Fitting dose-response models

A general model fitting function for analysis of various types of dose-response data.

Usage

drm(
  formula,
  curveid,
  pmodels,
  weights,
  data = NULL,
  subset,
  fct,
  type = c("continuous", "binomial", "Poisson", "negbin1", "negbin2", "event", "ssd"),
  bcVal = NULL,
  bcAdd = 0,
  start,
  na.action = na.omit,
  robust = "mean",
  logDose = NULL,
  control = drmc(),
  lowerl = NULL,
  upperl = NULL,
  separate = FALSE,
  pshifts = NULL,
  varcov = NULL
)

Arguments

formula: a symbolic description of the model to be fit. Either of the form response ~ dose or as a data frame with response values in first column and dose values in second column.
curveid: a numeric vector or factor containing the grouping of the data.
pmodels: a data frame with as many columns as there are parameters in the non-linear function. Or a list containing a formula for each parameter in the nonlinear function.
weights: a numeric vector containing weights. For continuous/quantitative responses, inverse weights are multiplied inside the squared errors (weights should have the same unit as the response). For binomial responses weights provide information about the total number of binary observations used to obtain the response.
data: an optional data frame containing the variables in the model.
subset: an optional vector specifying a subset of observations to be used in the fitting process.
fct: a list with three or more elements specifying the non-linear function, the accompanying self starter function, the names of the parameters in the non-linear function and, optionally, the first and second derivatives as well as information used for calculation of ED values. Use getMeanFunctions for a full list.
type: a character string specifying the distribution of the data. The default is "continuous", corresponding to a normal distribution. Other choices include "binomial", "Poisson", "negbin1", "negbin2", "event", and "ssd".
bcVal: a numeric value specifying the lambda parameter to be used in the Box-Cox transformation.
bcAdd: a numeric value specifying the constant to be added on both sides prior to Box-Cox transformation. The default is 0.
start: an optional numeric vector containing starting values for all mean parameters in the model. Overrules any self starter function.
na.action: a function for treating missing values (NAs). Default is na.omit.
robust: a character string specifying the rho function for robust estimation. Default is non-robust least squares estimation ("mean"). Available robust methods are: "median", "lms", "lts", "trimmed", "winsor", and "tukey".
logDose: a numeric value or NULL. If log dose values are provided the base of the logarithm should be specified (e.g., exp(1) for natural logarithm, 10 for base 10).
control: a list of arguments controlling constrained optimisation, maximum iterations, relative tolerance, and warnings. See drmc.
lowerl: a numeric vector of lower limits for all parameters in the model (the default corresponds to minus infinity for all parameters).
upperl: a numeric vector of upper limits for all parameters in the model (the default corresponds to plus infinity for all parameters).
separate: logical value indicating whether curves should be fit separately (independent of each other).
pshifts: a matrix of constants to be added to the matrix of parameters. Default is no shift for all parameters.
varcov: an optional user-defined known variance-covariance matrix for the responses. Default is the identity matrix (NULL), corresponding to independent response values with a common standard deviation estimated from the data.

Value

An object of (S3) class "drc".

Details

This function relies on optim for minimisation of the negative log likelihood function. For a continuous response this reduces to least squares estimation. Response values are assumed to be mutually independent unless varcov is specified. For robust estimation MAD (median absolute deviance) is used to estimate the residual variance. Setting lowerl and/or upperl automatically invokes constrained optimisation. Control arguments may be specified using drmc.

Author

Christian Ritz, Jens C. Streibig and Hannes Reinwald

Examples

## Fitting a four-parameter log-logistic model to the ryegrass data
model <- drm(rootl ~ conc, data = ryegrass, fct = LL.4())
summary(model)
#> 
#> Model fitted: Log-logistic (ED50 as parameter) (4 parms)
#> 
#> Parameter estimates:
#> 
#>               Estimate Std. Error t-value   p-value    
#> b:(Intercept)  2.98222    0.46506  6.4125 2.960e-06 ***
#> c:(Intercept)  0.48141    0.21219  2.2688   0.03451 *  
#> d:(Intercept)  7.79296    0.18857 41.3272 < 2.2e-16 ***
#> e:(Intercept)  3.05795    0.18573 16.4644 4.268e-13 ***
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error:
#> 
#>  0.5196256 (20 degrees of freedom)