Application of the Stochastic Response Surface Method (SRSM) to analyze uncertainty and variability in exposure models
A. Roy, S.S. Isukapalli, P.G. Georgopoulos (EOHSI, UMDNJ - R.W. Johnson Medical School and Rutgers University)
Stochastic Response Surface Methods (SRSMs) are demonstrated to be computationally efficient alternative to 2-D Monte Carlo simulation for estimating the effects of uncertainty and variability in the parameters and input variables of exposure models. Separate estimation of the effects of uncertainty and variability on the predictions of exposure models by 2-D Monte Carlo simulation requires nested sampling of the random variables specifying uncertainty and variability, which can lead to orders of magnitude increases in the number of model iterations relative to standard Monte Carlo simulation. The number of model iterations required for 2-D Monte Carlo simulations is often computationally impractical, and therefore compromises are generally made in the resolution of uncertainty or variability, or both.
SRSMs employ polynomials of random variables (polynomial chaos expansions) to express uncertainty and variability in the predictions of exposure models. These methods can thus provide separate estimates of the effect on model predictions of any one or more combinations of random variables. The effect of interactions among uncertain and variable model inputs are represented by second and higher order terms in the polynomial chaos expansion. Moreover, the magnitude of the coefficients in the polynomial chaos expansion are a quantitative measure of the sensitivity of model predictions to the corresponding uncertain and variable parameters.
This work describes the implementation and application in MENTOR (Modeling ENvironment for Total Risk) of SRSM-SVD.H, an SRSM that employs singular value decomposition to estimate the coefficients in a hermite polynomial, which is applied to an exposure model comprised of a microenvironmental model and a physiologically based pharmacokinetic model for chloroform, a drinking water disinfection by product. The microenvironmental model incorporates the effect of housing characteristics and human activity as uncertain and variable parameters, and the pharmacokinetic model incorporates the effect of uncertainty in physiological parameters.