Abstract
Chromosomal aberrations, such as micronuclei (MN), have served as biomarkers of genotoxic exposure and cancer risk. Guidelines for the process of scoring MN have been presented by the HUman MicroNucleus (HUMN) project. However, these guidelines were developed for assay performance but do not address how to statistically analyze the data generated by the assay. This has led to the application of various statistical methods that may render different interpretations and conclusions. By combining MN with data from other high-throughput genomic technologies such as gene expression microarray data, we may elucidate molecular features involved in micronucleation. Traditional methods that can model discrete (synonymously, count) data, such as MN frequency, require that the number of explanatory variables (P) is less than the number of samples (N). Due to this limitation, penalized models have been developed to enable model fitting for such over-parameterized datasets. Because penalized models in the discrete response setting are lacking, particularly when the count outcome is over-dispersed, herein we present our penalized negative binomial regression model that can be fit when P > N. Using simulation studies we demonstrate the performance of our method in comparison to commonly used penalized Poisson models when the outcome is over-dispersed and applied it to MN frequency and gene expression data collected as part of the Norwegian Mother and Child Cohort Study. Our countgmifs R package is available for download from the Comprehensive R Archive Network and can be applied to datasets having a discrete outcome that is either Poisson or negative binomial distributed and a high-dimensional covariate space.
Highlights
More than 85% of all cancers are associated with acquired chromosomal or genetic alterations
While various penalized Poisson models can be fit to highdimensional data, the focus of this paper is to extend the generalized monotone incremental forward stagewise (GMIFS) method to the negative binomial regression setting and demonstrate its effectiveness analyzing over-dispersed count outcome data
When examining the boxplots of the simulation results, we observed that our negative binomial (NB) GMIFS method performed well with respect to identifying true predictors (Fig 3) while minimizing the number of false predictors included in the model (Fig 4), as α and β increased
Summary
Poisson regressionWhen modeling the number of times an event occurs in either time or space, a generalized linear model (GLM) such as Poisson or negative binomial regression is commonly applied. We note that expressing a discrete response as a rate transforming the rate to get it to adhere to a Gaussian distribution so that traditional linear models can be fit, does not properly account for the variation observed in the numerator and denominator terms. The Poisson regression model for the expected count per unit of ci, where ci is the number of cells scored in our application, is Eðyi=ciÞ 1⁄4 mi 1⁄4 exp ðg0 þ x>i βÞ which is equivalent to mi 1⁄4 exp ðg0 þ x>i β þ log ðciÞÞ ð3Þ so that log(ci) is an offset term. For the rate-based model, the log-likelihood expressed with covariates is ‘ðmjyÞ 1⁄4 ðyiðg0 þ x>i β þ log ðciÞÞ À exp ðg0 þ x>i β þ log ðciÞÞ À log ðyi!ÞÞ: ð4Þ
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