Distributed lag non-linear models.
Environmental stressors often show effects that are delayed in time, requiring the use of statistical models that are flexible enough to describe the additional time dimension of the exposure-response relationship. Here we develop the family of distributed lag non-linear models (DLNM), a modelling framework that can simultaneously represent non-linear exposure-response dependencies and delayed effects. This methodology is based on the definition of a 'cross-basis', a bi-dimensional space of functions that describes simultaneously the shape of the relationship along both the space of the predictor and the lag dimension of its occurrence. In this way the approach provides a unified framework for a range of models that have previously been used in this setting, and new more flexible variants. This family of models is implemented in the package dlnm within the statistical environment R. To illustrate the methodology we use examples of DLNMs to represent the relationship between temperature and mortality, using data from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) for New York during the period 1987-2000.
Gasparrini
A
A
Public Health and Policy Department, London School of Hygiene and Tropical Medicine, Keppel Street, London W1C 7HT, U.K. antonio.gasparrini@lshtm.ac.uk
Armstrong
B
B
Kenward
M G
MG
D000465:Algorithms; D016208:Databases, Factual; D004781:Environmental Exposure / Q000009:adverse effects* / Q000706:statistics & numerical data*; D006801:Humans; D020407:Internet; D015233:Models, Statistical; D009026:Mortality; D009519:New York City / Q000453:epidemiology; D017711:Nonlinear Dynamics; D012306:Risk; D012984:Software; D013696:Temperature; D013997:Time Factors
Am J Epidemiol. 2000 Sep 1;152(5):397-406
10981451
Stat Med. 2005 Apr 15;24(7):1103-15
15558697
Epidemiology. 2001 Jan;12(1):55-61
11138820
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16024489
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16135936
Stat Med. 2008 Jul 30;27(17):3430-41
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11679794
Epidemiology. 2009 Mar;20(2):205-13
19194300
Epidemiology. 2008 Jul;19(4):558-60
18552590
Res Rep Health Eff Inst. 2004 Dec;(123):3-27; discussion 29-33
15757000
Biostatistics. 2008 Oct;9(4):613-20
18308697
Epidemiology. 2006 Nov;17(6):624-31
17028505
Am J Epidemiol. 2005 Jul 1;162(1):80-8
15961590
Environ Res. 2007 Jun;104(2):193-200
17362914
Biostatistics. 2000 Sep;1(3):279-92
12933509
Biometrics. 2006 Dec;62(4):1025-36
17156276
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16024496
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10784251
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11805591