This post is by Eric.

This Wednesday, at 12 pm ET, Kristian Brock is stopping by to talk to us about functional uniform priors for dose-response models. You can register here.

Abstract

Dose-response modeling frequently employs non-linear regression. Functional uniform priors are distributions that can be derived for parameters that convey approximate uniformity over the range of function shapes generated by the model. They provide a stark alternative to regular uniform priors, which in the non-linear setting can provide potentially undue influence on the estimated functional form. Using methods introduced by Bornkamp, we provide full analytical derivations of functional uniform priors for a range of non-linear dose-response models. We then examine the numerical performance of these two types of prior, and analogous maximum likelihood models, in a simulation study. We also investigate the incidence of several markers that question the adequacy of model fit, in simulated and real phase I clinical trial datasets.

We show that mean absolute errors of response estimates are smaller when using functional uniform priors instead of regular uniform priors. This effect was seen in all simulation scenarios at all sample sizes. Irrespective of the decreases in errors, biases tended to be slightly larger under functional uniform priors. When the analysis model and data generating model matched, functional uniform priors yielded very close to nominal coverage probabilities, even at the smallest sample size. This was not true for models that used regular uniform priors. Markers of model fit inadequacy using real and simulated datasets were much more common in maximum likelihood models, with parameters being estimated near the boundary being a notable problem. Functional uniform priors provide a general improvement over regular uniform priors in Bayesian dose-response modeling and should be preferred. The substantial mathematical work required to derive the priors is abrogated by the results derived in this research.