A Search for Thresholds and Other Nonlinearities in the Relationship Between Hexavalent Chromium and Lung Cancer

The exposure-response relationship for airborne hexavalent chromium exposure and lung cancer mortality is well described by a linear relative rate model. However, categorical analyses have been interpreted to suggest the presence of a threshold. This study investigates nonlinear features of the exposure response in a cohort of 2,357 chemical workers with 122 lung cancer deaths. In Poisson regression, a simple model representing a two-step carcinogenesis process was evaluated. In a one-stage context, fractional polynomials were investigated. Cumulative exposure dose metrics were examined corresponding to cumulative exposure thresholds, exposure intensity (concentration) thresholds, dose-rate effects, and declining burden of accumulated effect on future risk. A simple two-stage model of carcinogenesis provided no improvement in fit. The best-fitting one-stage models used simple cumulative exposure with no threshold for exposure intensity and had sufficient power to rule out thresholds as large as 30 microg/m3 CrO3 (16 microg/m3 as Cr+6) (one-sided 95% confidence limit, likelihood ratio test). Slightly better-fitting models were observed with cumulative exposure thresholds of 0.03 and 0.5 mg-yr/m3 (as CrO3) with and without an exposure-race interaction term, respectively. With the best model, cumulative exposure thresholds as large as 0.4 mg-yr/m3 CrO3 were excluded (two-sided upper 95% confidence limit, likelihood ratio test). A small departure from dose-rate linearity was observed, corresponding to (intensity)0.8 but was not statistically significant. Models in which risk-inducing damage burdens declined over time, based on half-lives ranging from 0.1 to 40 years, fit less well than assuming a constant burden. A half-life of 8 years or less was excluded (one-sided 95% confidence limit). Examination of nonlinear features of the hexavalent chromium-lung cancer exposure response in a population used in a recent risk assessment supports using the traditional (lagged) cumulative exposure paradigm: no intensity (concentration) threshold, linearity in intensity, and constant increment in risk following exposure.     

On the risk of mortality to primates exposed to anthrax spores.

Current events have heightened the importance of understanding the risks from inhalation exposure to small numbers of spores of Bacillus anthracis. Previously reported data sets have not been fully assessed using current understanding of microbial dose response. This article presents an assessment of the reported primate dose-response data. At low doses, the risk to large populations of low doses of inhaled spores (e.g., < 100) is not insignificant.     

Design of Developmental Toxicity Studies for Assessing Joint Effects of Dose and Duration

In the assessment of developmental and reproductive effects, the timing and duration of exposures to chemical compounds or other environmental contaminants are of particular interest, as the gestational cycle is known to have periods of increased sensitivity. The goal of this research is to identify optimal experimental designs for conducting developmental toxicity studies when the effects of both exposure level and duration of exposure are of interest. The elements of the study design considered in this evaluation are the allocation of animals to dose-duration exposure groups and the determination of the most efficient intermediate exposure levels. The optimality of various designs is assessed via the accuracy of the estimated excess risk as well as testing criteria. Simulation studies are conducted to compare these criteria and determine optimal design strategies under various underlying dose-response patterns. Asymptotic results are also derived to lend support to the simulation studies.     

Modeling Fetal Death and Malformation in Developmental Toxicity Studies

We review approaches to dose-response modeling and risk assessment for binary data from developmental toxicity studies. In particular, we focus on jointly modeling fetal death and malformation and use a continuation ratio formulation of the multinomial distribution to provide a model for risk. Generalized estimating equations are used to account for clustering of animals within litters. The fitted model is then used to calculate doses corresponding to a specified level of excess risk. Two methods of arriving at a lower confidence limit or Benchmark dose are illustrated and compared. We also discuss models based on single binary end points and compare our approach to a binary analysis of whether or not the animal was 'affected' (either dead or malformed). The models are illustrated using data from four developmental toxicity studies in EG, DEHP, TGDM, and DYME conducted through the National Toxicology Program.     

Optimal Designs for Estimating the Effective Dose in Developmental Toxicity Experiments

Recent advances in risk assessment have led to the development of joint dose-response models to describe prenatal death and fetal malformation rates in developmental toxicity experiments. These models can be used to estimate the effective dose corresponding to a 5% excess risk for both these toxicological endpoints, as well as for overall toxicity. In this article, we develop optimal experimental designs for the estimation of the effective dose for developmental toxicity using joint Weibull dose-response models for prenatal death and fetal malformation. Based on an extended series of developmental studies, near-optimal designs for prenatal death, malformation, and overall toxicity were found to involve three dose groups: an unexposed control group, a high dose equal to the maximum tolerated dose, and a low dose above or comparable to the effective dose. The effect on the optimal designs of changing the number of implants and the degree of intra-litter correlation is also investigated. Although the optimal design has only three dose groups in most cases, practical considerations involving model lack of fit and estimation of the shape of the dose-response curve suggest that, in practice, suboptimal designs with more than three doses will often be preferred.     

A randomized phase I Bayesian dose escalation design for the combination of anti‐cancer drugs

Nowadays, treatment regimens for cancer often involve a combination of drugs. The determination of the doses of each of the combined drugs in phase I dose escalation studies poses methodological challenges. The most common phase I design, the classic ‘3+3' design, has been criticized for poorly estimating the maximum tolerated dose (MTD) and for treating too many subjects at doses below the MTD. In addition, the classic ‘3+3' is not able to address the challenges posed by combinations of drugs. Here, we assume that a control drug (commonly used and well‐studied) is administered at a fixed dose in combination with a new agent (the experimental drug) of which the appropriate dose has to be determined. We propose a randomized design in which subjects are assigned to the control or to the combination of the control and experimental. The MTD is determined using a model‐based Bayesian technique based on the difference of probability of dose limiting toxicities (DLT) between the control and the combination arm. We show, through a simulation study, that this approach provides better and more accurate estimates of the MTD. We argue that this approach may differentiate between an extreme high probability of DLT observed from the control and a high probability of DLT of the combination. We also report on a fictive (simulation) analysis based on published data of a phase I trial of ifosfamide combined with sunitinib.Copyright © 2014 John Wiley & Sons, Ltd.     

Mechanistic Modeling of Emergency Events: Assessing the Impact of Hypothetical Releases of Anthrax

A modular system for source-to-dose-to-effect modeling analysis has been developed based on the modeling environment for total risk studies (MENTOR),^{( 1 )} and applied to study the impacts of hypothetical atmospheric releases of anthrax spores. The system, MENTOR-2E (MENTOR for Emergency Events), provides mechanistically consistent analysis of inhalation exposures for various release scenarios, while allowing consideration of specific susceptible subpopulations (such as the elderly) at the resolution of individual census tracts. The MENTOR-2E application presented here includes atmospheric dispersion modeling, statistically representative samples of individuals along with corresponding activity patterns, and population-based dosimetry modeling that accounts for activity and physiological variability. Two hypothetical release scenarios were simulated: a 100 g release of weaponized B. anthracis over a period of (a) one hour and (b) 10 hours, and the impact of these releases on population in the State of New Jersey was studied. Results were compared with those from simplified modeling of population dynamics (location, activities, etc.), and atmospheric dispersion of anthrax spores. The comparisons showed that in the two release scenarios simulated, each major approximation resulted in an overestimation of the number of probable infections by a factor of 5 to 10; these overestimations can have significant public health implications when preparing for and responding effectively to an actual release. This is in addition to uncertainties in dose-response modeling, which result in an additional factor of 5 to 10 variation in estimated casualties. The MENTOR-2E system has been developed in a modular fashion so that improvements in individual modules can be readily made without impacting the other modules, and provides a first step toward the development of models that can be used in supporting real-time decision making.     

Stochastic approximation methods and their use in bioassay and phase i clinical trials

Stochastic approximation procedures are sequential estimation methods which provide estimates for the point at which a general regression function attains a given value. The application of such methods to the problem of estimating the median effective does in bioassay and to the problem of estimating the maximally tolerated does in phase I clinical trials is discussed. it is argued that these methods could be very useful in practice.     

Analysis of dose-response in flexible dose titration clinical studies

Assessing dose-response from flexible-dose clinical trials (e.g., titration or dose escalation studies) is challenging and often problematic due to the selection bias caused by 'titration-to-response'. We investigate the performance of a dynamic linear mixed-effects (DLME) model and marginal structural model (MSM) in evaluating dose-response from flexible-dose titration clinical trials via simulations. The simulation results demonstrated that DLME models with previous exposure as a time-varying covariate may provide an unbiased and efficient estimator to recover exposure-response relationship from flexible-dose clinical trials. Although the MSM models with independent and exchangeable working correlations appeared to be able to recover the right direction of the dose-response relationship, it tended to over-correct selection bias and overestimated the underlying true dose-response. The MSM estimators were also associated with large variability in the parameter estimates. Therefore, DLME may be an appropriate modeling option in identifying dose-response when data from fixed-dose studies are absent or a fixed-dose design is unethical to be implemented.     

Expected loss functions as additional measures to assess performance of multiple testing procedures for combination drug dose finding

There are several measures that are commonly used to assess performance of a multiple testing procedure (MTP). These measures include power, overall error rate (family‐wise error rate), and lack of power. In settings where the MTP is used to estimate a parameter, for example, the minimum effective dose, bias is of interest. In some studies, the parameter has a set‐like structure, and thus, bias is not well defined. Nevertheless, the accuracy of estimation is one of the essential features of an MTP in such a context. In this paper, we propose several measures based on the expected values of loss functions that resemble bias. These measures are constructed to be useful in combination drug dose response studies when the target is to identify all minimum efficacious drug combinations. One of the proposed measures allows for assigning different penalties for incorrectly overestimating and underestimating a true minimum efficacious combination. Several simple examples are considered to illustrate the proposed loss functions. Then, the expected values of these loss functions are used in a simulation study to identify the best procedure among several methods used to select the minimum efficacious combinations, where the measures take into account the investigator's preferences about possibly overestimating and/or underestimating a true minimum efficacious combination. The ideas presented in this paper can be generalized to construct measures that resemble bias in other settings. These measures can serve as an essential tool to assess performance of several methods for identifying set‐like parameters in terms of accuracy of estimation. Copyright © 2012 John Wiley & Sons, Ltd.