Penalized negative binomial models for modeling an overdispersed count outcome with a high-dimensional predictor space: Application predicting micronuclei frequency

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.