Notes

Topics: Linear regression, Regression analysis, Function Pages: 40 (8866 words) Published: June 19, 2013
Distributed lag non-linear models in R: the package dlnm
Antonio Gasparrini and Ben Armstrong London School of Hygiene and Tropical Medicine, UK dlnm version 1.6.4 , 2012-08-22

Contents
1 Preamble 2 Installation and data 2.1 Installing the package dlnm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Distributed lag non-linear models 3.1 The issue . . . . . . . . . . . . . 3.2 The concept of basis . . . . . . . 3.3 Delayed effect: DLM’s . . . . . . 3.4 The extension to DLNM’s . . . . 4 The 4.1 4.2 4.3 4.4 4.5 (DLNM’s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 2 2 3 3 3 3 4 5 5 6 7 8 8 9 9 11 13 15 18 19 20 21

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functions in the package dlnm The function onebasis() . . . . . The function crossbasis() . . . . The function crosspred() . . . . . The function crossreduce() . . . Plotting functions . . . . . . . . .

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5 Some examples 5.1 Examples for onebasis() . . . . . . 5.2 Example 1: a simple DLM . . . . . . 5.3 Example 2: seasonal analysis . . . . 5.4 Example 3: a bi-dimensional DLNM 5.5 Example 4: reduce a DLNM . . . . . 6 Conclusions 7 Acknowledgements Bibliography

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1 This document is included as a vignette (a L T X document created using the R function Sweave()) of the A E package dlnm. It is automatically dowloaded together with the package and can be accessed through R typing vignette("dlnmOverview") .

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1

Preamble

The R package dlnm offers some facilities to run distributed lag non-linear models (DLNM’s), a modelling framework to describe simultaneously non-linear and delayed effects between predictors and an outcome in time-series data. This document complements the description of the package provided in Gasparrini (2011) (freely available at http://www.jstatsoft.org/v43/i08/), which represents the main reference to the package. The DLNM’s methodology has been previously described in Gasparrini et al. (2010), together with a detailed algebraical development. This framework was originally conceived and proposed to investigate the health effect of temperature by Armstrong (2006). The aim of this contribution is to provide an extended overview of the capabilities of the package, together with additional examples of application with real data. Some information on installation procedures and on the data included in the package are given in Section 2. The theory underlying the DLNM methodology is briefly illustrated in Section 3, while the functions included in the package are described in Section 4. Some examples of applications are provided in Section 5: users mainly interested in the application can skip the previous sections and and start with these examples. Finally, Section 6 offers some conclusions. Type citation("dlnm") in R to cite the dlnm package after installation (see Section 2). A list of changes included in the current and previous versions can...

References: S. Almon. The distributed lag between capital appropriations and expenditures. Econometrica, 33: 178–196, 1965. B. Armstrong. Models for the relationship between ambient temperature and daily mortality. Epidemiology, 17(6):624–31, 2006. M. Baccini, A. Biggeri, G. Accetta, T. Kosatsky, K. Katsouyanni, A. Analitis, H. R. Anderson, L. Bisanti, D. D’Ippoliti, J. Danova, B. Forsberg, S. Medina, A. Paldy, D. Rabczenko, C. Schindler, and P. Michelozzi. Heat effects on mortality in 15 European cities. Epidemiology, 19(5):711–9, 2008.
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A. L. Braga, A. Zanobetti, and J. Schwartz. The time course of weather-related deaths. Epidemiology, 12(6):662–7, 2001. J. Cao, M. F. Valois, and M. S. Goldberg. An S-Plus function to calculate relative risks and adjusted means for regression models using natural splines. Computer Methods and Programs in Biomedicine, 84(1):58–62, 2006. A. Gasparrini. Distributed lag linear and non-linear models in R: the package dlnm. Journal of Statistical Software, 43(8):1–20, 2011. URL http://www.jstatsoft.org/v43/i08/. A. Gasparrini, B. Armstrong, and M. G. Kenward. Distributed lag non-linear models. Statistics in Medicine, 29(21):2224–2234, 2010. A. Gasparrini, B. Armstrong, and M. G. Kenward. Reducing and meta-analyzing estimates from distributed lag non-linear models. (Submitted), 2012. S. Hajat, B. G. Armstrong, N. Gouveia, and P. Wilkinson. Mortality displacement of heat-related deaths: a comparison of Delhi, Sao Paulo, and London. Epidemiology, 16(5):613–20, 2005. S. Pattenden, B. Nikiforov, and B. G. Armstrong. Mortality and temperature in Sofia and London. Journal of Epidemiology and Community Health, 57(8):628–33, 2003. J. M. Samet, S. L. Zeger, F. Dominici, F. Curriero, I. Coursac, and D. W. Dockery. The National Morbidity, Mortality, and Air Pollution Study (NMMAPS). Part 2. Morbidity and mortality from air pollution in the United States. Technical report, Health Effects Institute, 2000a. J. M. Samet, S. L. Zeger, F. Dominici, D. Dockery, and J. Schwartz. The National Morbidity, Mortality, and Air Pollution Study (NMMAPS). Part 1. Methods and methodological issues. Technical report, Health Effects Institute, 2000b. J. Schwartz. The distributed lag between air pollution and daily deaths. Epidemiology, 11(3):320–6, 2000. J. Schwartz. Is there harvesting in the association of airborne particles with daily deaths and hospital admissions? Epidemiology, 12(1):55–61, 2001. J. Schwartz, J. M. Samet, and J. A. Patz. Hospital admissions for heart disease: the effects of temperature and humidity. Epidemiology, 15(6):755–61, 2004. L. J. Welty and S. L. Zeger. Are the acute effects of particulate matter on mortality in the National Morbidity, Mortality, and Air Pollution Study the result of inadequate control for weather and season? A sensitivity analysis using flexible distributed lag models. American Journal of Epidemiology, 162(1):80–8, 2005. S.N. Wood. Generalized additive models: an introduction with R. Chapman & Hall/CRC, 2006. A. Zanobetti and J. Schwartz. Mortality displacement in the association of ozone with mortality: an analysis of 48 cities in the United States. American Journal of Respiratory and Critical Care Medicine, 177(2):184–9, 2008. A. Zanobetti, M. P. Wand, J. Schwartz, and L. M. Ryan. Generalized additive distributed lag models: quantifying mortality displacement. Biostatistics, 1(3):279–92, 2000.
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