bmd: Benchmark dose estimation

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

Benchmark dose estimation

Description

Estimation of benchmark doses and benchmark dose lower limit from dose response model fits

Usage

bmd(object, bmr, backgType = c("modelBased", "absolute", "hybridSD", "hybridPercentile"), backg, controlSD,
def = c("excess", "additional", "relative", "extra", "added", "hybridExc", "hybridAdd", "point"), 
respTrans = c("none", "log", "sqrt"),
interval = c("delta","inv", "profile", "profileGrid"), sandwich.vcov=FALSE, display = TRUE,
level=0.95, profileGridSize = 20, profileProgressInfo = TRUE) 

Arguments

object	object of class drc
bmr	numeric value of benchmark response level for which to calculate the benchmark dose
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". For count data (Poisson, negbin1 or negbin2) the options are "modelBased" and "absolute". "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", "extra" and "added" definition for continuous or count response data. 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"
controlSD	numeric value specifying the standard deviation of the control group (used in the hybrid approach). If not specified the SD for the control group will be estimated as the square root of the residual variance (assuming variance homogeneity).
def	character string specifying the definition of the benchmark dose to use in the calculations. "excess", "additional" and "point" are for binomial response. "relative", "extra", "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 data "relative" - BMR is defined as: BMR = (f(BMD) - p0)/p0. Works for continuous and count response data "extra" - BMR is defined as: BMR = (f(BMD) - p0)/(f(Inf) - p0). Works for continuous and count response data "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
respTrans	if the dose-response model is fitted with a transformed response, specifying this option ensures that the background level for the BMD is computed on the original scale. Options include "none" (default), "log" (natural logarithm) and "sqrt"(square root).
interval	character string specifying the type of confidence interval to use: "delta" (default), "inv", "profile" or "profileGrid" "delta" - BMDL is based on the lower limit of a Wald confidence interval based on the delta method "inv" - BMDL is based on inverse regression, that is the dose associated with the upper limit of the pointwise confidence interval of the dose-response curve. Currently not available for a transformed response variable. "profile" - A profile confidence interval is computed by reparametrising the model. Only available for backgType in ("modelBased", "absolute"), def in ("excess", "additional","relative", "extra", "point") and dose-response models with model functions of types Log-Logistic, Log-Normal and Weibull 1 and 2. The limits of the confidence interval are searched for within a grid of size specified by the profileGridSize argument, however the values of the confidence interval are not limited to the values on the grid. "profileGrid" - A profile confidence interval is computed by creating a multi-dimensional grid of parameter values for the model. Then, a confidence region for the parameters in the model is estimated, and the BMD is estimated for all combinations of parameter values within the region. The interval for the BMD is then computed as the minimum and maximum values of BMD values within the region. Note that for models with several parameters (3-5), is might take a while to compute the confidence interval using this method. The number of grid points for each parameter can be specified by the profileGridSize argument.
sandwich.vcov	logical. If TRUE BMDL is based on confidence intervals based on robust standard errors from the sandwich covariance matrix
display	logical. If TRUE the results are displayed; otherwise they are not
level	numeric value specifying the levle of the confidence interval underlying BMDL. Default is 0.95
profileGridSize	integer specifying the number of grid points used for each parameter, when interval is either "profile" or "profileGridSearch". Defaults to 20 if not specified.
profileProgressInfo	logical. If TRUE, progress info is be printed while computed profile confidence intervals using the profileGrid method. Default is TRUE.

Details

The aim to provide an R package calculating the benchmark dose (BMD) and the lower limit of the corresponding 95% confidence interval (BMDL) for continuous and quantal dose-response data for a range of dose-response models based on the available definitions of the benchmark dose concepts.

Details on the implemented definitions and methods can be found in Crump (2002)

Value

A list of four elements: Results contain the estimated BMD and BMDL, bmrScaled is the response value corresponding to the BMD, interval gives the lower (BMDL) and upper (BMDU) end of the confidence interval of BMD, SE gives the standard error of BMD.

Author(s)

Signe M. Jensen and Jens Riis Baalkilde

References

Budtz-Jorgensen, E., Keiding, N., and Grandjean, P. (2001) Benchmark Dose Calculation from Epidemiological Data, Biometrics 57, 698–706.

Crump, K. (2002) Critical Issues in Benchmark Calculations from Continuous Data, Critical Reviews in Toxicology 32, 133–153.

Examples

## Fitting log-logistic two-parameter model to binomial data
deguelin.m1 <- drm(r/n~dose, weights=n, data=deguelin, fct=LL.2(), type="binomial")

## BMD for 5% additional risk with estimated background risk
bmd(deguelin.m1, 0.05, backgType = "modelBased", def = "additional")

## BMD for 10% additional risk with 2% background risk
bmd(deguelin.m1, 0.1, backg = 0.02 , backgType = "absolute", def = "additional")

## BMD for 5% excess risk and background 0
bmd(deguelin.m1, 0.05, backg = 0, backgType = "absolute", def = "excess")

## Dose resulting in 12% risk
bmd(deguelin.m1, 0.12, def = "point")

## Benchmark doses for a continuous response
ryegrass.m1 <- drm(rootl ~ conc, data = ryegrass, fct = LL.4())

## BMD as the dose resulting in a 5% change relative to the mean background level
bmd(ryegrass.m1, 0.05, backgType = "modelBased", def = "relative", display = TRUE)

## BMD using the hybrid method, background risk is 2 SD, hybrid definition using excess risk
bmd(ryegrass.m1, 0.05, backg = 2, backgType = "hybridSD", def = "hybridAdd", display = TRUE)

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