Although studies have provided estimates of premature deaths attributable to either heat or cold in selected countries, none has so far offered a systematic assessment across the whole temperature range in populations exposed to different climates. We aimed to quantify the total mortality burden attributable to non-optimum ambient temperature, and the relative contributions from heat and cold and from moderate and extreme temperatures. We collected data for 384 locations in Australia, Brazil, Canada, China, Italy, Japan, South Korea, Spain, Sweden, Taiwan, Thailand, UK, and USA. We fitted a standard time-series Poisson model for each location, controlling for trends and day of the week. We estimated temperature-mortality associations with a distributed lag non-linear model with 21 days of lag, and then pooled them in a multivariate metaregression that included country indicators and temperature average and range. We calculated attributable deaths for heat and cold, defined as temperatures above and below the optimum temperature, which corresponded to the point of minimum mortality, and for moderate and extreme temperatures, defined using cutoffs at the 2·5th and 97·5th temperature percentiles. We analysed 74,225,200 deaths in various periods between 1985 and 2012. In total, 7·71% (95% empirical CI 7·43-7·91) of mortality was attributable to non-optimum temperature in the selected countries within the study period, with substantial differences between countries, ranging from 3·37% (3·06 to 3·63) in Thailand to 11·00% (9·29 to 12·47) in China. The temperature percentile of minimum mortality varied from roughly the 60th percentile in tropical areas to about the 80-90th percentile in temperate regions. More temperature-attributable deaths were caused by cold (7·29%, 7·02-7·49) than by heat (0·42%, 0·39-0·44). Extreme cold and hot temperatures were responsible for 0·86% (0·84-0·87) of total mortality. Most of the temperature-related mortality burden was attributable to the contribution of cold. The effect of days of extreme temperature was substantially less than that attributable to milder but non-optimum weather. This evidence has important implications for the planning of public-health interventions to minimise the health consequences of adverse temperatures, and for predictions of future effect in climate-change scenarios. UK Medical Research Council.

Interrupted time series (ITS) analysis is a valuable study design for evaluating the effectiveness of population-level health interventions that have been implemented at a clearly defined point in time. It is increasingly being used to evaluate the effectiveness of interventions ranging from clinical therapy to national public health legislation. Whereas the design shares many properties of regression-based approaches in other epidemiological studies, there are a range of unique features of time series data that require additional methodological considerations. In this tutorial we use a worked example to demonstrate a robust approach to ITS analysis using segmented regression. We begin by describing the design and considering when ITS is an appropriate design choice. We then discuss the essential, yet often omitted, step of proposing the impact model a priori. Subsequently, we demonstrate the approach to statistical analysis including the main segmented regression model. Finally we describe the main methodological issues associated with ITS analysis: over-dispersion of time series data, autocorrelation, adjusting for seasonal trends and controlling for time-varying confounders, and we also outline some of the more complex design adaptations that can be used to strengthen the basic ITS design.

Environmental stressors often show effects that are delayed in time, requiring the use of statistical models that are flexible enough to describe the additional time dimension of the exposure–response relationship. Here we develop the family of distributed lag non‐linear models (DLNM), a modelling framework that can simultaneously represent non‐linear exposure–response dependencies and delayed effects. This methodology is based on the definition of a ‘cross‐basis’, a bi‐dimensional space of functions that describes simultaneously the shape of the relationship along both the space of the predictor and the lag dimension of its occurrence. In this way the approach provides a unified framework for a range of models that have previously been used in this setting, and new more flexible variants. This family of models is implemented in the package dlnm within the statistical environment R. To illustrate the methodology we use examples of DLNMs to represent the relationship between temperature and mortality, using data from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) for New York during the period 1987–2000. Copyright © 2010 John Wiley & Sons, Ltd.

The systematic evaluation of the results of time-series studies of air pollution is challenged by differences in model specification and publication bias. We evaluated the associations of inhalable particulate matter (PM) with an aerodynamic diameter of 10 μm or less (PM₁₀) and fine PM with an aerodynamic diameter of 2.5 μm or less (PM_2.5) with daily all-cause, cardiovascular, and respiratory mortality across multiple countries or regions. Daily data on mortality and air pollution were collected from 652 cities in 24 countries or regions. We used overdispersed generalized additive models with random-effects meta-analysis to investigate the associations. Two-pollutant models were fitted to test the robustness of the associations. Concentration–response curves from each city were pooled to allow global estimates to be derived. On average, an increase of 10 μg per cubic meter in the 2-day moving average of PM₁₀ concentration, which represents the average over the current and previous day, was associated with increases of 0.44% (95% confidence interval [CI], 0.39 to 0.50) in daily all-cause mortality, 0.36% (95% CI, 0.30 to 0.43) in daily cardiovascular mortality, and 0.47% (95% CI, 0.35 to 0.58) in daily respiratory mortality. The corresponding increases in daily mortality for the same change in PM_2.5 concentration were 0.68% (95% CI, 0.59 to 0.77), 0.55% (95% CI, 0.45 to 0.66), and 0.74% (95% CI, 0.53 to 0.95). These associations remained significant after adjustment for gaseous pollutants. Associations were stronger in locations with lower annual mean PM concentrations and higher annual mean temperatures. The pooled concentration–response curves showed a consistent increase in daily mortality with increasing PM concentration, with steeper slopes at lower PM concentrations. Our data show independent associations between short-term exposure to PM₁₀ and PM_2.5 and daily all-cause, cardiovascular, and respiratory mortality in more than 600 cities across the globe. These data reinforce the evidence of a link between mortality and PM concentration established in regional and local studies. (Funded by the National Natural Science Foundation of China and others.)

Distributed Lag Linear and Non-Linear Models in R: The Package dlnm

The two-stage time series design represents a powerful analytical tool in environmental epidemiology. Recently, models for both stages have been extended with the development of distributed lag non-linear models (DLNMs), a methodology for investigating simultaneously non-linear and lagged relationships, and multivariate meta-analysis, a methodology to pool estimates of multi-parameter associations. However, the application of both methods in two-stage analyses is prevented by the high-dimensional definition of DLNMs.