Antonio Gasparrini

Distributed lag non-linear models

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

Mortality risk attributable to high and low ambient temperature: a multicountry observational study.

Summary Background 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. Methods 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. Findings 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. Interpretation 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. Funding UK Medical Research Council.

Reducing and meta-analysing estimates from distributed lag non-linear models

BackgroundThe 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.MethodsIn this contribution we propose a method to synthesize DLNMs to simpler summaries, expressed by a reduced set of parameters of one-dimensional functions, which are compatible with current multivariate meta-analytical techniques. The methodology and modelling framework are implemented in R through the packages dlnm and mvmeta.ResultsAs an illustrative application, the method is adopted for the two-stage time series analysis of temperature-mortality associations using data from 10 regions in England and Wales. R code and data are available as supplementary online material.Discussion and ConclusionsThe methodology proposed here extends the use of DLNMs in two-stage analyses, obtaining meta-analytical estimates of easily interpretable summaries from complex non-linear and delayed associations. The approach relaxes the assumptions and avoids simplifications required by simpler modelling approaches.

Time series regression studies in environmental epidemiology

Time series regression studies have been widely used in environmental epidemiology, notably in investigating the short-term associations between exposures such as air pollution, weather variables or pollen, and health outcomes such as mortality, myocardial infarction or disease-specific hospital admissions. Typically, for both exposure and outcome, data are available at regular time intervals (e.g. daily pollution levels and daily mortality counts) and the aim is to explore short-term associations between them. In this article, we describe the general features of time series data, and we outline the analysis process, beginning with descriptive analysis, then focusing on issues in time series regression that differ from other regression methods: modelling short-term fluctuations in the presence of seasonal and long-term patterns, dealing with time varying confounding factors and modelling delayed (‘lagged’) associations between exposure and outcome. We finish with advice on model checking and sensitivity analysis, and some common extensions to the basic model.

Global variation in the effects of ambient temperature on mortality: a systematic evaluation

Background: Studies have examined the effects of temperature on mortality in a single city, country, or region. However, less evidence is available on the variation in the associations between temperature and mortality in multiple countries, analyzed simultaneously. Methods: We obtained daily data on temperature and mortality in 306 communities from 12 countries/regions (Australia, Brazil, Thailand, China, Taiwan, Korea, Japan, Italy, Spain, United Kingdom, United States, and Canada). Two-stage analyses were used to assess the nonlinear and delayed relation between temperature and mortality. In the first stage, a Poisson regression allowing overdispersion with distributed lag nonlinear model was used to estimate the community-specific temperature-mortality relation. In the second stage, a multivariate meta-analysis was used to pool the nonlinear and delayed effects of ambient temperature at the national level, in each country. Results: The temperatures associated with the lowest mortality were around the 75th percentile of temperature in all the countries/regions, ranging from 66th (Taiwan) to 80th (UK) percentiles. The estimated effects of cold and hot temperatures on mortality varied by community and country. Meta-analysis results show that both cold and hot temperatures increased the risk of mortality in all the countries/regions. Cold effects were delayed and lasted for many days, whereas heat effects appeared quickly and did not last long. Conclusions: People have some ability to adapt to their local climate type, but both cold and hot temperatures are still associated with increased risk of mortality. Public health strategies to alleviate the impact of ambient temperatures are important, in particular in the context of climate change.

Multivariate meta‐analysis for non‐linear and other multi‐parameter associations

In this paper, we formalize the application of multivariate meta-analysis and meta-regression to synthesize estimates of multi-parameter associations obtained from different studies. This modelling approach extends the standard two-stage analysis used to combine results across different sub-groups or populations. The most straightforward application is for the meta-analysis of non-linear relationships, described for example by regression coefficients of splines or other functions, but the methodology easily generalizes to any setting where complex associations are described by multiple correlated parameters. The modelling framework of multivariate meta-analysis is implemented in the package mvmeta within the statistical environment R. As an illustrative example, we propose a two-stage analysis for investigating the non-linear exposure–response relationship between temperature and non-accidental mortality using time-series data from multiple cities. Multivariate meta-analysis represents a useful analytical tool for studying complex associations through a two-stage procedure. Copyright

Interrupted time series regression for the evaluation of public health interventions: a tutorial

Abstract 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.

The effect of the late 2000s financial crisis on suicides in Spain: an interrupted time-series analysis

BACKGROUND The current financial crisis is having a major impact on European economies, especially that of Spain. Past evidence suggests that adverse macro-economic conditions exacerbate mental illness, but evidence from the current crisis is limited. This study analyses the association between the financial crisis and suicide rates in Spain. METHODS An interrupted time-series analysis of national suicides data between 2005 and 2010 was used to establish whether there has been any deviation in the underlying trend in suicide rates associated with the financial crisis. Segmented regression with a seasonally adjusted quasi-Poisson model was used for the analysis. Stratified analyses were performed to establish whether the effect of the crisis on suicides varied by region, sex and age group. RESULTS The mean monthly suicide rate in Spain during the study period was 0.61 per 100 000 with an underlying trend of a 0.3% decrease per month. We found an 8.0% increase in the suicide rate above this underlying trend since the financial crisis (95% CI: 1.009-1.156; P = 0.03); this was robust to sensitivity analysis. A control analysis showed no change in deaths from accidental falls associated with the crisis. Stratified analyses suggested that the association between the crisis and suicide rates is greatest in the Mediterranean and Northern areas, in males and amongst those of working age. CONCLUSIONS The financial crisis in Spain has been associated with a relative increase in suicides. Males and those of working age may be at particular risk of suicide associated with the crisis and may benefit from targeted interventions.

Cold and heat waves in the United States.

Extreme cold and heat waves, characterized by a number of cold or hot days in succession, place a strain on peoples cardiovascular and respiratory systems. The increase in deaths due to these waves may be greater than that predicted by extreme temperatures alone. We examined cold and heat waves in 99 US cities for 14 years (1987-2000) and investigated how the risk of death depended on the temperature threshold used to define a wave, and a waves timing, duration and intensity. We defined cold and heat waves using temperatures above and below cold and heat thresholds for two or more days. We tried five cold thresholds using the first to fifth percentiles of temperature, and five heat thresholds using the 95-99 percentiles. The extra wave effects were estimated using a two-stage model to ensure that their effects were estimated after removing the general effects of temperature. The increases in deaths associated with cold waves were generally small and not statistically significant, and there was even evidence of a decreased risk during the coldest waves. Heat waves generally increased the risk of death, particularly for the hottest heat threshold. Cold waves of a colder intensity or longer duration were not more dangerous. Cold waves earlier in the cool season were more dangerous, as were heat waves earlier in the warm season. In general there was no increased risk of death during cold waves above the known increased risk associated with cold temperatures. Cold or heat waves earlier in the cool or warm season may be more dangerous because of a build up in the susceptible pool or a lack of preparedness for extreme temperatures.

Modeling exposure–lag–response associations with distributed lag non-linear models

In biomedical research, a health effect is frequently associated with protracted exposures of varying intensity sustained in the past. The main complexity of modeling and interpreting such phenomena lies in the additional temporal dimension needed to express the association, as the risk depends on both intensity and timing of past exposures. This type of dependency is defined here as exposure–lag–response association. In this contribution, I illustrate a general statistical framework for such associations, established through the extension of distributed lag non-linear models, originally developed in time series analysis. This modeling class is based on the definition of a cross-basis, obtained by the combination of two functions to flexibly model linear or nonlinear exposure-responses and the lag structure of the relationship, respectively. The methodology is illustrated with an example application to cohort data and validated through a simulation study. This modeling framework generalizes to various study designs and regression models, and can be applied to study the health effects of protracted exposures to environmental factors, drugs or carcinogenic agents, among others.