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Bayesian Estimation of Inverse Dose Response
Author(s) -
Hu Bo,
Ji Yuan,
Tsui KamWah
Publication year - 2008
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2008.01013.x
Subject(s) - maximum a posteriori estimation , posterior probability , bayesian probability , bayesian inference , mathematics , posterior predictive distribution , statistics , prior probability , a priori and a posteriori , computer science , bayes estimator , inverse problem , bayesian linear regression , algorithm , maximum likelihood , mathematical analysis , philosophy , epistemology
Summary Inverse dose–response estimation refers to the inference of an effective dose of some agent that gives a desired probability of response, say 0.5. We consider inverse dose response for two agents, an application that has not received much attention in the literature. Through the posterior profiling technique (Hsu, 1995, The Canadian Journal of Statistics 23, 399–410), we propose a Bayesian method in which we approximate the marginal posterior distribution of an effective dose using a profile posterior distribution, and obtain the maximum a posteriori (MAP) estimate for the effective dose. We then employ an adaptive direction sampling algorithm to obtain the highest posterior density (HPD) credible region for the effective dose. Using the MAP and HPD estimates, investigators will be able to simultaneously calibrate the levels of two agents in dose–response studies. We illustrate our proposed Bayesian method through a simulation study and two practical examples.