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Remove unwanted variation retrieves unknown experimental designs

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  • Ingrid M. Lönnstedt
  • Terence P. Speed

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.

Suggested Citation

  • Ingrid M. Lönnstedt & Terence P. Speed, 2023. "Remove unwanted variation retrieves unknown experimental designs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 89-101, March.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:1:p:89-101
    DOI: 10.1111/sjos.12633
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    References listed on IDEAS

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    1. Xu Shi & Wang Miao & Jennifer C. Nelson & Eric J. Tchetgen Tchetgen, 2020. "Multiply robust causal inference with double‐negative control adjustment for categorical unmeasured confounding," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(2), pages 521-540, April.
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