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Bayesian isotonic regression and trend analysis.

Publication ,  Journal Article
Neelon, B; Dunson, DB
Published in: Biometrics
June 2004

In many applications, the mean of a response variable can be assumed to be a nondecreasing function of a continuous predictor, controlling for covariates. In such cases, interest often focuses on estimating the regression function, while also assessing evidence of an association. This article proposes a new framework for Bayesian isotonic regression and order-restricted inference. Approximating the regression function with a high-dimensional piecewise linear model, the nondecreasing constraint is incorporated through a prior distribution for the slopes consisting of a product mixture of point masses (accounting for flat regions) and truncated normal densities. To borrow information across the intervals and smooth the curve, the prior is formulated as a latent autoregressive normal process. This structure facilitates efficient posterior computation, since the full conditional distributions of the parameters have simple conjugate forms. Point and interval estimates of the regression function and posterior probabilities of an association for different regions of the predictor can be estimated from a single MCMC run. Generalizations to categorical outcomes and multiple predictors are described, and the approach is applied to an epidemiology application.

Duke Scholars

Published In

Biometrics

DOI

EISSN

1541-0420

ISSN

0006-341X

Publication Date

June 2004

Volume

60

Issue

2

Start / End Page

398 / 406

Related Subject Headings

  • Statistics & Probability
  • Regression Analysis
  • Premature Birth
  • Pregnancy
  • Monte Carlo Method
  • Markov Chains
  • Linear Models
  • Insecticides
  • Infant, Newborn
  • Humans
 

Citation

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Neelon, B., & Dunson, D. B. (2004). Bayesian isotonic regression and trend analysis. Biometrics, 60(2), 398–406. https://doi.org/10.1111/j.0006-341x.2004.00184.x
Neelon, Brian, and David B. Dunson. “Bayesian isotonic regression and trend analysis.Biometrics 60, no. 2 (June 2004): 398–406. https://doi.org/10.1111/j.0006-341x.2004.00184.x.
Neelon B, Dunson DB. Bayesian isotonic regression and trend analysis. Biometrics. 2004 Jun;60(2):398–406.
Neelon, Brian, and David B. Dunson. “Bayesian isotonic regression and trend analysis.Biometrics, vol. 60, no. 2, June 2004, pp. 398–406. Epmc, doi:10.1111/j.0006-341x.2004.00184.x.
Neelon B, Dunson DB. Bayesian isotonic regression and trend analysis. Biometrics. 2004 Jun;60(2):398–406.
Journal cover image

Published In

Biometrics

DOI

EISSN

1541-0420

ISSN

0006-341X

Publication Date

June 2004

Volume

60

Issue

2

Start / End Page

398 / 406

Related Subject Headings

  • Statistics & Probability
  • Regression Analysis
  • Premature Birth
  • Pregnancy
  • Monte Carlo Method
  • Markov Chains
  • Linear Models
  • Insecticides
  • Infant, Newborn
  • Humans