bmdIsoBoot: Benchmark dose estimation from isotonic regression

In DoseResponse/bmd: Benchmark dose estimation for dose-response data

Benchmark dose estimation from isotonic regression

Description

The function estimates BMD and BMDL using bootstrap based on isotonic regression.

Usage

bmd(formula, data, type, bmr, R=1000, boot="resample", backgType = c("modelBased", "absolute","hybridSD","hybridPercentile"), backg=NA, def = c("excess", "additional", "relative", "added", "hybridExc", "hybridAdd", "point")) 

Arguments

formula	an object of class "formula" expressing dose-response relationship. Details of model specification are given under 'Details'
data	data frame containing the variables in the model
type	character string specifying the type of data used in the model. "continuous" or "binomial" or "Poisson"
bmr	numeric value of benchmark response level for which to calculate the benchmark dose
R	number of bootstrap samples
boot	character string specifying type of bootstrap used. "resample" or "pseudorandom". Only option for count data is "resample"
backgType	character string specifying how the background level is specified. For binomial data the options are "modelBased" and "absolute". For continuous data the options are "modelBased", "absolute", "hybridSD" and "hybridPercentile" "modelBased" - the background level is obtained from the model as the level for dose 0: p0 = f(0) "absolute" - the background level is specified by the user through the backg argument: p0 = backg for binomial response and for the "relative" and "added" definition for continuous response. p0 = 1 - phi((back - f(0))/sigma) for "hybridExc" and "hybridAdd" definitions. "hybridSD" - the background risk is specified by the user in terms of number of SDs from the mean of the control group. p0 = 1 - phi(((backg*sigma + f(0)) - f(0))/sigma) = 1 - phi(backg), where phi is the normal distribution function and sigma is the SD for the control group. "hybridPercentile" - the background risk is specified by the user in terms of percentile from the control group distribution (assuming a normal distribution). p0 = 1 - phi((x0 - f(0))/sigma) = 1 - backg. where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group
backg	numeric value specifying the background level. Defaults to 0 for "absolute" background risk for binomial response (1 for decreasing dose-response models), 2 SD for "hybridSD" background and 0.9 for "hybridpercentile"
def	character string specifying the definition of the benchmark dose to use in the calculations. "excess", "additional" and "point" are for binomial response whereas "relative", "added", "hybridExc" (excess hybrid), "hybridAdd" (additional hybrid), and "point" are for continuous response. "relative", "extra", and "point" are for count response data. "excess" - BMR is defined as: BMR = (f(BMD) - p0)/(1 - p0). Works for binomial response. BMR should be between 0 and 1. "additional" - BMR is defined as: BMR = f(BMD) - p0. Works for binomial response. BMR should be between 0 and 1. "point" - The response level for which to find BMD is directly defined through the BMR level: BMR = f(BMD). Works for binomial, count and continuous response "relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. Works for count and continuous response "added" - BMR is defined as: BMR= f(BMD) + p0. Works for continuous response "hybridExc" - BMR is defined as: BMR = (1 - phi((x0 - f(BMD))/sigma) - p0)/ (1- p0), where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group. Works for continuous response "hybridAdd" - BMR is defined as: BMR = 1 - phi((x0 - f(BMD))/sigma) - p0, where x0 is the level for which the response is considered adverse, phi is the normal distribution function and sigma is the SD for the control group. Works for continuous response

Details

BMD and BMDL is defined as the median and the 5th percentile in the bootstrap distribution, respectively.

Formula should be specified as in the form number/total ~ dose for binomial data.

Bootstrapping with the argument boot = "resample" is done by sampling with replacement from the original data set. Bootstrapping with the argument boot = "pseudorandom" is done by sampling from norm(mean(Y_i),sd(Y_0)), assuming equal variance between groups, in case of continuous data. For binomial data, each bootstrap data set is sampled from binom(N_i,Y_i/N_i). In case of Y_i = 0 or Y_i = N_i shrinkage is used to avoid that the resampling always produces 0 or 1, respectively. In this case data is sampled from binom(N_i,(Y_i+1/3)/(N_i+1/3)).

All sampling is made within dose groups.

For details about the use of isotonic regression for BMD estimation see Piegorsch et al. (20014) and Lin et al. (2015).

Value

A matrix with two columns, one containing BMD and the other containing BMDL.

Author(s)

Signe M. Jensen

References

Piegorsch, W. W., Xiong, H., Bhattacharya, R. N., & Lin, L. (2014). Benchmark dose analysis via nonparametric regression modeling. Risk Analysis, 34(1), 135-151

Lin, L., Piegorsch, W. W. and Bhattacharya R. (2015). Nonparametric benchmark dose estimation with continuous dose-response data. Scandinavian Journal of Statistics, 42, 713-731

Examples

## Data on tumor incidence in rats after exposure to formaldehyde, from Piegorsch et al. (2014)
formaldehyde <- data.frame(conc = c(0.0, 0.7, 2.0, 6.0, 10.0, 15.0),
                          tumor.incidence = c(0, 0, 0, 3, 21, 150),
                          total = c(122, 27, 126, 113, 34, 182))
                          
# BMD and BMDL from isotonic regression using excess risk definition and a BMR=0.1
bmdIsoBoot(tumor.incidence/total ~ conc, 
      data=formaldehyde, 
      type="binomial",
      bmr=0.1,
      backgType = "modelBased",
      def = "excess")
      
      
## Data on root length in ryegrass after exposure to ferulic acid
require(drc)
data(ryegrass)

# As isotonic regression only wors for increasing dose-response relationship the association is turned
ryegrass1<-ryegrass
ryegrass1$rootl<-100-ryegrass1$rootl

# Estimating BMD from isotonic regression using relative risk definition and a BMR=0.05
bmdIsoBoot(rootl ~ conc, 
      data=ryegrass1, 
      type="continuous",
      bmr=0.05,
      backgType = "modelBased",
      def = "relative")

DoseResponse/bmd documentation built on March 29, 2025, 4:36 p.m.