A Generalized Linear Model Framework for Underdispersed Count Data with an Application to MiRNA Data

• Activity Number: 404
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Lieven Clement*+ and Peter Pipelers and Olivier Thas and Jean-Pierre Ottoy
• Companies: Katholieke Universiteit Leuven and Ghent University and Ghent University and Ghent University
• Keywords: Poisson regression ; underdispersion ; qPCR ; GAM ; miRNA ; Newton-Raphson

Abstract

miRNA's play an important role in gene regulation and they are often measured by quantitative PCR (qPCR). The output of qPCR is the number of cycles, Cq-value, that is needed for a certain target to exceed a threshold. The Cq-values can be considered as counts. But, they seem to be underdispersed with respect to the Poisson distribution, i.e. their variance is less than the mean. There exist a rich variety of regression frameworks for overdispersed count data. The choice of alternative distributions for underdispersed count data, however, is rather limited and regression frameworks are lacking. We introduce a tilted Poisson distribution for underdispersed counts. It has two parameters ? and ? for location and scale, respectively. We embed the tilted Poisson distribution in a generalized linear model (GLM) framework. Both parameters ? and ? can be modeled in function of covariates by using linear and/or smooth components. We propose a Newton-Raphson algorithm for parameter estimation and implement it as a new distributional family for the R-package VGAM. We illustrate our approach in a case study for assessing differential expression of miRNA's in the presence of confounders.