Application of Dempster-Shafer theory in dose response outcome analysis.

The Quantitative Analysis of Normal Tissue Effects in the Clinic (QUANTEC) reviews summarize the currently available three-dimensional dose/volume/outcome data from multi-institutions and numerous articles to update and refine the normal tissue dose/volume tolerance guidelines. As pointed out in the review, the data have limitations and even some inconsistency. However, with the help of new physical and statistical techniques, the information in the review could be updated so that patient care can be continually improved. The purpose of this work is to demonstrate the application of a mathematical theory, the Dempster-Shafer theory, in dose/volume/outcome data analysis. We applied this theory to the original data obtained from published clinical studies describing dose response for radiation pneumonitis. Belief and plausibility concepts were introduced for dose response evaluation. We were also able to consider the uncertainty and inconsistency of the data from these studies with Yager's combination rule, a special methodology of Dempster-Shafer theory, to fuse the data at several specific doses. The values of belief and plausibility functions were obtained at the corresponding doses. Then we applied the Lyman-Kutcher-Burman (LKB) model to fit these values and a belief-plausibility range was obtained. This range could be considered as a probability range to assist physicians and treatment planners in determining acceptable dose-volume constraints. Finally, the parameters obtained from the LKB model fitting were compared with those in Emami and Burman's papers and those from other frequentist statistics methods. We found that Emami and Burman's parameters are within the belief-plausibility range we calculated by the Dempster-Shafer theory.