Related Experiment Video
Updated: Jun 24, 2026

Advanced 3D Liver Models for In vitro Genotoxicity Testing Following Long-Term Nanomaterial Exposure
Published on: June 5, 2020
Joint models for toxicology studies with dose-dependent number of implantations
Andrew S Allen1, Huiman X Barnhart
1Department of Biostatistics and Bioinformatics and Duke Clinical Research Institute, Duke University Medical Center, Durham, NC 27715, USA. allen123@mc.duke.edu
Abstract:
Many chemicals interfere with the natural reproductive processes in mammals. The chemicals may prevent the fertilization of an egg or keep a zygote from implanting in the uterine wall. For this reason, toxicology studies with pre-implantation exposure often exhibit a dose-related trend in the number of observed implantations per litter. Standard methods for analyzing developmental toxicology studies are conditioned on the number of implantations in the litter and therefore cannot estimate this effect of the chemical on the reproductive process. This article presents a joint modeling approach to estimating risk in toxicology studies with pre-implantation exposure. In the joint modeling approach, both the number of implanted fetuses and the outcome of each implanted fetus is modeled. Using this approach we show how to estimate the overall risk of a chemical that incorporates the risk of lost implantation due to pre-implantation exposure. Our approach has several distinct advantages over previous methods: (1) it is based on fitting a model for the observed data and, therefore, diagnostics of model fit and selection apply; (2) all assumptions are explicitly stated; and (3) it can be fit using standard software packages We illustrate our approach by analyzing a dominant lethal assay data set (Luning et al., 1966, Mutation Research, 3, 444-451) and compare ourresults with those of Rai and Van Ryzin (1985, Biometrics, 41,1-9) and Dunson (1998, Biometrics, 54, 558-569). In a simulation study, our approach has smaller bias and variance than the multiple imputation procedure of Dunson.
Insights
This study introduces a novel joint modeling approach for toxicology studies. It accurately estimates chemical risks by considering both implantation success and fetal development, improving upon standard methods.
Area of Science:
- Toxicology
- Reproductive Biology
- Biostatistics
Background:
- Chemicals can disrupt mammalian reproduction by preventing fertilization or implantation.
- Developmental toxicology studies often show dose-related implantation loss, which standard methods cannot fully analyze.
- Existing methods for analyzing pre-implantation exposure effects are limited in scope and statistical rigor.
Purpose of the Study:
- To present a joint modeling approach for estimating chemical risks in toxicology studies with pre-implantation exposure.
- To develop a method that accounts for both implantation failure and post-implantation fetal outcomes.
- To provide a statistically robust and adaptable framework for risk assessment in reproductive toxicology.
Main Methods:
- A joint modeling approach is proposed, simultaneously analyzing the number of implanted fetuses and the outcome of each implanted fetus.
- The method models both the probability of implantation and the viability of implanted fetuses.
- The approach is demonstrated using a dominant lethal assay dataset and compared with existing methods.
Main Results:
- The joint modeling approach provides a comprehensive estimation of chemical risk, incorporating pre-implantation effects.
- This method allows for model fitting, explicit assumption statement, and utilization of standard statistical software.
- Simulation studies indicate that the proposed approach exhibits lower bias and variance compared to the multiple imputation procedure.
Conclusions:
- The joint modeling approach offers a superior method for analyzing developmental toxicology data with pre-implantation exposure.
- This approach enhances the accuracy of risk assessment for chemicals affecting reproductive processes.
- The presented method is statistically sound, adaptable, and offers advantages over traditional analytical techniques.
More Related Videos
Related Concept Videos
Pharmacokinetic Models: Overview
There are three primary types of models: empirical, compartment, and physiological. Empirical models, with minimal assumptions,...
Mechanistic Models: Compartment Models in Individual and Population Analysis
Drug Accumulation During Multiple Dosing: Repetitive IV Injections
Pharmacodynamic Models: Additive and Proportional Drug Effect Model
Drug Toxicity: Dose-Dependent Reactions
Toxicity Testing in Animals

