Quantitative Risk Assessment

European Organization for Research and Treatment of Cancer, Brussels, Belgium

In the area of risk assessment, the focus can be on a number of issues. Interest can be placed on the characterization of the dose-response relationship, i.e., studying the dependence of a particular outcome such as the risk of a malformed foetus, on the dose which is administered to the dam. Besides investigating the dose-response relation, another issue is quantitative risk assessment. This critically important area of risk assessment is based on the relationship between dose and response, to derive a safe dose. In quantitative risk assessment, there are a number of choices that have to be made, resulting in a variety of approaches. First, safe exposure levels can be derived from the NOAEL (No Observed

Adverse Effect Level) safety factor approach. The assumption made here is that if the dose administered to a dam is below some value (the threshold), then there will be no adverse effects on the foetuses of that dam (Williams and Ryan 1996). The NOAEL is defined as the experimental dose level immediately below the lowest dose that produces a statistically or biologically significant increase in an adverse effect in comparison with the control. An “acceptably safe” daily dose for humans is then calculated by dividing the NOAEL by a safety factor (commonly 100 or 1000). In this way, sensitive subgroups of the population and extrapolation from animal experiments to human risk are taken into account. Rather than basing quantitative risk assessment on the NOAEL procedure, dose-response modeling can also be used to determine safe doses. Due to the disadvantages of the NOAEL and the benefits of dose-response models, this chapter is concerned with statistical procedures to predict safe exposure levels based on such a modeling approach. Second, there are several ways to handle clustering. While dose-response

modeling is relatively straightforward in uncorrelated settings, it is less so in the clustered context. Of course, one can ignore the clustering altogether by treating the littermates as if they were independent. Also, the litter effect issue can be avoided by modeling the probability of an affected litter. Such models are generally too simplistic but there is a multitude of models which

do consider clustering. Indeed, as discussed in Chapter 4, different types of models (marginal, random effects, conditional) for clustered binary data can be formulated. In this chapter, the emphasis is on the beta-binomial model (Skellam 1948, Kleinman 1973), as well as on the conditional model of Molenberghs and Ryan (1999). Besides the choice of an appropriate dose-response model, parameters can be estimated via several inferential procedures. Estimation methods range from full likelihood to pseudo-likelihood (Chapters 6 and 7) and generalized estimating equations (Chapter 5). In this chapter, parameters are estimated using maximum likelihood methodology. Furthermore, the implications in terms of uncertainty of fitting a model based on a finite set of data are investigated. In Chapter 11, the effect of misspecifying the parametric response model on the estimation of a safe dose will be investigated. Third, quantitative risk assessment can be based on either foetus or on

litter-based risks. To perform dose-response modeling and assessment of safe doses, most authors take a foetus-based perspective, where the excess risk over background for an affected foetus is determined as a function of dose. The latter approach is straightforward for marginal models, which are expressed in terms of this marginal adverse event probability (Diggle, Liang and Zeger 1994, Pendergast et al. 1996). However, a disadvantage of this approach is that it may raise biological questions. Arguably, the entire litter is more representative of a human pregnancy than a single foetus. As a consequence, modeling litter-based excess risks is a very appealing alternative from a biological perspective. In the litter-based approach, quantitative risk assessment is based on the cluster of foetuses of a dam, i.e., the probability that at least one foetus of a dam has the adverse event under consideration is crucial. In this chapter, foetus and so-called litter-based risks are contrasted in the determination of safe doses. Fourth, one needs to acknowledge the stochastic nature of the number of

implants and the number of viable foetuses (i.e., the litter size) in a dam. Some methods (Ryan 1992) condition on the observed litter size when modeling the number of malformations. Others (e.g., Catalano et al. 1993) allow response rates to depend on litter size and then calculate a safe dose at an “average” litter size, thereby avoiding the need for direct adjustment. Krewski and Zhu (1995) use a model formulation that causes litter size to drop from the expression for excess risk. Rai and Van Ryzin (1985) compute risks by integrating over the litter size distribution. This approach will be used in this chapter. The relatively complex data structure forces the researcher to reflect on

several other questions: 1. Are linear or non-linear predictors used? 2. Are the malformation indices studied separately, collapsed into a single

indicator or treated as a multivariate outcome vector per foetus within a litter?