Matthew W. Wheeler

Comparing median lethal concentration values using confidence interval overlap or ratio tests

Experimenters in toxicology often compare the concentration-response relationship between two distinct populations using the median lethal concentration (LC50). This comparison is sometimes done by calculating the 95% confidence interval for the LC50 for each population, concluding that no significant difference exists if the two confidence intervals overlap. A more appropriate test compares the ratio of the LC50s to 1 or the log(LC50 ratio) to 0. In this ratio test, we conclude that no difference exists in LC50s if the confidence interval for the ratio of the LC50s contains 1 or the confidence interval for the log(LC50 ratio) contains 0. A Monte Carlo simulation study was conducted to compare the confidence interval overlap test to the ratio test. The confidence interval overlap test performs substantially below the nominal alpha = 0.05 level, closer to p = 0.005; therefore, it has considerably less power for detecting true differences compared to the ratio test. The ratio-based method exhibited better type I error rates and superior power properties in comparison to the confidence interval overlap test. Thus, a ratio-based statistical procedure is preferred to using simple overlap of two independently derived confidence intervals.

An Approach to Risk Assessment for TiO2

Titanium dioxide (TiO2) is a poorly soluble, low-toxicity (PSLT) particle. Fine TiO2 (<2.5 μm) has been shown to produce lung tumors in rats exposed to 250 mg/m3, and ultrafine TiO2 (< 0.1 μm diameter) has been shown to produce lung tumors in rats at 10 mg/m3. We have evaluated the rat dose-response data and conducted a quantitative risk assessment for TiO2. Preliminary conclusions are: (1) Fine and ultrafine TiO2 and other PSLT particles show a consistent dose-response relationship when dose is expressed as particle surface area; (2) the mechanism of TiO2 tumor induction in rats appears to be a secondary genotoxic mechanism associated with persistent inflammation; and (3) the inflammatory response shows evidence of a nonzero threshold. Risk estimates for TiO2 depend on both the dosimetric approach and the statistical model that is used. Using 7 different dose-response models in the U.S. Environmental Protection Agency (EPA) benchmark dose software, the maximum likelihood estimate (MLE) rat lung dose associated with a 1 per 1000 excess risk ranges from 0.0076 to 0.28 m2/g-lung of particle surface area, with 95% lower confidence limits (LCL) of 0.0059 and 0.042, respectively. Using the ICRP particle deposition and clearance model, estimated human occupational exposures yielding equivalent lung burdens range from approximately 1 to 40 mg/m3 (MLE) for fine TiO2, with 95% LCL approximately 0.7–6 mg/m3. Estimates using an interstitial sequestration lung model are about one-half as large. Bayesian model averaging techniques are now being explored as a method for combining the various estimates into a single estimate, with a confidence interval expressing model uncertainty.

Contributions of dust exposure and cigarette smoking to emphysema severity in coal miners in the United States

RATIONALE Previous studies have shown associations between dust exposure or lung burden and emphysema in coal miners, although the separate contributions of various predictors have not been clearly demonstrated. OBJECTIVES To quantitatively evaluate the relationship between cumulative exposure to respirable coal mine dust, cigarette smoking, and other factors on emphysema severity. METHODS The study group included 722 autopsied coal miners and nonminers in the United States. Data on work history, smoking, race, and age at death were obtained from medical records and questionnaire completed by next-of-kin. Emphysema was classified and graded using a standardized schema. Job-specific mean concentrations of respirable coal mine dust were matched with work histories to estimate cumulative exposure. Relationships between various metrics of dust exposure (including cumulative exposure and lung dust burden) and emphysema severity were investigated in weighted least squares regression models. MEASUREMENTS AND MAIN RESULTS Emphysema severity was significantly elevated in coal miners compared with nonminers among ever- and never-smokers (P < 0.0001). Cumulative exposure to respirable coal mine dust or coal dust retained in the lungs were significant predictors of emphysema severity (P < 0.0001) after accounting for cigarette smoking, age at death, and race. The contributions of coal mine dust exposure and cigarette smoking were similar in predicting emphysema severity averaged over this cohort. CONCLUSIONS Coal dust exposure, cigarette smoking, age, and race are significant and additive predictors of emphysema severity in this study.

Model Uncertainty and Risk Estimation for Experimental Studies of Quantal Responses

Experimental animal studies often serve as the basis for predicting risk of adverse responses in humans exposed to occupational hazards. A statistical model is applied to exposure-response data and this fitted model may be used to obtain estimates of the exposure associated with a specified level of adverse response. Unfortunately, a number of different statistical models are candidates for fitting the data and may result in wide ranging estimates of risk. Bayesian model averaging (BMA) offers a strategy for addressing uncertainty in the selection of statistical models when generating risk estimates. This strategy is illustrated with two examples: applying the multistage model to cancer responses and a second example where different quantal models are fit to kidney lesion data. BMA provides excess risk estimates or benchmark dose estimates that reflects model uncertainty.

Comparing model averaging with other model selection strategies for benchmark dose estimation

Model averaging (MA) has been proposed as a method of accommodating model uncertainty when estimating risk. Although the use of MA is inherently appealing, little is known about its performance using general modeling conditions. We investigate the use of MA for estimating excess risk using a Monte Carlo simulation. Dichotomous response data are simulated under various assumed underlying dose–response curves, and nine dose–response models (from the USEPA Benchmark dose model suite) are fit to obtain both model specific and MA risk estimates. The benchmark dose estimates (BMDs) from the MA method, as well as estimates from other commonly selected models, e.g., best fitting model or the model resulting in the smallest BMD, are compared to the true benchmark dose value to better understand both bias and coverage behavior in the estimation procedure. The MA method has a small bias when estimating the BMD that is similar to the bias of BMD estimates derived from the assumed model. Further, when a broader range of models are included in the family of models considered in the MA process, the lower bound estimate provided coverage close to the nominal level, which is superior to the other strategies considered. This approach provides an alternative method for risk managers to estimate risk while incorporating model uncertainty.

Benchmark Dose Estimation Incorporating Multiple Data Sources

With the increased availability of toxicological hazard information arising from multiple experimental sources, risk assessors are often confronted with the challenge of synthesizing all available scientific information into an analysis. This analysis is further complicated because significant between-source heterogeneity/lab-to-lab variability is often evident. We estimate benchmark doses using hierarchical models to account for the observed heterogeneity. These models are used to construct source-specific and population-average estimates of the benchmark dose (BMD). This is illustrated with an analysis of the U.S. EPA Region IXs reference toxicity database on the effects of sodium chloride on reproduction in Ceriodaphnia dubia. Results show that such models may effectively account for the lab-source heterogeneity while producing BMD estimates that more truly reflect the variability of the system under study. Failing to account for such heterogeneity may result in estimates having confidence intervals that are overly narrow.

Monotonic Bayesian Semiparametric Benchmark Dose Analysis

Quantitative risk assessment proceeds by first estimating a dose-response model and then inverting this model to estimate the dose that corresponds to some prespecified level of response. The parametric form of the dose-response model often plays a large role in determining this dose. Consequently, the choice of the proper model is a major source of uncertainty when estimating such endpoints. While methods exist that attempt to incorporate the uncertainty by forming an estimate based upon all models considered, such methods may fail when the true model is on the edge of the space of models considered and cannot be formed from a weighted sum of constituent models. We propose a semiparametric model for dose-response data as well as deriving a dose estimate associated with a particular response. In this model formulation, the only restriction on the model form is that it is monotonic. We use this model to estimate the dose-response curve from a long-term cancer bioassay, as well as compare this to methods currently used to account for model uncertainty. A small simulation study is conducted showing that the method is superior to model averaging when estimating exposure that arises from a quantal-linear dose-response mechanism, and is similar to these methods when investigating nonlinear dose-response patterns.

Confidence Interval Construction for Relative Toxicity Endpoints such as LD50 or LD90 Ratios

Abstract A common measure of the relative toxicity is the ratio of median lethal doses for responses estimated in two bioassays. Robertson and Preisler previously proposed a method for constructing a confidence interval for the ratio. The applicability of this technique in common experimental situations, especially those involving small samples, may be questionable because the sampling distribution of this ratio estimator may be highly skewed. To examine this possibility, we did a computer simulation experiment to evaluate the coverage properties of the Robertson and Preisler method. The simulation showed that the method provided confidence intervals that performed at the nominal confidence level for the range of responses often observed in pesticide bioassays. Results of this study provide empirical support for the continued use this technique.

Historical Context and Recent Advances in Exposure-Response Estimation for Deriving Occupational Exposure Limits

Virtually no occupational exposure standards specify the level of risk for the prescribed exposure, and most occupational exposure limits are not based on quantitative risk assessment (QRA) at all. Wider use of QRA could improve understanding of occupational risks while increasing focus on identifying exposure concentrations conferring acceptably low levels of risk to workers. Exposure-response modeling between a defined hazard and the biological response of interest is necessary to provide a quantitative foundation for risk-based occupational exposure limits; and there has been considerable work devoted to establishing reliable methods quantifying the exposure-response relationship including methods of extrapolation below the observed responses. We review several exposure-response modeling methods available for QRA, and demonstrate their utility with simulated data sets.

Incorporating uncertainty and variability in the assessment of occupational hazards

Uncertainty reflects ignorance associated with population traits (e.g. average exposure levels to a contaminant), with models used to predict risk (e.g. which statistical model is correct), and with a host of other considerations. Variability reflects an intrinsic property of a system (e.g. body mass indices possess a distribution across a population). The incorporation of uncertainty and variability in the assessment of occupational hazards is an important objective. General issues of uncertainty and variability in occupational risk estimation are discussed. This is followed by three illustrations where: firstly, the impact of variability in an exposure assessment and sampling variability in a regression model on risk estimates is considered; secondly, the impact of uncertainty in the size of a workforce on rate modelling is considered; and thirdly, the impact of using different models to predict risk is considered.