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Activity Number:
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264
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Type:
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Topic Contributed
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Date/Time:
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Tuesday, August 10, 2004 : 2:00 PM to 3:50 PM
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Sponsor:
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Biometrics Section
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| Abstract - #300726 |
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Title:
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Estimation of Binary Response with Order Restrictions
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Author(s):
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Jeremy M.G. Taylor*+ and Lu Wang
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Companies:
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University of Michigan and University of Michigan
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Address:
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Dept. of Biostatistics, Ann Arbor, MI, 48109,
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Keywords:
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biomarkers ; isotonic regression ; order restrictions ; multiple imputation
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Abstract:
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We consider the situation of two or more ordered categorical variables and a binary outcome variable, where one or more 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 categorical variables while incorporating the ordering. The probability of response is assumed to change monotonically as each of the categorical variables changes. Let q_ij be the probability that the categorical variables fall in cell ij, and p_ij be the probability of response. A model is developed in which the number of observations in each cell is multinomial(q) and the response is binomial with parameters p_ij for each ij. Three estimation approaches are compared, Gibbs sampling with order restrictions on p_ij, multiple imputation and isotonic regression. This problem is motivated by studies in which multiple biomarkers are measured on stored specimens and the outcome measure is response to treatment. Missing biomarker data is common in such settings. It is also biologically reasonable to assume that the probability of response changes monotonically as the biomarker values change.
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