Distributed Lag Linear and Non-Linear Models in R: The Package dlnm.

Distributed lag non-linear models (DLNMs) represent a modeling framework to flexibly describe associations showing potentially non-linear and delayed effects in time series data. This methodology rests on the definition of a crossbasis, a bi-dimensional functional space expressed by the combination of two sets of basis functions, which specify the relationships in the dimensions of predictor and lags, respectively. This framework is implemented in the R package dlnm, which provides functions to perform the broad range of models within the DLNM family and then to help interpret the results, with an emphasis on graphical representation. This paper offers an overview of the capabilities of the package, describing the conceptual and practical steps to specify and interpret DLNMs with an example of application to real data.

[1]  S. Hajat,et al.  Modelling the non-linear multiple-lag effects of ambient temperature on mortality in Santiago and Palermo: a constrained segmented distributed lag approach , 2008, Occupational and Environmental Medicine.

[2]  S L Zeger,et al.  Estimating particulate matter-mortality dose-response curves and threshold levels: an analysis of daily time-series for the 20 largest US cities. , 2000, American journal of epidemiology.

[3]  Joel Schwartz,et al.  Analysis of health outcome time series data in epidemiological studies , 2004 .

[4]  Luke Clancy,et al.  Cause-specific mortality and the extended effects of particulate pollution and temperature exposure. , 2003, Environmental health perspectives.

[5]  P. Rosenberg,et al.  Analysis of Exposure‐Time‐Response Relationships Using a Spline Weight Function , 2000, Biometrics.

[6]  Thomasma Dc.  Statistical methods for analyzing effects of temporal patterns of exposure on cancer risks. , 1983 .

[7]  Antonella Zanobetti,et al.  Mortality displacement in the association of ozone with mortality: an analysis of 48 cities in the United States. , 2008, American journal of respiratory and critical care medicine.

[8]  Paul Wilkinson,et al.  Mortality Displacement of Heat-Related Deaths: A Comparison of Delhi, São Paulo, and London , 2005, Epidemiology.

[9]  David B Richardson,et al.  Latency Models for Analyses of Protracted Exposures , 2009, Epidemiology.

[10]  B. Armstrong,et al.  Mortality and temperature in Sofia and London , 2003, Journal of epidemiology and community health.

[11]  M. Abrahamowicz,et al.  Joint estimation of time‐dependent and non‐linear effects of continuous covariates on survival , 2007, Statistics in medicine.

[12]  Ben Armstrong,et al.  Models for the Relationship Between Ambient Temperature and Daily Mortality , 2006, Epidemiology.

[13]  A Gasparrini,et al.  Distributed lag non-linear models , 2010, Statistics in medicine.

[14]  T. Louis,et al.  Model choice in time series studies of air pollution and mortality , 2006 .

[15]  Steven Roberts,et al.  A distributed lag approach to fitting non-linear dose-response models in particulate matter air pollution time series investigations. , 2007, Environmental research.

[16]  Vito M. R. Muggeo,et al.  Analyzing temperature effects on mortality within the R environment: the constrained segmented distributed lag parameterization , 2010 .

[17]  Michal Abrahamowicz,et al.  Flexible modeling of the cumulative effects of time‐dependent exposures on the hazard , 2009, Statistics in medicine.

[18]  Michelle L. Bell,et al.  A Meta-Analysis of Time-Series Studies of Ozone and Mortality With Comparison to the National Morbidity, Mortality, and Air Pollution Study , 2005, Epidemiology.

[19]  D C Thomas,et al.  Models for exposure-time-response relationships with applications to cancer epidemiology. , 1988, Annual Review of Public Health.

[20]  J Schwartz,et al.  The distributed lag between air pollution and daily deaths. , 2000, Epidemiology.

[21]  T. Hastie,et al.  Improved Semiparametric Time Series Models of Air Pollution and Mortality , 2004 .

[22]  Bryan Langholz,et al.  Using tensor product splines in modeling exposure–time–response relationships: Application to the Colorado Plateau Uranium Miners cohort , 2008, Statistics in medicine.

[23]  S. Wood.  Generalized Additive Models: An Introduction with R , 2006 .

[24]  D. Stram,et al.  Latency analysis in epidemiologic studies of occupational exposures: application to the Colorado Plateau uranium miners cohort. , 1999, American journal of industrial medicine.

[25]  J Schwartz,et al.  The temporal pattern of mortality responses to ambient ozone in the APHEA project , 2009, Journal of Epidemiology & Community Health.

[26]  P. Vacek,et al.  Assessing the effect of intensity when exposure varies over time. , 1997, Statistics in medicine.

[27]  M P Wand,et al.  Generalized additive distributed lag models: quantifying mortality displacement. , 2000, Biostatistics.

[28]  J. Schwartz,et al.  The National Morbidity, Mortality, and Air Pollution Study. Part II: Morbidity and mortality from air pollution in the United States. , 2000, Research report.

[29]  Annibale Biggeri,et al.  Parametric and semi-parametric approaches in the analysis of short-term effects of air pollution on health , 2007, Comput. Stat. Data Anal..

[30]  Michal Abrahamowicz,et al.  Comparison of alternative models for linking drug exposure with adverse effects , 2012, Statistics in medicine.

[31]  Francesca Dominici,et al.  Time-series analysis of air pollution and mortality: a statistical review. , 2004, Research report.

[32]  Antonio Gasparrini,et al.  Reducing and meta-analysing estimates from distributed lag non-linear models , 2013, BMC Medical Research Methodology.

[33]  Antonella Zanobetti,et al.  The Time Course of Weather-Related Deaths , 2001, Epidemiology.

[34]  D. Thomas.  Statistical methods for analyzing effects of temporal patterns of exposure on cancer risks. , 1983, Scandinavian journal of work, environment & health.

[35]  V. Muggeo,et al.  Modeling temperature effects on mortality: multiple segmented relationships with common break points. , 2008, Biostatistics.

[36]  Alan Y. Chiang,et al.  Generalized Additive Models: An Introduction With R , 2007, Technometrics.

[37]  Chi Wang,et al.  Model selection and health effect estimation in environmental epidemiology. , 2008, Epidemiology.

[38]  Paul Wilkinson,et al.  Comparison of mortality displacement of heat-related deaths in Delhi, Sao Paulo and London , 2004 .

[39]  Mc Borja,et al.  An Introduction to Generalized Linear Models, 3rd edition , 2009 .

[40]  Shirley Almon.  The Distributed Lag Between Capital Appropriations and Expenditures , 1965 .

[41]  Eric R. Ziegel,et al.  An Introduction to Generalized Linear Models , 2002, Technometrics.