PENALIZED LIKELIHOOD AND BAYESIAN METHODS FOR SPARSE CONTINGENCY TABLES: AN ANALYSIS OF ALTERNATIVE SPLICING IN FULL-LENGTH cDNA LIBRARIES

We develop methods to perform model selection and parameter estimation in loglinear models for the analysis of sparse contingency tables to study the interaction of two or more factors. Typically, datasets arising from so-called full-length cDNA libraries, in the context of alternatively spliced genes, lead to such sparse contingency tables. Maximum Likelihood estimation of log-linear model coefficients fails to work because of zero cell entries. Therefore new methods are required to estimate the coefficients and to perform model selection. Our suggestions include computationally efficient penalization (Lasso-type) approaches as well as Bayesian methods using MCMC. We compare these procedures in a simulation study and we apply the proposed methods to full-length cDNA libraries, yielding valuable insight into the biological process of alternative splicing

Penalized likelihood for sparse contingency tables with an application to full-length cDNA libraries

<p>Abstract</p> <p>Background</p> <p>The joint analysis of several categorical variables is a common task in many areas of biology, and is becoming central to systems biology investigations whose goal is to identify potentially complex interaction among variables belonging to a network. Interactions of arbitrary complexity are traditionally modeled in statistics by log-linear models. It is challenging to extend these to the high dimensional and potentially sparse data arising in computational biology. An important example, which provides the motivation for this article, is the analysis of so-called full-length cDNA libraries of alternatively spliced genes, where we investigate relationships among the presence of various exons in transcript species.</p> <p>Results</p> <p>We develop methods to perform model selection and parameter estimation in log-linear models for the analysis of sparse contingency tables, to study the interaction of two or more factors. Maximum Likelihood estimation of log-linear model coefficients might not be appropriate because of the presence of zeros in the table's cells, and new methods are required. We propose a computationally efficient ℓ₁-penalization approach extending the Lasso algorithm to this context, and compare it to other procedures in a simulation study. We then illustrate these algorithms on contingency tables arising from full-length cDNA libraries.</p> <p>Conclusion</p> <p>We propose regularization methods that can be used successfully to detect complex interaction patterns among categorical variables in a broad range of biological problems involving categorical variables.</p

Penalized Likelihood for Sparse Contingency Tables with an Application to Full-Length cDNA Libraries

Background: The joint analysis of several categorical variables is a common task in many areas of biology, and is becoming central to systems biology investigations whose goal is to identify potentially complex interaction among variables belonging to a network. Interactions of arbitrary complexity are traditionally modeled in statistics by log-linear models. It is challenging to extend these to the high dimensional and potentially sparse data arising in computational biology. An important example, which provides the motivation for this article, is the analysis of so-called full-length cDNA libraries of alternatively spliced genes, where we investigate relationships among the presence of various exons in transcript species. Results: We develop methods to perform model selection and parameter estimation in log-linear models for the analysis of sparse contingency tables, to study the interaction of two or more factors. Maximum Likelihood estimation of log-linear model coefficients is not appropriate because of the presence of zeros in the table’s cells, and new methods are required. We propose a computationally efficient ℓ1- penalization approach extending the Lasso algorithm to this context, and compare it to other procedures in a simulation study. We then illustrate these algorithms on contingency tables arising from full-length cDNA libraries. Conclusions: We propose regularization methods that can be used successfully to detect complex interactio