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. 2013 Aug;42(4):1187-95.
doi: 10.1093/ije/dyt092. Epub 2013 Jun 12.

Time series regression studies in environmental epidemiology

Krishnan Bhaskaran  1 , Antonio Gasparrini, Shakoor Hajat, Liam Smeeth, Ben Armstrong
Affiliations

Time series regression studies in environmental epidemiology

Krishnan Bhaskaran et al. Int J Epidemiol. 2013 Aug.

Abstract

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.

Keywords: Time series; air pollution; environmental epidemiology.

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Figures

Figure 1
Figure 1
Raw plots showing outcome (deaths) and exposure (ozone) data over time (London data)
Figure 2
Figure 2
Three alternative ways of modelling long-term patterns in the data (seasonality and trends)
Figure 3
Figure 3
Residual variation in daily deaths after ‘removing’ (i.e. modelling) season and long-term trend. Fitted values were from a spline model for season and long-term trend only (as illustrated in Fig 2c)
Figure 4
Figure 4
Modelling lagged (delayed) associations between exposure and outcome. Asterisk indicates that the constraint applied was that the lagged associations for days 1 and 2 were the same, and for days 3–7 were the same
See this image and copyright information in PMC

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