title: PCAN: Probabilistic correlation analysis of two non-normal data sets.
abstract: Most cancer research now involves one or more assays profiling various biological molecules, e.g., messenger RNA and micro RNA, in samples collected on the same individuals. The main interest with these genomic data sets lies in the identification of a subset of features that are active in explaining the dependence between platforms. To quantify the strength of the dependency between two variables, correlation is often preferred. However, expression data obtained from next-generation sequencing platforms are integer with very low counts for some important features. In this case, the sample Pearson correlation is not a valid estimate of the true correlation matrix, because the sample correlation estimate between two features/variables with low counts will often be close to zero, even when the natural parameters of the Poisson distribution are, in actuality, highly correlated. We propose a model-based approach to correlation estimation between two non-normal data sets, via a method we call Probabilistic Correlations ANalysis, or PCAN. PCAN takes into consideration the distributional assumption about both data sets and suggests that correlations estimated at the model natural parameter level are more appropriate than correlations estimated directly on the observed data. We demonstrate through a simulation study that PCAN outperforms other standard approaches in estimating the true correlation between the natural parameters. We then apply PCAN to the joint analysis of a microRNA (miRNA) and a messenger RNA (mRNA) expression data set from a squamous cell lung cancer study, finding a large number of negative correlation pairs when compared to the standard approaches.
authors.affiliation: Department of Epidemiology and Biostatistics, Texas A&M University, College Station, Texas, U.S.A.
authors.forename: Roger S
authors.initials: RS
authors.lastname: Zoh
authors.affiliation: Department of Statistics, Texas A&M University, College Station, Texas, U.S.A.
authors.forename: Bani
authors.initials: B
authors.lastname: Mallick
authors.affiliation: Department of Veterinary Medicine and Biomedical Sciences, Texas A&M University, Texas, U.S.A.
authors.forename: Ivan
authors.initials: I
authors.lastname: Ivanov
authors.affiliation: The University of Texas MD Anderson Cancer Center, 1515 Holcombe Blvd, Houston, Texas, U.S.A.
authors.forename: Veera
authors.initials: V
authors.lastname: Baladandayuthapani
authors.affiliation: The University of Texas MD Anderson Cancer Center, 1515 Holcombe Blvd, Houston, Texas, U.S.A.
authors.forename: Ganiraju
authors.initials: G
authors.lastname: Manyam
authors.affiliation: Program in Integrative Nutrition and Complex Diseases, Texas A&M University, Texas, U.S.A.
authors.forename: Robert S
authors.initials: RS
authors.lastname: Chapkin
authors.affiliation: Department of Epidemiology, University of Washington and the Fred Hutchinson Cancer Research Center Seattle, Washington, U.S.A.
authors.forename: Johanna W
authors.initials: JW
authors.lastname: Lampe
authors.affiliation: Department of Statistics, Texas A&M University, College Station, Texas, U.S.A.
authors.forename: Raymond J
authors.initials: RJ
authors.lastname: Carroll
mesh_terms: D002294:Carcinoma, Squamous Cell / Q000235:genetics; D059014:High-Throughput Nucleotide Sequencing / Q000706:statistics & numerical data*; D006801:Humans; D008175:Lung Neoplasms / Q000235:genetics; D035683:MicroRNAs / Q000032:analysis; D015233:Models, Statistical; D016012:Poisson Distribution; D012333:RNA, Messenger / Q000032:analysis
chemical_list: D035683:MicroRNAs; D012333:RNA, Messenger
keywords: Canonical correlation analysis; Correlation; Generalized linear models; Poisson regression; RNA-sequencing