zprime: Compute the Z'-factor quality score In imageHTS: Analysis of high-throughput microscopy-based screens

Description

Compute the Z'-factor quality score.

Usage

 1 zprime(a, b, method=c('mahalanobis', 'robust', 'fixsd', 'original'))

Arguments

 a, b Matrices of control features. method a character vector, indicating which method should be used to compute the Z'-factor. Default is mahalanobis. See Details.

Details

The Z'-factor is a popular metric measuring the separation of control features in high-throughput screens. The original paper describing the Z'-factor is Zhang, 1999, J Biomol Screen.

Several univariate Z'-factor scores exist. The original Z'-factor from Zhang, 1999 is computed by Z' = 1 - 3*(sd(a)+sd(b))/abs(mean(a)-mean(b)). A more rigorous definition of the score, implemented by the method fixsd is given by Z' = 1 - 3*sqrt(var(a)+var(b))/abs(mean(a)-mean(b)), where the pooled standard deviation is computed by the square root of the sum of the control variances. A robust method, less sensitive to outliers, is computed by the relation Z' = 1-3*(mad(a)+mad(b))/abs(median(a)-median(b)) where the control dispersions are computed with the mad and the control locations with the median.

A multivariate extension of the Z'-factor score can be designed by linearly transforming the multivariate data to one dimension and computing the standard (here, fixsd) Z'-factor. It can be shown that the linear transform that maximizes the score is the LDA. Moreover, one can demonstrate that the resulting Z'-factor score is equivalent of computing Z' = 1 - 3/dMaha(mu_a, mu_b, Sigma_a + Sigma_b) where dMaha is the Mahalanobis distance.

Value

The Z'-factor, a numeric ranging from -infinity to 1.

Author(s)

Gregoire Pau, gregoire.pau@embl.de, 2010

References

J. H. Zhang, T. D. Chung, K. R. Oldenburg. A Simple Statistical Parameter for Use in Evaluation and Validation of High Throughput Screening Assays. J Biomol Screening, 1999.