@article{52bd42a0ee1211ddbf70000ea68e967b,
title = "Microarray background correction: maximum likelihood estimation for the normal-exponential convolution",
abstract = "Background correction is an important preprocessing step for microarray data that attempts to adjust the data for the ambient intensity surrounding each feature. The {"}normexp{"} method models the observed pixel intensities as the sum of 2 random variables, one normally distributed and the other exponentially distributed, representing background noise and signal, respectively. Using a saddle-point approximation, Ritchie and others (2007) found normexp to be the best background correction method for 2-color microarray data. This article develops the normexp method further by improving the estimation of the parameters. A complete mathematical development is given of the normexp model and the associated saddle-point approximation. Some subtle numerical programming issues are solved which caused the original normexp method to fail occasionally when applied to unusual data sets. A practical and reliable algorithm is developed for exact maximum likelihood estimation (MLE) using high-quality optimization software and using the saddle-point estimates as starting values. {"}MLE{"} is shown to outperform heuristic estimators proposed by other authors, both in terms of estimation accuracy and in terms of performance on real data. The saddle-point approximation is an adequate replacement in most practical situations. The performance of normexp for assessing differential expression is improved by adding a small offset to the corrected intensities.",
author = "Silver, {Jeremy D} and Ritchie, {Matthew E} and Smyth, {Gordon K}",
year = "2009",
doi = "10.1093/biostatistics/kxn042",
language = "English",
volume = "10",
pages = "352--63",
journal = "Biostatistics",
issn = "1465-4644",
publisher = "Oxford University Press",
number = "2",
}