Four parameter logistic desirability function

Description

Maps a numeric variable to a 0-1 scale with a logistic function.

Usage

d.4pl(x, hill, inflec, des.min = 0, des.max = 1)

Arguments

Details

This function uses a four parameter logistic model to map a numeric variable onto a 0-1 scale. Whether high or low values are deemed desirable can be controlled with the hill parameter; when hill > 0 high values are desirable and when hill < 0 low values are desirable

Note that if the data contain both positive and negative values this function does not provide a monotonic mapping (see example).

Value

Numeric vector of desirability values.

See Also

d.low, d.high

Examples

# High values are desirable
x1 <- seq(80, 120, 0.01)
d1 <- d.4pl(x = x1, hill = 20, inflec = 100)
plot(d1 ~ x1, type="l")

# Low values are desirable (negative slope), with a minimum
# desirability of 0.3
d2 <- d.4pl(x = x1, hill = -30, inflec = 100, des.min=0.3)
plot(d2 ~ x1, type="l", ylim=c(0,1))

# Beware of how the function behaves when the data contain both
# positive and negative values
x2 <- seq(-20, 20, 0.01)
d3 <- d.4pl(x = x2, hill = 20, inflec = 1)
plot(d3 ~ x2, type="l")

Central values are desirable

Description

Maps a numeric variable to a 0-1 scale such that values in the middle of the distribution are desirable.

Usage

d.central(x, cut1, cut2, cut3, cut4, des.min = 0, des.max = 1, scale = 1)

Arguments

Details

Values less than cut1 and greater than cut4 will have a low desirability. Values between cut2 and cut3 will have a high desirability. Values between cut1 and cut2 and between cut3 and cut4 will have intermediate values. This function is useful when extreme values are undesirable. For example, outliers or values outside of allowable ranges. If cut2 and cut3 are close to each other, this function can be used when a target value is desirable.

Value

Numeric vector of desirability values.

See Also

d.ends

Examples

set.seed(1)
x <- rnorm(1000, mean=100, sd =5) # generate data
d <- d.central(x, cut1=90, cut2=95, cut3=105, cut4=110, scale=1)

# plot data
hist(x, breaks=30)
# add line
des.line(x, "d.central", des.args=c(cut1=90, cut2=95, cut3=105,
cut4=110, scale=1))

hist(x, breaks=30)
des.line(x, "d.central", des.args=c(cut1=90, cut2=95, cut3=105,
cut4=110, des.min=0.1, des.max=0.95, scale=1.5))

# target value
hist(x, breaks=30)
des.line(x, "d.central", des.args=c(cut1=90, cut2=99.9, cut3=100.1, cut4=110))

Extreme (both high and low) values are desirable

Description

Maps a numeric variable to a 0-1 scale such that values at the ends of the distribution are desirable.

Usage

d.ends(x, cut1, cut2, cut3, cut4, des.min = 0, des.max = 1, scale = 1)

Arguments

Details

Values less than cut1 and greater than cut4 will have a high desirability. Values between cut2 and cut3 will have a low desirability. Values between cut1 and cut2 and between cut3 and cut4 will have intermediate values. This function is useful when the data represent differences between groups; for example, log2 fold-changes in gene expression. In this case, both high an low values are of interest.

Value

Numeric vector of desirability values.

See Also

d.central

Examples

set.seed(1)
x <- rnorm(1000, mean=100, sd =5) # generate data
d <- d.ends(x, cut1=90, cut2=95, cut3=105, cut4=110, scale=1)

# plot data
hist(x, breaks=30)
# add line
des.line(x, "d.ends", des.args=c(cut1=90, cut2=95, cut3=105,
cut4=110, scale=1))

hist(x, breaks=30)
des.line(x, "d.ends", des.args=c(cut1=90, cut2=95, cut3=105,
cut4=110, des.min=0.1, des.max=0.95, scale=1.5))

High values are desirable

Description

Maps a numeric variable to a 0-1 scale such that high values are desirable.

Usage

d.high(x, cut1, cut2, des.min = 0, des.max = 1, scale = 1)

Arguments

Details

Values less than cut1 will have a low desirability. Values greater than cut2 will have a high desirability. Values between cut1 and cut2 will have intermediate values.

Value

Numeric vector of desirability values.

See Also

d.low, d.4pl

Examples

set.seed(1)
x <- rnorm(1000, mean=100, sd =5) # generate data
d <- d.high(x, cut1=90, cut2=110, scale=1)

# plot data
hist(x, breaks=30)
# add line
des.line(x, "d.high", des.args=c(cut1=90, cut2=110, scale=1))

hist(x, breaks=30)
des.line(x, "d.high", des.args=c(cut1=90, cut2=110, des.min=0.1,
des.max=0.95, scale=1.5))

Low values are desirable

Description

Maps a numeric variable to a 0-1 scale such that low values are desirable.

Usage

d.low(x, cut1, cut2, des.min = 0, des.max = 1, scale = 1)

Arguments

Details

Values less than cut1 will have a high desirability. Values greater than cut2 will have a low desirability. Values between cut1 and cut2 will have intermediate values.

Value

Numeric vector of desirability values.

See Also

d.high, d.4pl

Examples

set.seed(1)
x <- rnorm(1000, mean=100, sd =5) # generate data
d <- d.low(x, cut1=90, cut2=110, scale=1)

# plot data
hist(x, breaks=30)
# add line
des.line(x, "d.low", des.args=c(cut1=90, cut2=110, scale=1))

hist(x, breaks=30)
des.line(x, "d.low", des.args=c(cut1=90, cut2=110, des.min=0.1,
des.max=0.95, scale=1.5))

Combine individual desirabilities

Description

Combines any number of desirability values into an overall desirability.

Usage

d.overall(..., weights = NULL)

Arguments

Details

This function takes any number of individual desirabilities and combines them with a weighted geometric mean to give an overall desirability. The weights should be chosen to reflect the importance of the variables. The values of the weights do not matter, only their relative differences. Therefore weights of 4, 2, 1 are the same as 1, 0.5, 0.25. In both cases the second weight is half of the first, and the third weight is a quarter of the first.

Value

Numeric vector of desirability values.

Examples

set.seed(1)
x1 <- rnorm(1000, mean=100, sd =5) # generate data
x2 <- rnorm(1000, mean=100, sd =5) 

d1 <- d.high(x1, cut1=90, cut2=110, scale=1)
d2 <- d.low(x2, cut1=90, cut2=110, scale=1)

D <- d.overall(d1, d2, weights=c(1, 0.5))
plot(rev(sort(D)), type="l")

Converts values to ranks, then ranks to desirabilities

Description

Values are ranked from low to high or high to low, and then the ranks are mapped to a 0-1 scale.

Usage

d.rank(x, low.to.high, ties = "min")

Arguments

Details

If low values of a variable are desirable (e.g. p-values) set the argument low.to.high=TRUE, otherwise low.to.high=FALSE.

If extreme values in either direction are of interest (e.g. fold-changes), take the absolute value of the variable and use low.to.high=FALSE. See the example below.

This function is less flexible than the others but it can be used to compare the desirability approach with rank aggregation methods.

Value

Numeric vector of desirability values.

Examples

set.seed(1)
x1 <- rnorm(1000, mean=100, sd =5) # generate data
d <- d.rank(x1, low.to.high=TRUE)

# plot data
hist(x1, breaks=30)
# add line
des.line(x1, "d.rank", des.args=c(low.to.high=TRUE))

x2 <- rnorm(1000, mean=0, sd =5) # positive and negative values
# could be fold-changes, mean differences, or t-statistics
hist(abs(x2), breaks=30)
# add line
des.line(abs(x2), "d.rank", des.args=c(low.to.high=FALSE))

Plots a desirability function on an existing graph

Description

Plots any of the desirability functions on top of a graph, usually a histogram or density plot.

Usage

des.line(x, des.func, des.args, ...)

Arguments

Details

This function can be used to visualise how the desirabilities are mapped from the raw data to a 0-1 scale, which can help select suitable cut points. The scale of the y-axis has a minimum of 0 and a maximum of 1.

WARNING: If you set xlim values for the histogram or density plot, then you must pass the same xlim values to des.line; otherwise the data and desirability function (plotted line) will be misaligned. If xlim is not set, then the same default values will be used for the data and the function.

Value

Plotted values of the desirability function.

See Also

d.low, d.high, d.central, d.ends, d.4pl

Examples

set.seed(1)
x1 <- rnorm(100, 10, 2)
hist(x1, breaks=10)
des.line(x1, "d.high", des.args=c(cut1=10, cut2=11))
des.line(x1, "d.high", des.args=c(cut1=10, cut2=11,
des.min=0.1, scale=0.5))

Breast cancer microarray dataset

Description

1000 randomly selected probesets from a breast cancer microarray dataset (Farmer et al., 2005).

Format

A data frame with 1000 rows and 7 variables:

ProbeSet:

Affymetrix probesets from the U133A chip.

GeneID:

Gene symbol.

logFC:

Log2 fold change for the basal versus luminal comparison.

AveExpr:

Mean expression across all samples.

P.Value:

P-value for basal versus luminal comparison.

SD:

Standard deviation across all samples.

PCNA.cor:

Correlation with PCNA (a marker of proliferating cells).

Details

These data are the results from an analysis comparing the basal and luminal samples. The apocrine samples are excluded.

References

Farmer P, Bonnefoi H, Becette V, Tubiana-Hulin M, Fumoleau P, Larsimont D, Macgrogan G, Bergh J, Cameron D, Goldstein D, Duss S, Nicoulaz AL, Brisken C, Fiche M, Delorenzi M, Iggo R. Identification of molecular apocrine breast tumours by microarray analysis. Oncogene. 2005 24(29):4660-4671.