TITLE:
Dose-Injury Relation as a Model for Uncertainty Propagation from Input Dose to Target Dose
AUTHORS:
Hongyun Wang, Wesley A. Burgei, Hong Zhou
KEYWORDS:
Dose Injury Relation, Dose Propagation Uncertainty, Median Injury Dose, 10 - 90 Percentile Width, Skewness, Mapping Injury Model from One Population to Another
JOURNAL NAME:
American Journal of Operations Research,
Vol.8 No.5,
September
18,
2018
ABSTRACT: We study a general framework for assessing the injury probability corresponding
to an input dose quantity. In many applications, the true value of
input dose may not be directly measurable. Instead, the input dose is estimated
from measurable/controllable quantities via numerical simulations
using assumed representative parameter values. We aim at developing a simple
modeling framework for accommodating all uncertainties, including the
discrepancy between the estimated input dose and the true input dose. We
first interpret the widely used logistic dose-injury model as the result of dose
propagation uncertainty from input dose to target dose at the active site for
injury where the binary outcome is completely determined by the target dose.
We specify the symmetric logistic dose-injury function using two shape parameters:
the median injury dose and the 10 - 90 percentile width. We relate
the two shape parameters of injury function to the mean and standard deviation
of the dose propagation uncertainty. We find 1) a larger total uncertainty
will spread more the dose-response function, increasing the 10 - 90 percentile
width and 2) a systematic over-estimate of the input dose will shift the injury
probability toward the right along the estimated input dose. This framework
provides a way of revising an established injury model for a particular test
population to predict the injury model for a new population with different
distributions of parameters that affect the dose propagation and dose estimation.
In addition to modeling dose propagation uncertainty, we propose a
new 3-parameter model to include the skewness of injury function. The proposed
3-parameter function form is based on shifted log-normal distribution
of dose propagation uncertainty and is approximately invariant when other
uncertainties are added. The proposed 3-parameter function form provides a
framework for extending skewed injury model from a test population to a
target population in application.