Step-Function Approach to Time-Series: An Air Quality Application
Turkan K. Gardenier, PhD

Abstract
Estimating environmental exposure is a crucial component of health risk assessment. With the recent emphasis on personalized medicine and patient participation, data submitted to analysis and evaluation need to clear, retrievable and easy to merge. Patients, physicians, and public health officials may all be interested in individuals’ exposure histories. Large databases are now available and accessible to the public including, patients and caregivers. Some environmental data are monitored under mandate and are available for many years, thus making it feasible to trace change over time. When merging data over time, it is also important to remember that there is uncertainty in data elements; for example, discretized continuous data, incorporate a region of uncertainty between adjacent categories. A step-function based 3-category approach (trinary) is presented and discussed with reference to data collected between 1990-2010 for three criteria pollutants: Carbon Monoxide (CO), Nitrogen Dioxide (NO2), and Ozone (O3) in a rural and an urban city in northeastern United States. Correlation and regression analysis was applied, as well as a trace of successive data in a stepassignment of +1, 0 or -1 delineated using distance from the 20-year average for each city. Various distance allotments of bandwidth, were explored, including mean + or minus ½ standard deviation, 3rd minus 1st quartiles, 90th minus 10th percentiles and visual inspection. Switching patterns from +1 to 0 range and from 0 to -1 range were examined for CO, NO2 and O3 for the rural and urban areas with a view to quantifying a decision rule for stability of shifting pattern. This paper demonstrates how three-level categorizations of environmental exposure data (and potentially other measurement data as well) can simplify and clarify health related exposure histories. The analytic approach has broad applications in personalized medicine, epidemiology and public health policy.

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