Analysis on binary responses with ordered covariates and missing data.

Journal Article (Journal Article)

We consider the situation of two ordered categorical variables and a binary outcome variable, where one or both of the categorical variables may have missing values. The goal is to estimate the probability of response of the outcome variable for each cell of the contingency table of categorical variables while incorporating the fact that the categorical variables are ordered. The probability of response is assumed to change monotonically as each of the categorical variables changes level. A probability model is used in which the response is binomial with parameters p(ij) for each cell (i, j) and the number of observations in each cell is multinomial. Estimation approaches that incorporate Gibbs sampling with order restrictions on p(ij) induced via a prior distribution, two-dimensional isotonic regression and multiple imputation to handle missing values are considered. The methods are compared in a simulation study. Using a fully Bayesian approach with a strong prior distribution to induce ordering can lead to large gains in efficiency, but can also induce bias. Utilizing isotonic regression can lead to modest gains in efficiency, while minimizing bias and guaranteeing that the order constraints are satisfied. A hybrid of isotonic regression and Gibbs sampling appears to work well across a variety of scenarios. The methods are applied to a pancreatic cancer case-control study with two biomarkers.

Full Text

Duke Authors

Cited Authors

  • Taylor, JMG; Wang, L; Li, Z

Published Date

  • August 15, 2007

Published In

Volume / Issue

  • 26 / 18

Start / End Page

  • 3443 - 3458

PubMed ID

  • 17219376

International Standard Serial Number (ISSN)

  • 0277-6715

Digital Object Identifier (DOI)

  • 10.1002/sim.2815


  • eng

Conference Location

  • England