Successive Standardization: Application to Case-Control Studies

In this note we illustrate the use and applicability of successive standardization (or normalization), studied earlier by some of the same authors (see Olshen and Rajaratnam, Algorithms 5(1):98–112, 2012; Olshen and Rajaratnam, Proceeding of the 1st International Conference on Data Compression, Communication and Processing (CCP 2011), June 21–24, 2011; Olshen and Rajaratnam, Annals of Statistics 38(3):1638–1664, 2010), in the context of biomedical applications. Successive standardization constitutes a type of normalization that is applied to rectangular arrays of numbers. An iteration first begins with operations on rows: first subtract the mean of each row from elements of the particular row; then row elements are divided by their respective row standard deviations. This constitutes half an iteration. These two operations are then applied successively at the level of columns, constituting the other half of the iteration. The four operations together constitute one full iteration. The process is repeated again and again and is referred to as “successive standardization.” Work in Olshen and Rajaratnam, Algorithms 5(1):98–112, 2012; Olshen and Rajaratnam, Proceeding of the 1st International Conference on Data Compression, Communication and Processing (CCP 2011), June 21–24, 2011; Olshen and Rajaratnam, Annals of Statistics 38(3):1638–1664, 2010 is about both theoretical and numerical properties of the successive standardization procedure, including convergence, rates of convergence, and illustrations. In this note, we consider the application of successive standardization to a specific biomedical context, that of case–control studies in cardiovascular biology. We demonstrate that successive standardization is very useful for identifying novel gene therapeutic targets. In particular, we demonstrate that successive standardization identifies genes that otherwise would have been rendered not significant in a Significance Analysis of Microarrays (SAM) study had standardization not been applied.