
(0.962) (0.937) (0.939) (0.993) (0.975)
Abbreviations: AT, apparent temperature; RH, relative humidity.
3. Results
New Previous
0.842
The Pearson correlations between the measures of temperature and humidity are shown in Table 1. The biggest changes after correctly using degrees Celsius for apparent temperature were generally smaller correlations between apparent temperature and relative humidity. The other correlations were similarly strong and positive. The mean cross-validated residuals for the 14 models by age group are in Fig. 1. There was very little difference in the predictive ability of apparent temperature when it was calculated using degrees Celsius or Fahrenheit. There was a small difference in the oldest age group, with the new apparent temperature doing worse than the previous, and the new minimum apparent temperature doing slightly better.
0.840 0.838 0.836 0.834
Mean residual
0.756 0.755
4. Discussion
0.754 0.753 0.752
0.955 0.954 0.953 0.952
in ea n A M pp ax A M pp in A H pp um M id ax ex + H M u in m1 M + ea Hu n m1 + H M ax um 1 + M Hu in m2 M +H ea n um 2 + H um 2
M
M
N
on e M ax
0.951
Fig. 1. Mean cross-validated residuals (and 95% credible intervals) for the 14 different models by age group: o 65 years (top row), 65–74 years (middle row), Z 75 years (bottom row). The smaller the residual, the better the model. App ¼apparent; Hum1 ¼ humidity with the same natural spline basis as temperature; Hum2 ¼ same day humidity using a natural spline with 3 degrees of freedom. The new results using degrees Celsius for apparent temperature are in black, and the previous results using degrees Fahrenheit are in gray.
temperature measure together with its 95% credible interval. We give the credible interval rather than the confidence interval as the model was fitted using a Bayesian paradigm. To summarize the correlations between the daily measures of temperature and humidity we calculated the Pearson correlations in each city and then averaged these correlations over the 107 cities.
Wrongly calculating apparent temperature made no difference to its ability to predict mortality. The mistake had a relatively minor impact because of the strong positive correlation between apparent temperatures calculated using either degrees Fahrenheit or Celsius (Eq. (1)). This strong correlation made for similar mortality predictions, and hence similar conclusions about apparent temperature’s ability to predict mortality. The main conclusion from our previous analysis holds: that there was no one temperature measure that was superior to the others. Future studies on the health effects of temperature should use a temperature measure that (i) has a good coverage across the study area from multiple monitoring sites, (ii) has few missing values, (iii) is easily understood by the public (e.g., mean temperature). This last point is particularly true for heat-warnings systems, as warnings on scales that people do not understand are often ignored (Bickerstaff, 2004). Bobb et al. (2011) recently aimed to find which of the 33 different combinations of maximum and dew-point temperature was the best predictor of mortality in heat waves, and they also used the NMMAPS data. Similar to our study, they found that no model was dominant, as there was a great variability in the best temperature model between cities. Other experts in the field have also recently commented on how estimates of mortality differ little for different temperature measures (Basu et al., 2008; Hajat and Kosatky, 2010). When estimating the health effects of temperature the choice of the temperature measure is of less importance compared with other model choices, such as the length of the longest exposure lag, and whether heat waves are modeled as additional effects.
Acknowledgments Thanks to the Department of Biostatistics at the Johns Hopkins Bloomberg School of Public Health and the Health Effects Institute
˚ om / Environmental Research 118 (2012) 149–151 A.G. Barnett, C. Astr¨
for making the National Morbidity and Mortality Air Pollution Study data publicly available. Computational resources and services used in this work were provided by the High Performance Computer and Research Support Unit, Queensland University of Technology, Brisbane, Australia. References Barnett, A., Tong, S., Clements, A., 2010. What measure of temperature is the best predictor of mortality? Environ. Res. 110 (6), 604–611. Basu, R., Feng, W.-Y., Ostro, B.D., 2008. Characterizing temperature and mortality in nine California counties. Epidemiology 19, 138–145.
151
Bickerstaff, K., 2004. Risk perception research: socio-cultural perspectives on the public experience of air pollution. Environ. Int. 30, 827–840. Bobb, J.F., Dominici, F., Peng, R.D., 2011. A Bayesian model averaging approach for estimating the relative risk of mortality associated with heat waves in 105 U.S. cities. Biometrics 67, 1605–1616. Gasparrini, A., Armstrong, B., Kenward, M.G., 2010. Distributed lag non-linear models. Stat. Med. 29 (21), 2224–2234. Hajat, S., Kosatky, T., 2010. Heat-related mortality: a review and exploration of heterogeneity. J. Epidemiol. Community Health 64 (9), 753–760. Samet, J.M., Dominici, F., Zeger, S.L., et al., 2000. National Morbidity, Mortality, and Air Pollution Study. Part I: Methods and Methodologic Issues. Technical Report, Health Effects Institute. Available from /http://pubs.healtheffects. org/view.php?id=118S. Zanobetti, A., Schwartz, J., 2008. Temperature and mortality in nine US cities. Epidemiology 19 (4), 563–570.