A Product Partition Model With Regression on Covariates

We propose a probability model for random partitions in the presence of covariates. In other words, we develop a model-based clustering algorithm that exploits available covariates. The motivating application is predicting time to progression for patients in a breast cancer trial. We proceed by repo...

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Bibliographic Details
Published in:Journal of computational and graphical statistics Vol. 20; no. 1; pp. 260 - 278
Main Authors: Müller, Peter, Quintana, Fernando, Rosner, Gary L.
Format: Journal Article
Language:English
Published: United States Taylor & Francis 01.03.2011
JCGS Management Committee of the American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America
Taylor & Francis Ltd
Subjects:
Bayesian Nonparametrics
Clustering
Inference
Linear regression
Mathematical models
Modeling
Nonparametric Bayes
Nonparametric models
Optimization algorithms
Parametric models
Predictive modeling
Probabilities
Probability distribution
Random variables
Regression analysis
Spatial models
Statistical models
Studies
Tumors
Variable selection
ISSN:1061-8600, 1537-2715
Online Access:Get full text
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Summary:We propose a probability model for random partitions in the presence of covariates. In other words, we develop a model-based clustering algorithm that exploits available covariates. The motivating application is predicting time to progression for patients in a breast cancer trial. We proceed by reporting a weighted average of the responses of clusters of earlier patients. The weights should be determined by the similarity of the new patient's covariate with the covariates of patients in each cluster. We achieve the desired inference by defining a random partition model that includes a regression on covariates. Patients with similar covariates are a priori more likely to be clustered together. Posterior predictive inference in this model formalizes the desired prediction. We build on product partition models (PPM). We define an extension of the PPM to include a regression on covariates by including in the cohesion function a new factor that increases the probability of experimental units with similar covariates to be included in the same cluster. We discuss implementations suitable for any combination of continuous, categorical, count, and ordinal covariates. An implementation of the proposed model as R-package is available for download.
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ISSN:1061-8600
1537-2715
DOI:10.1198/jcgs.2011.09066