Estimate Bootstrapped Confidence Intervals on Hill Model Parameters

Description

By bootsttrapping a large number of vectors, this function estimates confidence intervals on the paramters of the given Hill model. If the model already has confidence intervals estimated, they will be replaced with a warning

Usage

calcHillBootstrap(hfit, ciLevs = c(0.025, 0.975), numBoot = NULL)

Arguments

Value

An object of class hillrm, containing all the values found in any hillrm object (see fitHillModel()) as well as the following three values:

• ciLevs: the values used to set the bounds of the confidence intervals

• ciCoefs: a width-4 array of all bootstrapped Hill model coefficents sampled by the function

• ciMat: a 2-by-4 array of values representing the estimated confidence intervals on the four Hill model parameters

Examples

conc <- c(0,2^(-6:3),Inf)
hpar <- c(1,3,0,75)
response <- evalHillModel(conc, hpar) + rnorm(length(conc),sd=7.5)

hfit <- fitHillModel(conc,response,c(1,2,3,4),start=c(0.5,1,0,100))
cihfit <- calcHillBootstrap(hfit)

Estimate an confidence interval on a Hill model property

Description

Given a function from Hill model parameters to one or more model properties, this function produces a confidence interval on that value or those values using the bootstrapped model coefficents produced by calcHillBootstrap(). This is useful for estimating confidence intervals on other values like IC50, or generating confidence intervals on fitted values for plots.

Usage

calcHillConfInt(hfit, parfunc, civals = NULL)

Arguments

Value

An n-by-3 array, where n is the length of the vector produced by parfunc. The first row is the lower bound of the confidence interval, the second row is the function evaluated at the best-fit Hill model, and the third row is the upper bound of the confidence interval.

Examples

conc <- c(0,2^(-6:3),Inf)
hpar <- c(1,3,0,75)
response <- evalHillModel(conc, hpar) + rnorm(length(conc),sd=7.5)

hfit <- fitHillModel(conc,response,c(1,2,3,4),start=c(0.5,1,0,100))
cihfit <- calcHillBootstrap(hfit)

ic50_ci <- calcHillConfInt(cihfit,function(h) invertHillModel(50,h))

Calculate the area under the curve for a Hill dose response model

Description

The area under the curve, or AUC, is a commonly used and robust metric for evaluating and comparing dose response models. The area is calculated in a log-concentration space, and so is dependent not only on the concentration bounds, but also on the base of the logarithm used. By default, this function follows the common convention of using base 10.

Usage

calculateHillAUC(hpar, range, baseline = 0, logbase = 10)

Arguments

Value

A single value specifying the area under the curve in the given range

Examples

auc <- calculateHillAUC(c(1,3,0,75), c(0.05,10))

# Area *over* the curve in survival studies
aoc <- -calculateHillAUC(c(0.1,2,1,0.1), c(0.01,1), baseline=1)

Estimate Akaike Information Criterion

Description

Estimate Akaike Information Criterion

Usage

estimateAIC(resid, npar)

Arguments

Value

The Akaike informtion criterion (AIC) value for the fit

Examples

conc <- c(0,2^(-6:3),Inf)
hpar <- c(1,3,0,75)
response <- evalHillModel(conc, hpar) + rnorm(length(conc),sd=7.5)

hfit4p <- fitHillModel(conc,response,c(1,2,3,4),start=c(0.5,1,0,100))
hfit3p <- fitHillModel(conc,response,c(1,2,4),start=c(0.5,1,0,100))

aic4p <- estimateAIC(residuals(hfit4p),4)
aic3p <- estimateAIC(residuals(hfit3p),3)

Estimate Bayesian Information Criterion

Description

Estimate Bayesian Information Criterion

Usage

estimateBIC(resid, npar)

Arguments

Value

The Bayesian informtion criterion (BIC) value for the fit

Examples

conc <- c(0,2^(-6:3),Inf)
hpar <- c(1,3,0,75)
response <- evalHillModel(conc, hpar) + rnorm(length(conc),sd=7.5)

hfit4p <- fitHillModel(conc,response,c(1,2,3,4),start=c(0.5,1,0,100))
hfit3p <- fitHillModel(conc,response,c(1,2,4),start=c(0.5,1,0,100))

aic4p <- estimateBIC(residuals(hfit4p),4)
aic3p <- estimateBIC(residuals(hfit3p),3)

Evaluate a Hill dose response model

Description

Evaluate a Hill dose response model

Usage

evalHillModel(conc, hpar)

Arguments

Value

A vector of response values the same length as conc

Examples

conc <- c(0,2^(-6:3),Inf)
hpar <- c(1,3,0,100)

response <- evalHillModel(conc, hpar)

Selects a best-fitting Hill model given defaults

Description

Using the function fitHillModel(), this function fits four Hill models with minimal and maximal effects either varying or fixed at the given default values; it then selects the best fitting model based on the Bayesian information criterio or Akaike information criterion, and returns a Hill fit object with information from all fits included.

Usage

findBestHillModel(
  formula,
  data,
  defaults,
  weights = NULL,
  start = NULL,
  direction = 0,
  lower = NULL,
  upper = NULL,
  useBIC = TRUE
)

Arguments

Value

An object of class hillrm. Contains all of the values found in any hillrm object (see fitHillModel()), as well as allfits, a named list of lists containing the coefficients and parvectors for each of the individual fits, as well as the Bayesian information criterion (bic) and Akaike informtion criterion (aic) values for each fit.

Examples

conc <- c(0,2^(-6:3),Inf)
hpar <- c(1,3,0,75)
response <- evalHillModel(conc, hpar) + rnorm(length(conc),sd=7.5)

hfit <- findBestHillModel(conc,response,defaults=c(0,100))

Fit a Hill dose response model to data

Description

This function uses the R stats function optim to fit a Hill dose response model to a given set of dose and response values. Four different model settings are allowed, in which the minimal and maximal effects are either fixed at a provided value or allowed to be fit to the data.

Usage

fitHillModel(
  formula,
  data,
  model,
  weights = NULL,
  start = NULL,
  direction = 0,
  lower = NULL,
  upper = NULL
)

Arguments

Value

An object of class hillrm, containing the following values:

• conc: the given vector of concentraitons

• act: the given vector of responses

• weights: the vector of measurement weights used in minimizing the sum of squared errors

• coefficients: the full four-parameter Hill parameter vector (accessible by the function coef())

• par: the vector of paramters that were actually fit

• fitted.values: the predicted responses of the best fit model (accessible by the functoin fitted())

• residuals: the difference between the actual responses and the predicted responses (accessible by the function residuals())

• model: the vector of values between 1 and 4 specifying the precise model that was fit

• mname: a character string naming the precise model that was fit. One of "m2p", "m3plc", "m3puc", or "m4p"

• start: a four-value parameter vector used as the starting value for the model fit

• direction: the direction constraint used in the fit

• pbounds: a two-by-four matrix of values specifying the lower and upper bounds used in the fit

Examples

conc <- c(0,2^(-6:3),Inf)
hpar <- c(1,3,0,75)
response <- evalHillModel(conc, hpar) + rnorm(length(conc),sd=7.5)
data <- data.frame(conc=conc,response=response,weight=c(0.5,rep(1,10),0.1))

hfit <- fitHillModel(conc,response,c(1,2,3,4),start=c(0.5,1,0,100))
hfit2 <- fitHillModel(response~conc,data,c(1,2,4),weight,start=c(0.5,1,0,100),
                      direction=0,lower=c(NA,NA,0,0))

Calculates the required doses of a Hill dose response model

Description

This funciton takes one or more desired response values and determines the doses that will produce the desired effects given a particular Hill dose response model. This is useful for estimating things like IC50.

Usage

invertHillModel(effect, hpar, invalidNA = FALSE)

Arguments

Value

A vector of concentrations the same length as effect.

Examples

invertHillModel(0.5, c(1,2,0,0.7))

invertHillModel(seq(0.1,0.9,by=0.1), c(0.1,4,0,0.65), invalidNA=TRUE)