Limitations of the Odds Ratio in Gauging the Performance of a Diagnostic or Prognostic Marker

A marker that is strongly associated with outcome (or disease) is often assumed to be effective for classifying individuals according to their current or future outcome. However, for this to be true, the associated odds ratio must be of a magnitude rarely seen in epidemiological studies. An illustration of the relationship between odds ratios and receiver operating characteristic (ROC) curves shows, for example, that a marker with an odds ratio as high as 3 is in fact a very poor classification tool. If a marker identifies 10 percent of controls as positive (false positives) and has an odds ratio of 3, then it will only correctly identify 25 percent of cases as positive (true positives). Moreover, the authors illustrate that a single measure of association such as an odds ratio does not meaningfully describe a marker’s ability to classify subjects. Appropriate statistical methods for assessing and reporting the classification power of a marker are described. The serious pitfalls of using more traditional methods based on parameters in logistic regression models are illustrated.

TRENDS IN PARTICULATE MATTER AND MORTALITY: AN APPROACH TO THE ASSESSMENT OF UNMEASURED CONFOUNDING

We propose a method for diagnosing confounding bias under a model which links a spatially and temporally varying exposure and health outcome. We decompose the association into orthogonal components, corresponding to distinct spatial and temporal scales of variation. If the model fully controls for confounding, the exposure effect estimates should be equal at the different temporal and spatial scales. We show that the overall exposure effect estimate is a weighted average of the scale-specific exposure effect estimates. We use this approach to estimate the association between monthly averages of fine particles (PM2.5) over the preceding 12 months and monthly mortality rates in 113 U.S. counties from 2000-2002. We decompose the association between PM2.5 and mortality into two components: 1) the association between “national trends” in PM2.5 and mortality; and 2) the association between “local trends,” defined as county-specificdeviations from national trends. This second component provides evidence as to whether counties having steeper declines in PM2.5 also have steeper declines in mortality relative to their national trends. We find that the exposure effect estimates are different at these two spatio-temporalscales, which raises concerns about confounding bias. We believe that the association between trends in PM2.5 and mortality at the national scale is more likely to be confounded than is the association between trends in PM2.5 and mortality at the local scale. If the association at the national scale is set aside, there is little evidence of an association between 12-month exposure to PM2.5 and mortality.