hillConcCorrect {braidrm}

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

\hat{y} \sim N(y,\sigma)

\log_{10} c \sim N(\log_{10}\hat{c},\frac{\sigma}{r})

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