Statistical methods for chip calibration and saturation effects in antibody-spiked gene expression data

Oligonucleotide microarrays are amongst, a set of technologies that allow for high throughput assessment of vast numbers of gene expressions. In order to evaluate gene expressions given detection limits, antibody spiking is often used providing one with an expression curve relating antibody treated expression and non-antibody treated expression. These curves can exhibit different functional shapes across chips and hence need to be standardized. In addition, each curve is subject to saturation effects, which are typically dealt with by extrapolating a linear fit to the subset of the data not visually subject to saturation. In this paper we introduce methods for the non-parametric standardization of expression curves using univariate smoothers. We also explore parametric methods for more efficient analysis of the standardized curves. We demonstrate an alternate method of parametric analysis using a weighted linear mixed effects model that does not arbitrarily delete data beyond an observed saturation point; allows for natural grouping of genes and provides significantly more accurate predictions than naive linear extrapolation. Both methodologies are studied through sets of simulations.