A Semiparametric Approach to Risk Assessment for Quantitative Outcomes

Characterizing the dose-effect relationship and estimating acceptable exposure levels are the primary goals of quantitative risk assessment. A semiparametric approach is proposed for risk assessment with continuously measured or quantitative outcomes which has advantages over existing methods by requiring fewer assumptions. The approach is based on pairwise ranking between the response values in the control group and those in the exposed groups. The work generalizes the rank-based Wilcoxon-Mann-Whitney test, which for the two-group comparison is effectively a test of whether a response from the control group is different from (larger than) a response in an exposed group. We develop a regression framework that naturally extends this metric to model the dose effect in terms of a risk function. Parameters of the regression model can be estimated with standard software. However, inference requires an additional step to estimate the variance structure of the estimated parameters. An effective dose (ED) and associated lower confidence limit (LED) are easily calculated. The method is supported by a simulation study and is illustrated with a study on the effects of aconiazide. The method offers flexible modeling of the dose effect, and since it is rank-based, it is more resistant to outliers, nonconstant variance, and other departures from normality than previously described approaches.