# Compendium for "Seasonal analyses of air pollution and mortality in 100 U.S. cities" by Peng, et al. (2005)

## Abstract

Time series models relating short-term changes in air pollution levels to daily mortality counts typically assume that the effects of air pollution on the log relative rate of mortality do not vary with time. However, these short-term effects might plausibly vary by season. Changes in the sources of air pollution and meteorology can result in changes in characteristics of the air pollution mixture across seasons. The authors developed Bayesian semiparametric hierarchical models for estimating time-varying effects of pollution on mortality in multisite time series studies. The methods were applied to the database of the National Morbidity and Mortality Air Pollution Study, which includes data for 100 US cities, for the period 1987--2000. At the national level, a 10-Âµg/m3 increase in particulate matter less than 10 Âµm in aerodynamic diameter at a 1-day lag was associated with 0.15% (95% posterior interval (PI): -0.08, 0.39), 0.14% (95% PI: -0.14, 0.42), 0.36% (95% PI: 0.11, 0.61), and 0.14% (95% PI: -0.06, 0.34) increases in mortality for winter, spring, summer, and fall, respectively. An analysis by geographic region found a strong seasonal pattern in the Northeast (with a peak in summer) and little seasonal variation in the southern regions of the country. These results provide useful information for understanding particle toxicity and guiding future analyses of particle constituent data.

The full text of the article is available from the American Journal of Epidemiology.

## Vignette/Compendium

The file seasonal.Rnw is contains the text for the paper and the R code for creating the figures and tables. The file can be processed using the Sweave function in R after running the two "core" analyses below.

To process the vignette, you first need to have a working LaTeX system and R. R can be downloaded from CRAN.

Save the vignette file in a directory on your computer. You also need to download the BibTeX bibliography database to create the final product. After starting up R:

1. Run the core analyses below by executing the code in core1.R and core2.R. Make sure that the "Other Code and Data" files are in the "data" sub-directory.
2. The core analyses should create a directory "results" where the results of analyses are cached. In R, run the following:
Sweave("seasonal.Rnw")  ## This will take a few minutes
library(tools)
texi2dvi("seasonal.tex", pdf = TRUE)

This will create a PDF file in the working directory called "seasonal.pdf".
3. To extract the code for the figures and tables, run
library(tools)
Stangle("seasonal.Rnw", split = TRUE)

This will create a separate file for each figure/table containing the relevant code.

## Required R Packages

 NMMAPSdata R package containing all of the mortality, air pollution, and weather data for the National Morbidity, Mortality, and Air Pollution Study, 1987--2000, 108 U.S. cities. tlnise Two-Level Normal Independent Sampler Estimation software for R (S-PLUS original by Phil Everson) tsModelSpec Tools for time series regression model specification

Packages not listed here that are necessary for reproducing the results are available from CRAN.

## Other Code and Data

The following code files should reside in a subdirectory called "data".

 model-fitting.R Model fitting functions utils.R Miscellaneous utility functions for pooling coefficients and processing results multipollutant.R Data processing function for multi-pollutant database cityList.R List of cities used in 100 city analysis analysis (also including Anchorage, AK and Honolulu, HI) copoll-cityList.R List of cities used in 45 city copollutant analysis citynames.csv Names of cities used

## Core Data Analysis

The code below creates a sub-directory "results" where specific results are stored for later use.

Core analysis 1:
1. Build database for co-pollutant models (PM10, ozone, SO2, NO2)
2. Compute smooth seasonally varying effects of PM10 on non-accidental mortality
3. Compute separate seasonal effects of PM10 on non-accidental mortality adjusting for gases
4. Compute separate seasonal effects of PM10 on non-accidental mortality (no adjustment for gases)
 Code core1.R
Core analysis 2:
1. Compute non-seasonal effects of PM10 on non-accidental mortality
2. Compute smooth seasonally varying effects of PM10 on non-accidental mortality using orthogonal sine/cosine basis
3. Sensitivity analysis with respect to the degrees of freedom in the smooth fucnction of time used to adjust for smooth time varying confounders
 Code core2.R

## Breakdown of Figures and Tables

Boxplots of square root daily mortality by season for the 10 largest U.S. cities, 1987--2000.
 Data CityDataCombined.rda Code Figure 1
Boxplots of regionally averaged daily levels of particulate matter less than 10 $\mu$m in aerodynamic diameter (PM10) by season for 100 U.S. cities, 1987--2000.
 Data CityDataCombined.rda Code Figure 2
National and regional smooth seasonal effects of PM10 (particulate matter less than 10 $\mu$m in aerodynamic diameter) at lag 1 for 100 U.S. cities, 1987--2000. Estimates were obtained by pooling city-specific coefficients from the sine/cosine model (equation 2). Dotted lines indicate pointwise 95 posterior intervals.
 Code Figure 3
Samples from the national and regional joint posterior distributions of the pooled coefficients $\beta_1$ and $\beta_2$ from sine/cosine seasonal model (equation 2) for PM10 at lag 1, 100 U.S. cities, 1987--2000. The solid and dashed lines indicate the 75% and 95% regions for the joint posterior distribution of $\beta_1$ and $\beta_2$, given the data. Each panel includes the marginal posterior probabilities of each coefficient being greater than 0. Posterior probabilities closer to 1 indicate stronger evidence of seasonal patterns.
 Code Figure 4
Sensitivity of national and regional estimates of smooth seasonal effects for PM10 at lag 1 to the degrees of freedom assigned to the smooth function of time, 100 U.S. cities, 1987--2000. The degrees of freedom chosen were 3 (short dashed), 5 (dotted), 7 (solid), 9 (dot-dashed), and 11 (long dashed) degrees of freedom per year of data.
 Code Figure 5
Sensitivity of national and regional estimates of smooth seasonal effects to PM10 exposure lag, 100 U.S. cities, 1987--2000. Solid black lines indicate the log relative rate estimate and pointwise 95% posterior intervals for PM10 at lag 1. Also shown are the log relative rate estimates for PM10 at lag 0 (short dashed) and lag 2 (dot-dashed).
 Code Figure 6
Table 2: National average estimates of the overall and season-specific effects of PM10 at lags of 0, 1, and 2 days for 100 US cities, National Morbidity and Mortality Air Pollution Study, 1987--2000
 Code Table 2
Table 3: National average estimates of season-specific lag 1 PM10 log relative rates adjusted for other pollutants, National Morbidity and Mortality Air Pollution Study, 1987--2000
 Code Table 3