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Motivated by the need to model dose–response or dose‐toxicity curves in clinical trials, we develop a new horseshoe‐based prior for Bayesian isotonic regression modeling a binary outcome against an ordered categorical predictor, where the probability of the outcome is assumed to be monotonically non‐decreasing with the predictor. The set of differences between outcome probabilities in consecutive categories of the predictor is equipped with a multivariate prior having support over simplex. The Dirichlet distribution, which can be derived from a normalized sum of independent gamma‐distributed random variables, is a natural choice of prior, but using mathematical and simulation‐based arguments, we show that the resulting posterior is prone to underflow and other numerical instabilities, even under simple data configurations. We propose an alternative prior based on horseshoe‐type shrinkage that is numerically more stable. We show that this horseshoe‐based prior is not subject to the numerical instability seen in the Dirichlet/gamma‐based prior and that the horseshoe‐based posterior can estimate the underlying true curve more efficiently than the Dirichlet‐based one. We demonstrate the use of this prior in a model predicting the occurrence of radiation‐induced lung toxicity in lung cancer patients as a function of dose delivered to normal lung tissue. Our methodology is implemented in the R package isotonicBayes and therefore suitable for use in the design of dose‐finding studies or other dose–response modeling contexts. [ABSTRACT FROM AUTHOR]

The impacts of runoff events on external suspended solids loading to Schoharie Reservoir, New York, and patterns of light scattering and sediment deposition in this reservoir are assessed. The assessment is based on monitoring of suspended solids concentrations in the reservoir's primary tributary, detailed vertical profiles of optical backscattering (a surrogate measure of light scattering) in the reservoir water column, and analysis of sediment trap collections, over a seven-month interval of high runoff. These impacts are reported to be tightly temporally coupled and strongly positively related to the magnitude of runoff events. The primary tributary entered the reservoir as a plunging inflow during runoff events, causing conspicuous subsurface peaks in light scattering, with vertical patterns that varied strongly for different events. Deposition quantified by near-bottom trap deployments is reported to be more representative than results from metalimnetic deployments that were generally within, rather than below, the turbid layers. Direct inputs of sediment, transported by density currents, are found to drive deposition, rather than resuspension/redeposition. More than 50 percent of the reported deposition occurred in less than 15 percent of the study period, associated with the four largest runoff events. [ABSTRACT FROM AUTHOR]