{"doi":"10.1002/pst.2372","title":"Shrinkage priors for isotonic probability vectors and binary data modeling, with applications to dose–response modeling","abstract":"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.","journal":"Pharmaceutical Statistics","year":2024,"id":482894,"datarank":0.16479184330021646,"base_score":1.0986122886681096,"endowment":1.0986122886681096,"self_citation_contribution":0.16479184330021646,"citation_network_contribution":0.0,"self_endowment_contribution":0.16479184330021646,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":2,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9517,"is_data_producer":true,"deposit_databanks":{"ClinicalTrials.gov":["NCT02492867)"]},"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2024-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":762202,"name":"Daniel Owen","orcid":"0000-0003-1106-3616","position":1,"is_corresponding":false},{"id":1323392,"name":"Jian Kang","orcid":"0000-0002-0841-9039","position":2,"is_corresponding":false},{"id":107459,"name":"Philip S. Boonstra","orcid":"0000-0001-8545-9133","position":0,"is_corresponding":true}],"reference_count":35,"raw_metadata":null,"created_at":"2026-07-19T02:07:18.280369Z","pmid":"38400582","pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}