Simulations to improve experimental designs for u-shaped dose-response modeling

A web-based tool for designing experimental studies to detect hormesis and estimate the threshold dose

Hormesis has been widely observed and debated in a variety of context in biomedicine and toxicological sciences. Detecting its presence can be an important problem with wide ranging implications. However, there is little work on constructing an efficient experiment to detect its existence or estimate the threshold dose. We use optimal design theory to develop a variety of locally optimal designs to detect hormesis, estimate the threshold dose and the zero-equivalent point (ZEP) for commonly used models in toxicology and risk assessment. To facilitate use of more efficient designs to detect hormesis, estimate threshold dose and estimate the ZEP in practice, we implement computer algorithms and create a user-friendly web site to help the biomedical researcher generate different types of optimal designs. The online tool facilitates the user to evaluate robustness properties of a selected design to various model assumptions and compare designs before implementation.

Testing Threshold and Hormesis in a Random Effects Dose-Response Model Applied to Developmental Toxicity Data

Here we describe a random effects threshold dose-response model for clustered binary-response data from developmental toxicity studies. For our model we assume that a hormetic effect occurs in addition to a threshold effect. Therefore, the dose-response curve is based on two components: relationships below the threshold (hormetic u-shaped model) and those above the threshold (logistic model). In the absence of hormesis and threshold effects, the estimation procedure is straightforward. We introduce score tests that are derived from a random effects hormetic-threshold dose-response model. The model and tests are applied to clustered binary data from developmental toxicity studies of animals to test for hormesis and threshold effects. We also compare the score test and likelihood ratio test to test for hormesis and threshold effects in a simulated study.

A parametric model for detecting hormetic effects in developmental toxicity studies

Hormetic effects have been observed at low exposure levels based on the dose-response pattern of data from developmental toxicity studies. This indicates that there might actually be a reduced risk of exhibiting toxic effects at low exposure levels. Hormesis implies the existence of a threshold dose level and there are dose-response models that include parameters that account for the threshold. We propose a function that introduces a parameter to account for hormesis. This function is a subset of the set of all functions that could represent a hormetic dose-response relationship at low exposure levels to toxic agents. We characterize the overall dose-response relationship with a piecewise function that consists of a hormetic u-shape curve at low dose levels and a logistic curve at high dose levels. We apply our model to a data set from an experiment conducted at the National Toxicology Program (NTP). We also use the beta-binomial distribution to model the litter response data. It can be seen by observing the structure of these data that current experimental designs for developmental studies employ a limited number of dose groups. These designs may not be satisfactory when the goal is to illustrate the existence of hormesis. In particular, increasing the number of low-level doses improves the power for detecting hormetic effects. Therefore, we also provide the results of simulations that were done to characterize the power of current designs in detecting hormesis and to demonstrate how this power can be improved upon by altering these designs with the addition of only a few low exposure levels.

Dose and litter allocations in the design of teratological studies for detecting hormesis

BACKGROUND

Hormesis is being recognized in the field of toxicology due to the stimulating effects of some toxic compounds at low exposure levels. Therefore, it is desirable that experimental designs for toxicological studies be flexible enough to aid in the detection of hormetic effects. Current designs may still not have enough power to do this.

METHODS

A simulation study was conducted to determine teratological study designs that would yield more power over standard designs in detecting hormesis. Developmental toxicity endpoints of interest are the number of dead/resorbed or malformed fetuses in a litter. The simulation designs mimic teratological experiments in terms of sample size and number of dose levels. Modified designs with even dose spacing at low levels and reallocated litters are investigated to determine the power of hormetic detection.

RESULTS

Designs with reallocated litters (with more litters at low exposure levels than at high levels) and even dose spacing have more power than those with equal litters per group and uneven dose spacing.

CONCLUSIONS

Through appropriate modifications of current experimental designs, such as reallocation of litters and even dose spacing, we can better detect hormetic effects.