Calculate z/zlog Values

Calculates the z or z(log) values for laboratory measurement standardisation as proposed in Hoffmann 2017 et al.

z(x, limits, probs = c(0.025, 0.975), log = FALSE)

zlog(x, limits, probs = c(0.025, 0.975))

Arguments

x: numeric, laboratory values.
limits: numeric or matrix, lower and upper reference limits. Has to be of length 2 for numeric or a two-column matrix with as many rows as elements in x.
probs: numeric, probabilities of the lower and upper reference limit, default: c(0.025, 0.975) (spanning 95 %). Has to be of length 2 for numeric or a two-column matrix with as many rows as elements in x.
log: logical, should z (log = FALSE, default) or z(log) (log = TRUE) calculated?

Value

numeric, z or z(log) values.

Details

The z value is calculated as follows (assuming that the limits where 0.025 and 0.975 quantiles): \(z = (x - (limits_1 + limits_2 )/2) * 3.92/(limits_2 - limits_1)\).

The z(log) value is calculated as follows (assuming that the limits where 0.025 and 0.975 quantiles): \(z = (\log(x) - (\log(limits_1) + \log(limits_2))/2) * 3.92/(\log(limits_2) - \log(limits_1))\).

zlog is an alias for z(..., log = TRUE).

References

Georg Hoffmann, Frank Klawonn, Ralf Lichtinghagen, and Matthias Orth. 2017. "The Zlog-Value as Basis for the Standardization of Laboratory Results." LaboratoriumsMedizin 41 (1): 23–32. doi:10.1515/labmed-2016-0087 .

Author

Sebastian Gibb

Examples

z(1:10, limits = c(2, 8))
#>  [1] -2.6132853 -1.9599640 -1.3066427 -0.6533213  0.0000000  0.6533213
#>  [7]  1.3066427  1.9599640  2.6132853  3.2666066

# from Hoffmann et al. 2017
albumin <- c(42, 34, 38, 43, 50, 42, 27, 31, 24)
zlog(albumin, limits = c(35, 52))
#> [1] -0.15472223 -2.24698167 -1.14569028  0.07826303  1.57162335 -0.15472223
#> [7] -4.52949253 -3.16160843 -5.69571148

bilirubin <- c(11, 9, 2, 5, 22, 42, 37, 200, 20)

limits <- cbind(
    lower = rep(c(35, 2), c(length(albumin), length(bilirubin))),
    upper = rep(c(52, 21), c(length(albumin), length(bilirubin)))
)
zlog(c(albumin, bilirubin), limits = limits)
#>  [1] -0.15472223 -2.24698167 -1.14569028  0.07826303  1.57162335 -0.15472223
#>  [7] -4.52949253 -3.16160843 -5.69571148  0.88198551  0.54745164 -1.95996398
#> [13] -0.43243508  2.03751652  3.11549499  2.90418990  5.71721785  1.87862693