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There are a number of applied settings where a response is measured repeatedly over time, and the impact of a stimulus at one time is distributed over several subsequent response measures. In the motivating application, the stimulus is an air pollutant such as airborne particulate matter and the response is mortality. However, several other variables (e.g. daily temperature) impact the response in a possibly non-linear fashion. To quantify the effect of the stimulus in the presence of covariate data we combine two established regression techniques: generalized additive models and distributed lag models. Generalized additive models extend multiple linear regression by allowing for continuous covariates to be modeled as smooth, but otherwise unspecified, functions. Distributed lag models aim to relate the outcome variable to lagged values of a time-dependent predictor in a parsimonious fashion. The resultant, which we call generalized additive distributed lag models, are seen to effectively quantify the so-called 'mortality displacement effect' in environmental epidemiology, as illustrated through air pollution/mortality data from Milan, Italy.
презентация тут, картинка из неё
кортинко тыцабельно и много лутшэ качеством
There are a number of applied settings where a response is measured repeatedly over time, and the impact of a stimulus at one time is distributed over several subsequent response measures. In the motivating application, the stimulus is an air pollutant such as airborne particulate matter and the response is mortality. However, several other variables (e.g. daily temperature) impact the response in a possibly non-linear fashion. To quantify the effect of the stimulus in the presence of covariate data we combine two established regression techniques: generalized additive models and distributed lag models. Generalized additive models extend multiple linear regression by allowing for continuous covariates to be modeled as smooth, but otherwise unspecified, functions. Distributed lag models aim to relate the outcome variable to lagged values of a time-dependent predictor in a parsimonious fashion. The resultant, which we call generalized additive distributed lag models, are seen to effectively quantify the so-called 'mortality displacement effect' in environmental epidemiology, as illustrated through air pollution/mortality data from Milan, Italy.
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During heat waves, for instance, there are often additional deaths observed in the population, affecting especially older adults and those who are sick. After some periods with excess mortality, however, there has also been observed a decrease in overall mortality during the subsequent weeks. Such short-term forward shift in mortality rate is also referred to as harvesting effect. The subsequent, compensatory reduction in mortality suggests that the heat wave had affected especially those whose health was already so compromised that they "would have died in the short term anyway"
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