Demographic and epidemiologic studies have shown clear seasonal patterns in mortality, with peaks in winter and dips in summer.1–4 This trend is consistent across the world and for various causes of death.1,5–7 Several investigations have evaluated the subject further by describing long-term trends in seasonality,1–3 gaps between winter and summer mortality rates,8,9 or the amplitude and the acrophase of the sinusoidal curve representing the mortality time-series on an annual time scale.4,5,10 To our knowledge, few investigators have explored how winter mortality levels may influence the impact of high temperatures and heat waves on mortality during summer. Three papers have considered this issue, one in a brief discussion,11 another as a commentary,12 and only the third analytically.13
The health effects of summer heat waves emerged as a scientific issue after the August 2003 heat wave in Europe, which caused several thousand deaths.14–16 Scenarios of future climate changes predict increases in frequency and intensity in heat waves that are likely to increase mortality.17,18 Recent epidemiologic investigations have described a variable impact of high temperature on mortality19–21 with effect estimates ranging from 5% (15°C–29°C) to 34% (20°C–30°C). Temperature ranges, population characteristics and adaptation, and use of air conditioning may modify these effects. We postulate that the size of the susceptible subgroup exposed to high summer temperatures may also affect temperature-related mortality.
We propose a simple compartmental model22,23 in which the overall population is composed of 2 pools of subjects: a low-risk pool, which constitutes the majority, and a smaller high-risk pool, of a susceptible population. Two simple transitions can occur: a healthy person can become frail or ill and a person in this frail group can die. On a given day, there are transitions from a healthy to a frail state, and from a frail state to death. Environmental stressors such as air pollution, heat waves, and cold spells can affect such transitions. We assume that the high-risk pool increases in winters with low mortality, making a larger number of subjects at risk for dying from high temperatures during the next summer. Conversely, if winter mortality is particularly high, the susceptible pool may decrease, with the less susceptible surviving until the next summer. In this case, the strength of the association between high summer temperature and mortality would be less. We explore this hypothesis using data from Rome.
The study population consisted of 314,496 subjects 65 years of age or older who were residents of Rome and died in the city from natural causes (International Classification of Diseases, 9th revision–ICD-9: 1–799) between 1987 and 2005. The information on underlying causes of death was available, and we identified 2 major groups of causes for further analysis: cardiovascular diseases (ICD-9: 390–459; n = 146,048) and respiratory diseases (ICD-9: 460–519; n = 20,333).
Information on daily environmental variables was obtained from the Italian Air Force Meteorological Service, which provided data on air temperature (°C), dew point temperature (°C), and barometric pressure (hPa). We decided a priori to use apparent temperature as our exposure measure, to take into account the actual physical stress experienced on days with extreme temperature and humidity. Apparent temperature was calculated using the formula of Steadman and Kalkstein24,25:
Apparent temperature = −2.653 + 0.994×(Air temperature) + 0.0153 × (Dew-point temperature)2.
We evaluated the association between summer apparent temperature (lag 0–1) and mortality (by cause of death, among subjects aged 65 years or older). We tested the hypothesis that such an association was modified by the level of mortality (from all natural causes) in the preceding winter. First, we applied Fourier decomposition26 to the daily series of natural deaths (of people aged ≥65 years) to remove the long-term component and focus on the yearly and seasonal fluctuations in mortality. Fourier discrete transform is a technique widely used in econometrics27 to isolate different wavelengths in a time-series and describe an original variable according to a set of orthogonal components. In the present context, a long-term trend was defined as a cycle longer than 6 years.
Second, we ranked the 19 winters according to the mean daily number of natural deaths (with the long-term component removed), and defined 3 categories: low mortality (the 3 winters with the lowest all-cause mortality), high mortality (the 3 winters with the highest all-cause mortality), and intermediate mortality (the remaining 13 winters). All deaths in summer were considered, with previous-winter mortality rate as an effect modifier of the temperature/mortality association.
Third, a time-series approach was used to study the association between summer apparent temperature and mortality, within the generalized linear models (GLM) framework.28 In particular, the daily count of deaths was assumed to be Poisson distributed, and was regressed against daily mean apparent temperature (the exposure variable, defined as the average of current and previous day, lag 0–1), time-trends (see below), current day mean barometric pressure (1 linear term), population decreases during the summer (a 3-level variable assuming value “2” for the 2-week period around 15 August, “1” from 16 July to 31 August with the exception of the aforementioned 2-week period, and “0” on the remaining days), and holidays (1 dummy variable), while allowing for overdispersion.28 The 0–1 lag window for apparent temperature was chosen a priori to take into account immediate health effects of heat.
The adjustment of time-trend was crucial, because seasonal and longer-term trends are closely related to the study outcome as well as to apparent temperature. This is particularly true in the present context, in which strict control for seasonality was necessary to isolate the summer temperature effects from spurious associations with other seasonal factors. To this end, time trend was adjusted by adding a triple interaction between year of death, month of death, and day of the week. This choice was motivated by the need to control seasonality, and by theoretical results that show such adjustment is equivalent to a case-crossover design with the “time-stratified” approach for the selection of control days.29–31 Sensitivity analyses were performed with alternative strategies to control long-term and seasonal time trends, and results did not change consistently.
Because the relation between apparent temperature and mortality has been shown to be exponential for the highest temperatures,21,32,33 we modeled this relationship with a linear piecewise spline having 6 inner knots at 22, 24, 26, 28, 30, and 32°C, and with the slope constrained to zero below 20°C. This choice was motivated by a desire for simplicity, and supported by an exploratory analysis using penalized cubic regression splines.34 The same model was applied to the entire summer period, stratifying by the previous winter mortality variable and using natural, cardiovascular, and respiratory mortality as alternative outcomes.
For each model, we estimated the relative risk (RR) and 95% confidence interval (CI) of dying on a day with 30°C lagged (0–1 day) apparent temperature compared with a day with 20°C.
Relative effect modification was evaluated among categories of previous winter mortality, comparing the effect estimate of summer temperatures on mortality in the high-level stratum (chosen as the reference group) with estimates from the other 2 categories. The corresponding P value is reported.
We also computed the percentage of attributable risk in exposed subjects. In particular, for each 2-degree centigrade increase in apparent temperature from 20°C onward, attributable risk was computed as (RR – 1)/RR.35 The numbers of attributable deaths were derived for each 2°C interval as the product of the percentage of attributable risk for that interval, and the total number of deaths occurring on days with apparent temperature in the interval. Finally, the total number of deaths attributable to high summer temperatures was derived by summing all interval-specific numbers, and the corresponding percentage of attributable risk is calculated as a ratio of total attributable deaths and total summer deaths.
Several sensitivity analyses were performed to check robustness of the main results. First, we ran summer-specific analysis of the apparent temperature–mortality association, and regressed the 19 log-RRs (of dying on a summer day with 30°C compared with a summer day with 20°C) against previous winter mean mortality levels to show that the general decreasing effect of summer temperature with increasing winter mortality levels was insensitive to the choice of “high-” and “low-” mortality categories. Second, we regressed the time-series of daily counts of deaths (age ≥65 years) against trend (modeled with a fourth degree polynomial), and used the residuals from this model to rank winters according to their mean mortality levels (as an alternative to the Fourier decomposition). Third, we adjusted for seasonal trend in the summer apparent temperature–mortality association by adding a penalized spline of time trend with 1 knot for each summer, plus an independent effect of the days of the week (an alternative to the triple interaction between year, month, and day of the week as used in the main analysis). Fourth, to take into account a possible midterm harvesting due to spring mortality, we ranked the 19 years according to mean mortality level of winter and spring together, and used this variable as an effect modifier of the summer temperature–mortality association. Finally, we restricted the analysis to the period 1992–2005 for which information was available on ozone, and added the lagged 0–1 air pollutant (1 linear term) as potential confounder in the summer temperature–mortality association analysis.
Table 1 provides a summary of mortality counts and environmental variables for the whole year and stratified by season. Of 314,496 subjects aged 65 years or older who died of natural causes between 1987 and 2005, 88,718 (28%) died in the winter season, whereas only 72,580 (23%) died during the summer. The gap increases when considering cardiovascular mortality (30% in winter vs. 22% in summer) and respiratory mortality (33% in winter vs. 21% in summer). The mean number of winter deaths was 52 (range 24–92; interquartile range 13) whereas the mean number of summer deaths was 42 (17–92; 12); the variability was higher for cardiovascular and respiratory diseases. The average apparent temperature (lag 0–1) across the full-year series was 15°C, with a high variability between winter (6°C) and summer (26°C). Once the long-term component was removed from the mortality data, the daily mean number of deaths was 36 (range 35–37) during the “low” mortality winters, 40 (range 38–42) during the “mid” mortality winters, and 46 (range 44–47) in the “high” mortality category.
Table 2 displays results from the analysis of the association between apparent temperature (lag 0–1) and mortality in the summer season, by cause of death and level of natural mortality in the preceding winter: results are expressed as relative risks, with corresponding 95% CIs, of dying on a summer day with an apparent temperature of 30°C (lag 0–1) compared with a summer day with 20°C. A test of relative effect modification was performed. The actual impact of high temperatures on mortality was estimated as the percentage of attributable risk. The effect estimate across all 19 summers was 1.39 (1.32–1.47) for natural mortality, 1.44 (1.34–1.55) for cardiovascular mortality, and 1.70 (1.39–2.08) for respiratory mortality. A strong effect modification was apparent in relation to the mean level of previous winter mortality: the effect of summer apparent temperature on natural mortality was much larger when average mortality was low during the previous winter (RR = 1.73 [CI = 1.50–2.01]), compared with medium or high winter mortality levels (1.32 [1.25–1.41], and 1.34 [1.17–1.55], respectively). A similar pattern was apparent for cardiovascular mortality. The P value for relative effect modification was 0.015 for natural mortality and 0.113 for cardiovascular mortality. Results for respiratory mortality were inconsistent. The actual impact of summer temperature on mortality, measured as the percentage of attributable risk, was also strongly differential across categories of previous-winter mortality: the percentages of attributable risk were 18% for natural mortality in the previous winters with both high and mid mortality, whereas it was 28% in the low category. Corresponding values for cardiovascular mortality were 14% in the high-mortality level from the previous winter, 20% in the mid level, and 26% in the low level.
The exposure–response relationship between summer apparent temperature (lag 0–1) and natural mortality is displayed in Figure 1 for the entire summer season and stratified by the previous-winter mortality variable (with the long-term component removed). Relative risks (and 95% CIs) are expressed as risks from 20°C to increasing values of apparent temperature, as reported on the x-axis of the figure. The slope of the relationship is steepest for the low winter mortality category, and gradually decreases in the mid- and the high winter mortality categories.
Figure 2 shows results from the first sensitivity analysis, which evaluated whether the main results were sensitive to the choice of the cut-off points defining low, mid and high previous-winter mortality. We estimated the effect of apparent temperature on natural mortality for each one of the 19 summers separately, ranked by previous-winter mean mortality level. Effect estimates are expressed as log-relative risks (RR), with corresponding 95% CIs, of dying on a summer day with an apparent temperature of 30°C (lag 0–1) compared with a summer day with 20°C. A regression line of the 19 points is shown, with relative slope and 95% CI. The results suggest a decreasing trend in the effect estimates of summer apparent temperature on natural mortality as the average previous-winter mortality increases.
Table 3 reports results from the other sensitivity analyses, expressed as relative risks and corresponding 95% confidence intervals, P of the relative effect modification by previous-winter mortality level categories, and percentage of attributable risks in the exposed population. The main results, as reported in the “base model” section of the table, hold regardless of the way of adjustment for long-term trend and seasonality, and whether control for air pollution is performed. Interestingly, when previous-spring mortality rates are taken into account in addition to winter levels, a stronger effect modification emerges, with P for relative effect modification of 0.030 and 0.000 when comparing “mid” and “low” mortality categories with “high,” respectively.
The present study was designed to test the analytical hypothesis that summer temperature exerts a differential effect on mortality according to the mean mortality level in the previous winter. We found a higher effect in years with lower winter mortality than in years with winter mortality at or above the long-term seasonal average. Although the results were strong for natural and cardiovascular causes of death, the evidence for respiratory mortality was weaker.
Previous studies have identified strong seasonal patterns in mortality, with winter peaks and summer dips.1–4 This trend has been seen in Europe,2,4,8 America,1 and Asia,5 in both hemispheres,36,37 and holds for different causes of deaths5,6,10 and subgroups of the population.3,4,38,39 As our study indicates, there is a certain variability in winter mortality. Although several factors could be responsible, the most likely explanations are viral epidemics, including influenza, and cold-related mortality. A few studies3,7,38,39 have concentrated on more vulnerable individuals such as the elderly, subjects with chronic conditions, and those of poor socioeconomic status, and found greater discrepancy in mean mortality levels between summer and winter, compared with younger and healthier subgroups of the population. It has been suggested that the strong seasonality of mortality in frailer subjects is partially attributable to a “harvesting” (or “mortality displacement”) mechanism, according to which those subjects were bound to die soon anyway, and their deaths were precipitated only by a few days or weeks by seasonal factors such as extreme winter temperatures, influenza epidemics, or other infections.4,11,39 Only 1 recent study13 has addressed the issue analytically.
Summer temperature has been shown to be strongly associated with mortality, with an exposure–response relationship generally j-shaped, characterized by minimum risk from intermediate temperatures, and risk that rises exponentially as temperatures reach extremely high values.21,32,33 Several individual characteristics have been suggested as potential effect modifiers, such as old age,21,40,41 high socioeconomic deprivation,19 and the presence of chronic and acute conditions (for example, cerebrovascular diseases,21,42 depression,21,43 psychoses,21,43 and diabetes).44 Although several studies have addressed the issue of individual effect modifiers, the question about the net effect of summer temperature on the temporal dynamics on susceptible populations is still open. Some attempts have been made to explore the “harvesting” hypothesis related to heat waves on a short time scale,45–47 as has been done already with reference to air pollution.48–51 Although evidence is against the pure harvesting phenomenon for air pollution, results of heat waves suggest that short-term harvesting is an important component.
The seasonal patterns of mortality, and the variability in the amplitude of the sinusoidal curve describing this pattern, also suggest that long-term harvesting could be an issue contributing to the discrepancy in mortality between winter and summer. More specifically, we observed that higher winter peaks in mortality were generally followed by deeper summer troughs, and smaller winter peaks from smaller dips on the next summer (data not shown). Winter mortality can exert an important effect on the size of the susceptible subpopulation, leading to a larger number of subjects dying during summer when more vulnerable individuals have survived a “mild” winter, as opposed to years with “frigid” winters that harvest the frailest people and lead only to the healthiest surviving. Three papers4,11,39 have addressed this issue in their discussions, and another one as a commentary,12 arguing that the most suitable way to investigate seasonal harvesting would be to analyze it prospectively in a dynamic cohort of susceptible individuals. This would enable the recording of both entries from the general population and exits for deaths, referring events to well-defined denominators of vulnerable subgroups. The present study, although not prospective in design, represents an attempt to explore the long-term harvesting phenomenon. Another recent paper, ecological in design as the present one, tried to investigate the long-term harvesting issue, and found that high temperatures effect on summer mortality is higher when preceded by a winter characterized by low death rates, especially for respiratory or cardiovascular causes.13
It has been suggested that seasonality in mortality is decreasing over time due to improved heating conditions and better insulation from the outdoor environment in colder months, as well as lower mortality from pneumonia and infectious diseases. Lower winter mortality can increase the size of the susceptible population. Climate changes toward warmer temperatures and higher frequency of extreme hot spells make high summer temperatures of increasing importance in characterizing the size and composition of the more vulnerable subgroups of the population. In the present study, the analysis of effect modification due to winter mortality levels in the summer temperature/mortality association showed a much greater effect of high temperatures in years characterized by low mortality during the preceding winter. The seasonal average number of deaths attributable to heat was 1009 in summers in which previous winter mortality was low, compared with only 690 when previous winter mortality was intermediate or high (data not shown): this is a difference of about 300 subjects per summer. In other terms, although the differential effect is not negligible, it applies to a susceptible population whose size is modest. It should be considered, however, that we focused in our calculation on the effect of winter mortality to test our main hypothesis. In additional analyses, spring mortality level was also an important effect modifier, thus increasing the size of the susceptible population.
It should be noted that although strong effect modification of winter mortality was found in the summer temperature–mortality association, for all natural and cardiovascular diseases, the results for respiratory causes were weak. Although power was more limited for this condition, this anomaly should be further investigated and the role of influenza vaccination over the years should be explored.
Our study has several strengths that deserve consideration. First, the study took place over almost 2 decades and involved about 315,000 deaths. Second, only mortality of elderly people (≥65 years) was considered, a subgroup of the population already at increased risk and more susceptible to the harmful effects of environmental stressors, as many epidemiologic studies have shown.21,40,41 Third, the availability of information on the causes of death enabled us to focus on cardiovascular and respiratory mortality, known from previous investigations to exhibit the highest seasonality5,6,10 and the strongest association with summer apparent temperature.52,53 Fourth, the application of time-series decomposition allowed us to isolate the seasonal components of mortality, to disregard the long-term time trend and describe the seasonal patterns of mortality and the effects of temperature on subannual cycles only. Finally, several sensitivity analyses were performed, all confirming the main results.
Some limitations also have to be acknowledged. Given the duration of the time-series involved, data on air pollutants, potential confounders of the temperature–mortality association, could not be collected for the entire period (data on particulate matter smaller than 10 μ in diameter—PM10, and ozone were available only from 1992). However, when the confounding effect of ozone was evaluated in the sensitivity analysis, the results were confirmed and it is unlikely that air pollutants play a major role in the effect modification we found.
In conclusion, our study suggests that the mortality rate during winter modifies the impact of summer high temperature during the subsequent summer. This phenomenon could partly explain the heterogeneity of the temperature-related mortality effect that has been observed within and across cities in recent years.19–21
We thank Margaret Becker for her editorial support.
1. Rosenwaike I. Seasonal variation of deaths in the United States, 1951–1960. J Am Stat Assoc
2. Momiyama M, Katayama K. Deseasonalization of mortality in the world. Int J Biometeorol
3. McDowall M. Long term trends in seasonal mortality. Popul Trends
4. Gemmell I, McLoone P, Boddy FA, Dickinson GJ, Watt GCM. Seasonal variation in mortality in Scotland. Int J Epidemiol
5. Becker S, Weng S. Seasonal patterns of deaths in Matlab, Bangladesh. Int J Epidemiol
6. van Rossum CT, Shipley MJ, Hemingway H, Grobbee DE, Mackenbach JP, Marmot MG. Seasonal variation in cause-specific mortality: are there high-risk groups? Twenty-five-year follow-up of civil servants from the first Whitehall study. Int J Epidemiol
7. Feinstein CA. Seasonality of deaths in US by age and cause. Demogr Res
8. Lerchl A. Changes in the seasonality of mortality in Germany from 1946 to 1995: the role of temperature. Int J Biometeorol
9. Carson C, Hajat S, Armstrong B, Wilkinson P. Declining vulnerability to temperature-related mortality in London over the 20th century. Am J Epidemiol
10. Crawford VL, McCann M, Stout RW. Changes in seasonal deaths from myocardial infarction. Q J Med
11. Simón F, Lopez-Abente G, Ballester E, Martinez F. Mortality in Spain during the heat waves of summer 2003. Euro Surveill
12. Sunyer J. Evaluating response to heat waves [commentary]. Int J Epidemiol
13. Rocklöv J, Forsberg B, Meister K. Winter mortality modifies the heat-mortality association the following summer. Eur Respir J
14. Dhainaut JF, Claessens YE, Ginsburg C, Riou B. Unprecedented heat-related deaths during the 2003 heat wave in Paris: consequences on emergency departments. Crit Care
15. Michelozzi P, de'Donato F, Accetta G, et al. Impact of heat waves on mortality—Rome, Italy, June-August 2003. Morb Mortal Wkly Rep
16. Michelozzi P, Kirchmayer U, Katsouyanni K, et al. Assessment and prevention of acute health effects of weather conditions in Europe, the PHEWE project: background, objectives, design. Environ Health
17. Intergovernmental Panel on Climate Change, United Nations Environment Program. Available at: http://22.214.171.124/
. Accessed November 20, 2007.
18. Ron WN, Pinkerton KE, Martin WJ, Forastiere F. Global warming: a challenge to all American Thoracic Society members [editorial]. Am J Respir Crit Care Med
19. O'Neill MS, Zanobetti A, Schwartz J. Modifiers of the temperature and mortality association in seven US cities. Am J Epidemiol
20. Hajat S, Armstrong BG, Gouveia N, Wilkinson P. Mortality displacement of heat-related deaths—a comparison of Delhi, São Paulo, and London. Epidemiology
21. Stafoggia M, Forastiere F, Agostini D, et al. Vulnerability to heat-related mortality—a multicity, population-based, case-crossover analysis. Epidemiology
22. Zeger SL, Dominici F, Samet J. Harvesting-resistant estimates of air pollution effects on mortality. Epidemiology
23. Schwartz J. Is there harvesting in the association of airborne particles with daily deaths and hospital admissions? Epidemiology
24. Steadman RG. The assessment of sultriness. Part I: a temperature-humidity index based on human physiology and clothing science. J Appl Meteorol
25. Kalkstein LS, Valimont KM. An evaluation of summer discomfort in the United States using a relative climatological index. Bull Am Meteorol Soc
26. Bloomfield P. Fourier Analysis of Time Series: An Introduction
. New York: John Wiley & Sons, Inc; 1976.
27. Rachev ST, Mittnik S, Fabozzi FJ, Focardi SM, Jašić T. Financial Econometrics: From Basics to Advanced Modeling Techniques
. New York: John Wiley and Sons, Inc; 2007.
28. McCullagh P, Nelder J. Generalized Linear Models
. 2nd ed. New York: Chapman and Hall; 1989.
29. Lu Y, Zeger SL. On the equivalence of case-crossover and time series methods in environmental epidemiology. Biostatistics
30. Maclure M. The case-crossover design: a method for studying transient effects on the risk of acute events. Am J Epidemiol
31. Levy D, Lumley T, Sheppard L, Kaufman J, Checkoway H. Referent selection in case-crossover analyses of acute health effects of air pollution. Epidemiology
32. Armstrong BG. Models for the relationship between ambient temperature and daily mortality. Epidemiology
33. Hajat S, Armstrong BG, Baccini M, et al. Impact of high temperatures on mortality—is there an added heat wave effect? Epidemiology
34. Wood SN, Augustin NH. GAMs with integrated model selection using penalized regression splines and applications to environmental modelling. Ecol Model
35. Bruzzi P, Green SB, Byar DP, Brinton LA, Schairer C. Estimating the population attributable risk for multiple risk factors using case–control data. Am J Epidemiol
36. Douglas AS, Russell D, Allan TM. Seasonal, regional, and secular variations of cardiovascular and cerebrovascular mortality in New Zealand. Aust N Z J Med
37. Weerasinghe DP, MacIntyre CR, Rubin GL. Seasonality of coronary artery deaths in New South Wales, Australia. Heart
38. Aylin P, Morris S, Wakefield J, Grossinho A, Jarup L, Elliott P. Temperature, housing, deprivation and their relationship to excess winter mortality in Great Britain, 1986–1996. Int J Epidemiol
39. Rau R, Doblhammer G. Seasonal mortality in Denmark: the role of sex and age. Demogr Res
40. Basu R, Samet JM. An exposure assessment study of ambient heat exposure in an elderly population in Baltimore, Maryland. Environ Health Perspect
41. Diaz J, Garcia R, Velazquez de Castro F, Hernández E, López C, Otero A. Effects of extremely hot days on people older than 65 years in Seville (Spain) from 1986 to 1997. Int J Biometeorol
42. Michelozzi P, de'Donato FK, Bisanti L, et al. The impact of the summer 2003 heat waves on mortality in four Italian cities. Euro Surveill
43. Bark N. Deaths of psychiatric patients during heat waves. Psychiatr Serv
44. Schwartz J. Who is sensitive to extreme of temperature—a case-only analysis. Epidemiology
45. Braga AL, Zanobetti A, Schwartz J. The time course of weather-related deaths. Epidemiology
46. Gosling SN, McGregor GR, Páldy A. Climate change and heat-related mortality in six cities. Part 1: model construction and validation. Int J Biometeorol
47. Rey G, Jougla E, Fouillet A, et al. The impact of major heat waves on all-cause and cause-specific mortality in France from 1971 to 2003. Int Arch Occup Environ Health
48. Kelsall JE, Zeger SL, Samet JM. Frequency domain log-linear models; air pollution and mortality. Appl Stat
49. Dominici F, McDermott A, Zeger SL, Samet JM. Airborne particulate matter and mortality: timescale effects in four US cities. Am J Epidemiol
50. Fung K, Krewski D, Burnett R, Dominici F. Testing the harvesting hypothesis by time-domain regression analysis: baseline analysis. J Toxicol Environ Health A
51. Schwartz J. Harvesting and long term exposure in the relation between air pollution and mortality. Am J Epidemiol
52. Basu R, Samet JM. Relation between elevated ambient temperature and mortality: a review of the epidemiologic evidence. Epidemiol Rev
53. Curriero FC, Heiner KS, Samet JM, Zeger SL, Strug L, Patz JA. Temperature and mortality in eleven cities of the eastern United States. Am J Epidemiol