Some useful statistical methods for model validation

Although formal hypothesis tests provide a convenient framework for display ing the statistical results of empirical comparisons, standard tests should not be used without consideration of underlying measurement error structur e. As part of the validation process, predictions of individual blood lead concentrations from models with site-specific input parameters are often co mpared with blood lead concentrations measured in field studies that also r eport lead concentrations in environmental media (soil, dust, water, paint) as surrogates for exposure. Measurements of these environmental media are subject to several sources of variability, including temporal and spatial s ampling, sample preparation and chemical analysis, and data entry or record ing. Adjustments for measurement error must be made before statistical test s can be used to empirically compare environmental data with model predicti ons. This report illustrates the effect of measurement error correction usi ng a real dataset oi child blood lead concentrations for an undisclosed mid western community. We illustrate both the apparent failure of some standard regression tests and the success oi adjustment of such tests for measureme nt error using the SIMEX (simulation-extrapolation) procedure. This procedu re adds simulated measurement error to model predictions and then subtracts the total measurement error, analogous to the method of standard additions used by analytical chemists.