Statistical estimation of ozone exposure metrics

Data from recent experiments at North Carolina State University and other locations provide a unique opportunity to study the effect of ambient ozone on the growth of clover. The data consist of hourly ozone measurements over a 140 day growing season at eight sites in the US, coupled with clover growth response data measured every 28 days. The objective is to model an indicator of clover growth as a function of ozone exposure. A common strategy for dealing with the numerous hourly ozone measurements is to reduce these to a single summary measurement, a so-called exposure metric, for the growth period of interest. However, the mean ozone value is not necessarily the best summarization, as it is widely believed that low levels of ozone have a negligible effect on growth, whereas peak ozone values are deleterious to plant growth. There are also suspected interactions with available sunlight, temperature and humidity. A number of exposure metrics have been proposed that reflect these beliefs by assigning different weights to ozone values according to magnitude, time of day, temperature and humidity. These weighting schemes generally depend on parameters that have, to date, been subjectively determined. We propose a statistical approach based on profile likelihoods to estimate the parameters in these exposure metrics.