chap6 - CHAPTER 6: Two CASE STUDIES AIR POLLUTION AND DAILY...

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Unformatted text preview: CHAPTER 6: Two CASE STUDIES AIR POLLUTION AND DAILY MORTALITY IN BIRMINGHAM, ALABAMA This analysis is intended to illustrate regres- sion analysis in the context of an issue of much public interest. We are not claiming that all of the checks and tests given here are needed to provide an adequate analysis of the public in- terest question. However, it provides explicit examples of many of the diagnostics that we have discussed, and should be read in that con- text, as a compendium of possible techniques that might or might not be applied to other problems of a similar nature, rather than an exhaustive analysis of one particular data set. 1 Background: the interpretation of epidemio- logical data relating adverse human health ef- fects to air pollution. Detailed analysis from Birmingham, Alabama, 19851988. One of very many data sets in the literature. Main question: to what extent variations in daily deaths are associated specifically with air pollution as opposed to other sources of vari- ability, e.g. meteorological effects, flu epi- demics, etc. Daily data are available on deaths, meteorol- ogy and atmospheric particulate matter, but we have to decide exactly how to process this data in the form of a statistical model. 2 Modeling Decisions 1. Selection of mortality data: we used Jef- ferson County, all deaths from nonaccidental causes among those aged 65 and over. Alternative possibilities: other age groups, other causes of deaths (e.g. restrict to cardiovascu- lar deaths) 2. Meteorological data: daily max and min temperature ( o C), specific humidity. Other possibilities: dewpoint, relative humidity, pres- sure, windspeed, etc. etc. 3. PM 10 (defined to be particulate matter 10 m or smaller in diameter). New (proposed) standards are based on PM 2 . 5 , but no data on PM 2 . 5 was available at the time of this study. Which monitors to include? strongest cor- relation is found with Birmingham city monitor (i.e. ignore others in surrounding area) so just use this. 3 Transformations of the response variable Response of interest is daily deaths, but how to transform? Variance stabilizing arguments suggest square root transform is this the best? 4 Three response variables considered are y t = M t , y t = C 1 radicalbig M t , (1) y t = C 2 log M t , where M t is the number of deaths on day t and the normalizing constants C 1 and C 2 are chosen to make the scales of the three vari- ables comparable. According to the theory of Section 5.3.4, this will be true if we define C 1 = 2 M , C 2 = M , where M is the geo- metric mean of the M t . This was done for the initial stages of the analysis in which we are comparing the three transformations, though later on, after selecting the square root trans- formation as the best of the three, we ignore the constant C 1 and just define y t = M t ....
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This note was uploaded on 11/17/2011 for the course STOR 664 taught by Professor Staff during the Fall '11 term at UNC.

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chap6 - CHAPTER 6: Two CASE STUDIES AIR POLLUTION AND DAILY...

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