skrmdb package

The skrmdb package provides functionality to compute the median effective dose (ED50) using the Dragstedt-Behrens, Reed-Muench, and Spearman-Kärber estimators.

Usage

DragBehr(formula, data, y, n, x, autosort = TRUE, warn.me = TRUE, show = FALSE)

ReedMuench(
  formula,
  data,
  y,
  n,
  x,
  autosort = TRUE,
  warn.me = TRUE,
  show = FALSE
)

SpearKarb(
  formula,
  data,
  y,
  n,
  x,
  autosort = TRUE,
  warn.me = TRUE,
  show = FALSE
)

Arguments

formula

a formula of the form y + n ~ x or cbind(y, n) ~ x

data

a data frame

y

an integer vector corresponding to the number responding at each log dilution or dose.

n

an integer vector corresponding to the group size at each log dilution or dose.

x

a vector corresponding to the log dilution or dose for each group.

autosort

Default TRUE. If TRUE will sort the data according to either sort(x) or sort(-x) so that y / n appears to be increasing with the index. This is how the three methods assume the data to be ordered.

warn.me

if TRUE, warnings and messages related to the processing of the data will be displayed.

show

if TRUE, will print the intermediary statistics used to calculate ED50.

Value

An object of class skrmdb

Details

The Dragstedt-Behrens and Reed-Muench methods estimate the median effective dose by interpolating between the two doses that bracket the dose producing median response. They accumulate sums in both directions by assuming that those that responded at a lower dose would respond at a higher dose, and those that did not respond at a higher dose would not respond at a lower dose. The Dragstedt-Behrens method estimates ED50 by interpolating on the line that connects the hypothetical fractions of the bracketing doses for ED50, while the Reed-Muench method estimates ED50 as the intersection of the lines connecting the two sets of cumulative sums between bracketing doses.

The Spearman-Karber method gives a non-parametric estimate of the mean of an tolerance distribution from its empirical distribution (EDF). The empirical PMF is derived from the EDF by differencing and the estimator is \(\sum{ x f(x)}\). If the EDF does not cover the entire support of x, SpearKarb() extends it by assuming the next lower dilution would produce zero response and the next higher dilution would produce complete response.

Note

These methods assume that the y is monotonic in x, however ED50 will still be computed if this is not the case. These methods also assume that data brackets ED50. If the data does not bracket ED50, a result could still be returned, but the accuracy of this value in estimating ED50 is suspect.

Many microbiology texts mistakenly present the Dragstedt-Behrens method as the Reed-Muench method.

References

Behrens, B. (1929) Zur Auswertung der Digitalisblätter im Froschversuch. Arkiv für Experimentelle Pathologie und Pharmakologie. 140: 237-256.

Dragstedt, C. A., Lang, V. F. (1928). Respiratory Stimulants in Acute Cocaine Poisoning in Rabbits. J. of Pharmacology and Experimental Therapeutics. 32: 215–222.

Kärber, G. (1931). Beitrag zur kollektiven Behandlung Parmakogischer Reihenversuche. Archiv für Experimentelle Pathologie und Pharmakologie. 162: 480–483.

Miller, Rupert G. (1973). Nonparametric Estimators of the Mean Tolerance in Bioassay. Biometrika. 60: 535 - 542.

Reed LJ, Muench H (1938). A Simple Method of Estimating Fifty Percent Endpoints. American Journal of Hygiene. 27: 493–497.

Spearman, C. (1908). The Method of "Right and Wrong Cases" ("Constant Stimuli") without Gauss's Formulae. Brit. J. of Psychology. 2: 227–242.

See also

Useful links:

• https://github.com/ABS-dev/skrmdb/

• https://abs-dev.github.io/skrmdb/

• Report bugs at https://github.com/ABS-dev/skrmdb/issues/

Author

Maintainer: CVB Statistics CVB.Data.Help@usda.gov [former owner]

Authors:

• David Siev (until 2019)

• Marie Vendettuoli (until 2019)

• Thomas Kent (starting 2020)

Examples

# All examples are with `SpearKarb`, however, the usage for
# `DragBehr` and `ReedMuench` is identical.

## Monotonically increasing data
# The three calls are equivalent.
dead <- c(0, 3, 5, 8, 10, 10)
total <- rep(10, 6)
dil <- 1:6
data <- data.frame(y = dead, n = total, x = dil)
SpearKarb(dead + total ~ dil)
#> ED50 by the Spearman-Karber method
#> ed:   2.9 
#> Count trend is increasing with dilution.
SpearKarb(y + n ~ x, data)
#> ED50 by the Spearman-Karber method
#> ed:   2.9 
#> Count trend is increasing with dilution.
SpearKarb(y = dead, n = total, x = dil)  # depreciated
#> Warning: skrmdb :: Calling this function with the parameters y, n, x is depreciated.
#> ED50 by the Spearman-Karber method
#> ed:   2.9 
#> Count trend is increasing with dilution.

## Decreasing data
# The function will reverse the order of the data
# and two calls are equivalent.
dead <- c(10, 10, 8, 5, 3, 0)
total <- rep(10, 6)
dil <- 1:6
SpearKarb(dead + total ~ dil)
#> ED50 by the Spearman-Karber method
#> ed:   4.1 
#> Count trend is decreasing with dilution.
SpearKarb(rev(dead) + rev(total) ~ rev(dil))
#> ED50 by the Spearman-Karber method
#> ed:   4.1 
#> Count trend is decreasing with dilution.

## Unordered data
# Observe that the data is not monotonic after being sorted by dil.
dead <- c(10, 8, 5, 3, 0)
total <- rep(10, 5)
dil <- c(1, 3, 2, 4, 5)
SpearKarb(dead + total ~ dil)
#> skrmdb :: y is not monotonic. ED50 may be unreliable.
#> ED50 by the Spearman-Karber method
#> ed:   3.1 
#> Count trend is decreasing with dilution.
#> y is not monotonic. ED50 may be unreliable.