Interlitter Response Variability in a Threshold Dose-Response Model

In this article, we extend a previously formulated threshold dose-response model with random litter effects that was applied to a data set from a developmental toxicity study. The dose-response pattern of the data indicates that a threshold dose level may exist. Additionally, there is noticeable variation between the responses across the dose levels. With threshold estimation being critical, the assumed variability structure should adequately model the variation while not taking away from the estimation of the threshold as well as the other parameters directly involved in the dose-response relationship. In the prior formulation, the random effect was modeled assuming identical variation in the interlitter response probabilities across all dose levels, that is, the model had a single parameter to account for the interlitter variability. In this new model, the random effect is modeled as having different response variability across dose levels, that is, multiple interlitter variability parameters. We performed the likelihood ratio test (LRT) to compare our extended model to the previous model. We conducted a simulation study to compare the bias of each model when fit to data generated with the underlying parametric structure of the opposing model. The extended threshold dose-response model with multiple response variation was less biased.