Updated the R code previously included in various published articles. Click on the related link to access the code and the original publication.

## Two-stage analysis of short-term risks of air pollution using multi-country data

An example of applications of the two-stage time series design for the analysis of short-term effects of air pollution using a multi-country multi-city dataset. The analysis is published in an article on an investigation of the short-term mortality risks of sulphur dioxide (SO2), and it is reproduced using simulated data. The example illustrates all the steps of the analysis, including the first-stage regression, complex second-stage meta-analyses, and methods to assess complex associations such as non-linerities, lagged effects, and temporal variations in risks.

## Extended two-stage designs for environmental research

An illustration of a unified framework that enables several design extensions of standard two-stage analyses applied in environmental epidemiology. The various extensions are illustrated in an article describing two-stage analyses of health effects associated with environmental stressors using the database collected as part of the National Morbidity, Mortality and Air Pollution Study (NMMAPS). The article provides details on the extended meta-analytical framework and its software implementation, and it demonstrates each extension using a case study that addresses a specific research question.

## The application of the case time series design for small-area analysis

A case-study illustration of the application of the case time series design for the analysis of small-area data in environmental epidemiology. This tutorial article describes an analysis of the association between heat and mortality in two summers (2006 and 2013) across 983 middle layer super output areas (MSOAs) in London, UK. The tutorial demonstrates the application of the case time series design and provides a step-by-step description of the analysis, as well as methodological and practical aspects. A more complex modelling framework based on a two-stage design is illustrated in another article on temperature-related mortality impacts.

## Analysis of the impact of lockdown policies in reducing air pollution and related mortality with a spatio‑temporal Bayesian non‑linear mixed effect model

An analysis of the differential effects of various lockdown policies implemented during the first COVID-19 pandemic wave in 2020 in reducing exposure to air pollution and related short-term mortality across Europe. The analysis makes use of a spatio‑temporal Bayesian non‑linear mixed effect model to estimate the association between the stringency of the policies and the concentration of a number of pollutants. This is illustrated in an article with links to the code to download the original data, perform the full analysis, and extract the full set of results, making the research completely reproducible.

## A cross-sectional analysis of meteorological factors and SARS-CoV-2 transmission

An analysis of the association between a number of meteorological factors and the effective reproduction number of SARS-CoV-2 infections across 409 cities in 26 countries. The modelling framework is based on a multilevel meta-regression models with two levels (cities nested within countries) to determine linear and non-linear associations. This is illustrated in an article with links to the code to download the original data, perform the full analysis, and extract the full set of results, making the research completely reproducible.

## The case time series design

A new study design for epidemiological investigations of transient health risks associated with time-varying exposures. The design combines individual-level and self-matched setting of case-only methods with the modelling flexibility and temporal structure of time series methods. The new case time series methodology is illustrated in an article that includes two case studies used as tutorials for applications in various epidemiological areas, and a thorough simulation study that assesses the design under increasingly complex scenarios.

## The burden of heat-related mortality attributable to recent human-induced climate change

An impact heatlh assessment to quantify the proportion of heat-related deaths that occurred because of changes in climate due to anthropogenic activities. The original analysis, illustrated in the article, applied an extended two-stage framework for estimating location-specific risks and then derive the impacts under climate scenarios with and withouth anthropogenic emissions. The analysis is reproduced here using a set of simulated climate and mortality data for 10 cities.

## A spatio-temporal model embedding distributed lag non-linear models in a Bayesian framework with integrated nested Laplace approximation (INLA)

The analysis combines distributed lag non-linear models with a spatiotemporal Bayesian hierarchical model framework to determine the exposure-lag-response association between the relative risk (RR) of dengue and a drought severity index. This is illustrated in an article with links to the code to load the original data, perform the full analysis, and extract the full set of results, making the research completely reproducible.

## A two-stage interrupted time-series analysis to estimate excess mortality during the COVID-19 outbreak

An analysis of excess mortality experienced in Italy during the first wave of COVID-19 in spring 2020. The model is based on a novel two-stage interrupted time series design using publicly available data. This is illustrated in an article with links to the code to download the original data, perform the full analysis, and extract the full set of results, making the research completely reproducible. The work is complemented by a Shiny app to visualize results in maps and other graphs.

## The role of humidity in temperature-mortality associations

An assessment of the role of humidity in associations between temperature and mortality. The R code and data are used in a simplified example that replicates the analysis in a publisheed article.

## An extended mixed-effects framework for meta-analysis

A general framework for meta-analysis based on linear mixed-eﬀects models, where potentially complex patterns of eﬀect sizes are modelled through an extended and ﬂexible structure of ﬁxed and random terms. This deﬁnition includes, as special cases, multivariate, network, multilevel, dose-response, and longitudinal meta-analysis and meta-regression. This is illustrated in an article that also presents the R package mixmeta implementing the extended modelling framework.

## A modelling framework for projections of climate change impacts on health

A methodological framework to estimate future health impacts under climate change scenarios based on advanced statistical techniques

developed in time-series analysis in environmental epidemiology. Illustrated in an article through a step-by-step hands-on tutorial structured in well-defined sections that cover the main methodological steps. Complemented with a practical example using real data and a series of R scripts.

developed in time-series analysis in environmental epidemiology. Illustrated in an article through a step-by-step hands-on tutorial structured in well-defined sections that cover the main methodological steps. Complemented with a practical example using real data and a series of R scripts.

## A penalized version of distributed lag linear and non-linear models

The extension of distributed lag linear and non-linear models (DLMs and DLNMs) thorugh generalized additive models via penalized splines. The methodology is implemented by embedding functions in the R packages dlnm and mgcv. The code reproduces two examples of application in time series and survival analysis, respectively, and the results of the simulation study, described in the methodological article.

## Identification of the minimum of an exposure-response relationship and quantification of its uncertainty

A methodology to identify the minimum of an exposure-response relationship estimated from a regression model, and to quantify the related uncertainty through empirical standard errors and confidence intervals. The method is demonstrated in an article illustrating an application for invesigating the minimum mortality temperature (MMT) in a set of cities in Spain.

**Modelling lagged associations in environmental time series data: a simulation study**

A simulation study comparing methods to model lagged effects in environmental time series, specifically moving averages and distributed lag models. The code fully reproduces the results illustrated in the article, and it adds a simple example to simulate the data based on scenarios of exposure-lag-response associations, to fit the regression models and to display/summarize the results.

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

A tutorial on the use of interrupted time series (ITS) analysis in public health and epidemiological research. The code follows the examples illustrated in the article that described the most common steps in the application of the ITS design.

## Association of inter and intra-day temperature change with mortality

An illustrative example of the analysis published in an article assessing the association between indices of inter and intra-day temperature variability and mortality. The indices are built following specific assumptions about the impact of temperature variability and absolute temperature. The code reproduces the results for London, one of the six cities included in the analysis.

**Attributable risk from distributed lag models**

Examples partly reproducing the results published in two articles describing how to compute attributable risk measures from distributed lag linear and non-linear models. The code accompanying a first methodological article shows an application in single-city analyses, using functions in the R package dlnm. The code accompanying a second article illustrates an application in multi-city analyses, using functions in the R packages dlnm and mvmeta. The material includes the function attrdl (not available in the R package dlnm) with documentation.

## Conditional Poisson models: a flexible alternative to conditional logistic case cross-over analysis

Illustration of conditional Poisson models as an alternative method in analyses of environmental data. In particular, this represents a computationally convenient alternative to both conditional logistic case-crossover models (when data are aggregated in time series form) and to standard Poisson regression for long time series (when control for time is achieved with computationally expensive spline functions). The code follows the examples included in the article that illustrates the methodology and some applications.

**Modelling temporal ****variations** with time-varying distributed lag non-linear models

**variations**with time-varying distributed lag non-linear models

Two applications of time-varying DLNMs, specified through an interaction between cross-basis variables and the time variable, to model temporal variations in exposure-lag-response associations between heat and mortality in a multi-country multi-city (MCC) data set. The first application illustrates how to model long term variations, partly reproducing the analysis described in this article. The second application shows instead how to model within season variations, partly reproducing the analysis described in this article. The code uses functions in the R packages dlnm and mvmeta.

## Extending distributed lag non-linear models beyond time series data

An example illustrating the extension of DLNMs for modelling exposure-lag-response associations beyond time series analysis. The code completely reproduces the examples and simulation study described in the article, and it is complemented by the vignette dlnmExtended included in the R package dlnm, showing applications in alternative settings.

## Time series regression studies in environmental epidemiology

A tutorial on time series analysis applied to environmental epidemiology, with an example on the association of mortality with air pollution and temperature. The R code reproduces completely the example included in the article, illustrating the various analytical steps. Simple analyses with DLMs are also included, using functions in the R package dlnm.

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

An illustration on methods for reducing estimates of bi-dimensional exposure-lag-response associations obtained by DLNMs from multiple studies, and then pooling them. The example reproduces the example included in the paper. The code uses functions in the R packages dlnm and mvmeta.

## Multivariate meta-analysis for non-linear and other multi-parameter associations

An application of multivariate meta-analysis for pooling estimates of non-linear associations from multiple studies. The code included is applicable beyond the specific setting of time series analysis of temperature-health relationships. The example is different than that included in the paper, as the original data are not available any more. The code primarily uses functions in the R package mvmeta, but functions in the R package dlnm are applied as well.

## Distributed lag linear and non-linear models in R: the package dlnm

A tutorial on the use of DLNMs in time series analysis, illustrating the capabilities of the R package dlnm. The R code displayed in the article refers to an old version of the R package with an outdated syntax.

## The impact of heat waves on mortality

A comparative analysis of the main and added effects of temperature on mortality. The code, originally reproducing the example included in the article, is based on data which are not available any more. Functions in the in the R package dlnm are used for modelling the main effect and graphically representing the added effect, while functions in the R package mvmeta are applied for pooling the results from multiple studies.