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REGRESSION ON MEDIANS OF PROBABILITY DISTRIBUTIONS
Citation:
Sumler, M., H. Fisher, AND L. Hall. REGRESSION ON MEDIANS OF PROBABILITY DISTRIBUTIONS. U.S. Environmental Protection Agency, Washington, D.C., EPA/600/D-91/048.
Description:
The median is a fundamental parameter in the area of lifetime and survival statistics. n toxicodynamics the LD50, lethal dose that results in 50% mortality, is frequently used. he median is also used to describe the incidence of cancer and other disease states. Factors such as nutritional status, age of animal, and exposure to a second chemical can cause the LD50 to shift. t is therefore desirable to determine a functional relationship between the median of a distribution and a cofactor. n this paper we use SAS to examine the use of median regression to predict a continuous dependent variable as a function of a single cofactor and compare these results to the standard ordinary least squares regression techniques. wo data sets were generated using the SAS RANUNI and NORMAL functions. n one, the median line was proportional to the mean line, and both the median and mean had positive slopes with respect to a cofactor. n the other, the slope of the median line was positive while that of the mean line was negative. hus, the values of the median increased and the mean decreased as the cofactor increased. edians in both data sets were calculated using discrete and running intervals. esults of median and mean regressions can contradict each other in some cases, as shown with the second data set performing both mean and median regressions can provide a more complete picture of the statistical relationship between the dependent and independent variables.