Inverse Prediction Using SAS® Software: A Clinical Application

An important application of regression methodology is in the area of prediction. Oftentimes investigators are interested in predicting a value of a response variable (Y) based on the known value of the predictor variable (X). However, sometimes there is a need to predict a value of the predictor variable (X) based on the known value of the response variable (Y). In such situations, it is improper to simply switch the roles of the response and predictor variables to get the desired predictions i.e., regress X on Y. A method that accounts for the underlying assumptions while estimating or predicting X from known Y is known as inverse prediction. This approach will be illustrated using the PROC REG, and PROC GPLOT procedures in SAS®. The calculations for the 95% confidence limits for a predicted X from a known Y will also be presented. The macro and its application will be demonstrated using data from clinical / laboratory studies.