A semiparametric approach to risk assessment for quantitative outcomes

Benchmark Dose Analysis via Nonparametric Regression Modeling

Estimation of benchmark doses (BMDs) in quantitative risk assessment traditionally is based upon parametric dose-response modeling. It is a well-known concern, however, that if the chosen parametric model is uncertain and/or misspecified, inaccurate and possibly unsafe low-dose inferences can result. We describe a nonparametric approach for estimating BMDs with quantal-response data based on an isotonic regression method, and also study use of corresponding, nonparametric, bootstrap-based confidence limits for the BMD. We explore the confidence limits' small-sample properties via a simulation study, and illustrate the calculations with an example from cancer risk assessment. It is seen that this nonparametric approach can provide a useful alternative for BMD estimation when faced with the problem of parametric model uncertainty.

SIMULTANEOUS CONFIDENCE BOUNDS FOR LOW-DOSE RISK ASSESSMENT WITH NONQUANTAL DATA

We study the use of simultaneous confidence bounds for making low-dose inferences in quantitative risk analysis. Confidence limits are constructed for outcomes measured on a continuous scale, assuming a simple linear model for the observed response. From the simultaneous confidence bounds, simultaneous lower limits on the benchmark dose associated with a particular risk are also constructed.

The role of the benchmark dose in a regulatory context

The use of no observed adverse effect levels (NOAELs) as a way of interpreting toxicology studies carries a number of problems, and the benchmark dose (BMD), or its lower confidence limit have been proposed as potential replacements. In practice, the theoretical advantages of the BMD approach are often outweighed by the practical disadvantages posed in a regulatory context. Attempts to seek consensus for the routine use of BMD methodology tend to involve diluting its potential advantages as much as they address the disadvantages, resulting in a relatively complex interpolation tool that delivers little more than the NOAEL. It is time to recognise that the BMD will never entirely replace the NOAEL. The two methods can have complementary roles. The NOAEL is well suited as a routine simple summary of effects in toxicology studies, whilst the BMD can be a higher tier approach for the interpretation of the most critical studies in a regulatory data package.

Quantitative Risk Assessment for Multivariate Continuous Outcomes with Application to Neurotoxicology: The Bivariate Case

The neurotoxic effects of chemical agents are often investigated in controlled studies on rodents, with multiple binary and continuous endpoints routinely collected. One goal is to conduct quantitative risk assessment to determine safe dose levels. Such studies face two major challenges for continuous outcomes. First, characterizing risk and defining a benchmark dose are difficult. Usually associated with an adverse binary event, risk is clearly definable in quantal settings as presence or absence of an event; finding a similar probability scale for continuous outcomes is less clear. Often, an adverse event is defined for continuous outcomes as any value below a specified cutoff level in a distribution assumed normal or log normal. Second, while continuous outcomes are traditionally analyzed separately for such studies, recent literature advocates also using multiple outcomes to assess risk. We propose a method for modeling and quantitative risk assessment for bivariate continuous outcomes that address both difficulties by extending existing percentile regression methods. The model is likelihood based; it allows separate dose-response models for each outcome while accounting for the bivariate correlation and overall characterization of risk. The approach to estimation of a benchmark dose is analogous to that for quantal data without the need to specify arbitrary cutoff values. We illustrate our methods with data from a neurotoxicity study of triethyl tin exposure in rats.

Combining uncertainty factors in deriving human exposure levels of noncarcinogenic toxicants

Acceptable levels of human exposure to noncarcinogenic toxicants in environmental and occupational settings generally are derived by reducing experimental no-observed-adverse-effect levels (NOAELs) or benchmark doses (BDs) by a product of uncertainty factors (Barnes and Dourson, Ref. 1). These factors are presumed to ensure safety by accounting for uncertainty in dose extrapolation, uncertainty in duration extrapolation, differential sensitivity between humans and animals, and differential sensitivity among humans. The common default value for each uncertainty factor is 10. This paper shows how estimates of means and standard deviations of the approximately log-normal distributions of individual uncertainty factors can be used to estimate percentiles of the distribution of the product of uncertainty factors. An appropriately selected upper percentile, for example, 95th or 99th, of the distribution of the product can be used as a combined uncertainty factor to replace the conventional product of default factors.

Procedures for calculating benchmark doses for health risk assessment

Safety assessment for noncancer health effects generally has been based upon dividing a no observed adverse effect (NOAEL) by uncertainty (safety) factors to provide an acceptable daily intake (ADI) or reference dose (RfD). Since the NOAEL does not utilize all of the available dose-response data, allows higher ADI from poorer experiments, and may have an unknown, unacceptable level of risk, the benchmark dose (BD) with a specified, controlled low level of risk has become popular as an adjunct to the NOAEL or the low observed adverse effect level (LOAEL) in the safety assessment process. The purpose of this paper is to summarize statistical procedures available for calculating BDs and their confidence limits for noncancer endpoints. Procedures are presented and illustrated for quantal (binary), quasicontinuous (proportion), and continuous data. Quasicontinuous data arise in developmental studies where the measure of an effect for a fetus is quantal (normal or abnormal) but the experimental unit is the mother (litter) so that results can be expressed as the proportion of abnormal fetuses per litter. However, the correlation of effects among fetuses within a litter poses some additional statistical problems. Also, developmental studies usually include some continuous measures, such as fetal body weight or length. With continuous data there generally is not a clear demarcation between normal and adverse measurements. In such cases, extremely high and/or low measurements at some designated percentile(s) can be considered abnormal. Then the probability (risk) of abnormal individuals can be estimated as a function of dose. The procedure for estimating a BD with continuous data is illustrated using neurotoxicity data. When multiple measures of adverse effects are available, a BD can be estimated based on a selected endpoint or the appearance of any combination of endpoints. Multivariate procedures are illustrated using developmental and reproductive toxicity data.