Remove unwanted variation retrieves unknown experimental designs. (21st February 2023)

• Record Type: Journal Article
• Authors: Lönnstedt, Ingrid M.; Speed, Terence P.
• Is Part Of: Scandinavian journal of statistics. Volume 50:Number 1(2023)
• Page Start: 89
• Page End: 101
• Publication Date: 2023-02-21
• Subjects: balanced incomplete block design (BIBD) -- block design -- multivariate design of experiments -- recovery of interblock information -- remove unwanted variation (RUV) -- remove unwanted variation inverse method (RUV‐inverse); Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12633
• Languages: English
• ISSNs: 0303-6898

Abstract

Abstract: Remove unwanted variation (RUV) is an estimation and normalization system in which the underlying correlation structure of a multivariate dataset is estimated from negative control measurements, typically gene expression values, which are assumed to stay constant across experimental conditions. In this paper we derive the weight matrix which is estimated and incorporated into the generalized least squares estimates of RUV‐inverse, and show that this weight matrix estimates the average covariance matrix across negative control measurements. RUV‐inverse can thus be viewed as an estimation method adjusting for an unknown experimental design. We show that for a balanced incomplete block design (BIBD), RUV‐inverse recovers intra‐ and interblock estimates of the relevant parameters and combines them as a weighted sum just like the best linear unbiased estimator (BLUE), except that the weights are globally estimated from the negative control measurements instead of being individually optimized to each measurement as in the classical, single measurement BIBD BLUE.