Model-Based Co-Clustering for Censored Data

Abstract

Co-clustering jointly partitions the rows and columns of a data matrix. Standard co-clustering methods for continuous data typically assume that entries are observed exactly. Matrices with censored entries, such as assay measurements below a detection limit, are therefore commonly completed by substitution or imputation before co-clustering. Since the completed values are treated as exact, the estimated block means and partitions depend on the completion rule. We propose the censored Gaussian latent block model (CGLBM), in which each censored entry contributes the probability of its reported interval. We establish identifiability under a known Type I censoring design. Approximate standard errors for the block means follow from the Fisher information under censoring. CGLBM is fitted by a generalized expectation--maximization algorithm, and its row and column class numbers are selected by a BIC approximation to the integrated classification likelihood. In simulation studies, boundary substitution and truncated normal imputation attenuate the contrasts between block means, whereas the partition recovery of multiple imputation drops the most under heavy censoring. CGLBM preserves the contrasts, and its partition recovery drops the least. The method is implemented in the R package CGLBM.