hillConcCorrect {braidrm}R Documentation

Hill-Based Concentration Correction

Description

Estimates actual underlying concentrations leading to a given set of response measurements based on the assumption that actual concentrations are log-normally distributed around target concentrations, response errors are normally distributed, and the actual underlying relationship between concentration and response is represented by the given Hill dose-response model.

Usage

hillConcCorrect(conc, act, parv, sigr = 1)

Arguments

conc

a vector of expected or target concentrations, around which actual concentrations are assumed to be log-normally distributed

act

a vector of response values

parv

a four-parameter vector specifying a Hill model as described in evalHillEqn which is assumed to be the actual relationship between concentration and response

sigr

the estimated ratio of the noises in response- and log (base10) concentration-space

Details

Suppose that c^\hat{c} is a given target concentration, and cc is the actual concentration in given well, plate, or condition. Suppose also that yy is the actual response that would result from the concentration in the given Hill dose-response model, and y^\hat{y} is the measured response value. This function assumes that

y^N(y,σ)\hat{y} \sim N(y,\sigma)

log10cN(log10c^,σr)\log_{10} c \sim N(\log_{10}\hat{c},\frac{\sigma}{r})

for some σ\sigma, where NN is a normal distribution, and rr is the ratio specified by the parameter sigr. Based on these assumptions, the function uses Bayes' rule to calculate the maximum likelihood estimate of cc for every given value of c^\hat{c} and y^\hat{y}.

Value

A vector of concentrations representing the maximum likelihood estimates of the actual concentrations which produced the given responses.

Author(s)

Nathaniel R. Twarog

See Also

evalHillEqn, runBRAIDanalysis

Examples

data(es8olatmz)
drv <- es8olatmz$compound2=="DMSO"
hfit <- findBestHill(act~conc1,es8olatmz[drv,],defaults=c(0,-2.7))
drvpos <- drv & es8olatmz$conc1>0
cconc <- hillConcCorrect(es8olatmz$conc1[drvpos],es8olatmz$act[drvpos],
			coef(hfit$allfits[[hfit$bestModIdx]]),sigr=1)

[Package braidrm version 0.71 Index]