Mods: Define dose-response models

In DoseFinding: Planning and Analyzing Dose Finding Experiments

Define dose-response models

Description

The Mods functions allows to define a set of dose-response models. The function is used as input object for a number of other different functions.

Usage

Mods(
  ...,
  doses,
  placEff = 0,
  maxEff,
  direction = c("increasing", "decreasing"),
  addArgs = NULL,
  fullMod = FALSE
)

getResp(fmodels, doses)

plotMods(
  ModsObj,
  nPoints = 200,
  superpose = FALSE,
  xlab = "Dose",
  ylab = "Model means",
  modNams = NULL,
  trafo = function(x) x
)

## S3 method for class 'Mods'
plot(
  x,
  nPoints = 200,
  superpose = FALSE,
  xlab = "Dose",
  ylab = "Model means",
  modNams = NULL,
  plotTD = FALSE,
  Delta,
  ...
)

Arguments

...	In function Mods: Dose-response model names with parameter values specifying the guesstimates for the \theta_2 parameters. See drmodels for a complete list of dose-response models implemented. See below for an example specification. In function plot.Mods: Additional arguments to the ‘⁠xyplot⁠’ call.
doses	Dose levels to be used, this needs to include placebo.
placEff, maxEff	Specify used placebo effect and the maximum effect over placebo. Either a numeric vector of the same size as the number of candidate models or of length one. When these parameters are not specified ‘⁠placEff = 0⁠’ is assumed, for ‘⁠maxEff = 1⁠’ is assumed, if ‘⁠direction = "increasing"⁠’ and ‘⁠maxEff = -1⁠’ is assumed, for ‘⁠direction = "decreasing"⁠’.
direction	Character determining whether the beneficial direction is ‘⁠increasing⁠’ or ‘⁠decreasing⁠’ with increasing dose levels. This argument is ignored if ‘⁠maxEff⁠’ is specified.
addArgs	List containing two entries named "scal" and "off" for the "betaMod" and "linlog". When addArgs is NULL the following defaults are used ‘⁠list(scal = 1.2*max(doses), off = 0.01*max(doses), nodes = doses)⁠’.
fullMod	Logical determining, whether the model parameters specified in the Mods function (via the ... argument) should be interpreted as standardized or the full model parameters.
fmodels	An object of class Mods
ModsObj	For function ‘⁠plotMods⁠’ the ‘⁠ModsObj⁠’ should contain an object of class ‘⁠Mods⁠’.
nPoints	Number of points for plotting
superpose	Logical determining, whether model plots should be superposed
xlab, ylab	Label for y-axis and x-axis.
modNams	When ‘⁠modNams == NULL⁠’, the names for the panels are determined by the underlying model functions, otherwise the contents of ‘⁠modNams⁠’ are used.
trafo	For function ‘⁠plotMods⁠’ there is the option to plot the candidate model set on a transformed scale (e.g. probability scale if the candidate models are formulated on log-odds scale). The default for ‘⁠trafo⁠’ is the identity function.
x	Object of class Mods with type Mods
plotTD	‘⁠plotTD⁠’ is a logical determining, whether the TD should be plotted. ‘⁠Delta⁠’ is the target effect to estimate for the TD.
Delta	Delta: The target effect size use for the target dose (TD) (Delta should be > 0).

Details

The dose-response models used in this package (see drmodels for details) are of form

f(d) = \theta_0+\theta_1 f^0(d,\theta_2)

where the parameter \theta_2 is the only non-linear parameter and can be one- or two-dimensional, depending on the used model.

One needs to hand over the effect at placebo and the maximum effect in the dose range, from which \theta_0,\theta_1 are then back-calculated, the output object is of class ‘⁠"Mods"⁠’. This object can form the input for other functions to extract the mean response (‘⁠getResp⁠’) or target doses (TD and ED) corresponding to the models. It is also needed as input to the functions powMCT, optDesign

Some models, for example the beta model (‘⁠scal⁠’) and the linlog model (‘⁠off⁠’) have parameters that are not estimated from the data, they need to be specified via the ‘⁠addArgs⁠’ argument.

The default plot method for ‘⁠Mods⁠’ objects is based on a plot using the ‘⁠lattice⁠’ package for backward compatibility. The function ‘⁠plotMods⁠’ function implements a plot using the ‘⁠ggplot2⁠’ package.

NOTE: If a decreasing effect is beneficial for the considered response variable it needs to specified here, either by using ‘⁠direction = "decreasing"⁠’ or by specifying a negative "maxEff" argument.

Value

Returns an object of class ‘⁠"Mods"⁠’. The object contains the specified model parameter values and the derived linear parameters (based on ‘⁠"placEff"⁠’ and ‘⁠"maxEff"⁠’) in a list.

Author(s)

Bjoern Bornkamp

References

Pinheiro, J. C., Bornkamp, B., and Bretz, F. (2006). Design and analysis of dose finding studies combining multiple comparisons and modeling procedures, Journal of Biopharmaceutical Statistics, 16, 639–656

See Also

Mods, drmodels, optDesign, powMCT

Examples

## Example on how to specify candidate models

## Suppose one would like to use the following models with the specified
## guesstimates for theta2, in a situation where the doses to be used are
## 0, 0.05, 0.2, 0.6, 1

## Model            guesstimate(s) for theta2 parameter(s) (name)
## linear           -
## linear in log    -
## Emax             0.05 (ED50)
## Emax             0.3 (ED50)
## exponential      0.7 (delta)
## quadratic       -0.85 (delta)
## logistic         0.4  0.09 (ED50, delta)
## logistic         0.3  0.1 (ED50, delta)
## betaMod          0.3  1.3 (delta1, delta2)
## sigmoid Emax     0.5  2 (ED50, h)
## linInt           0.5 0.75 1 1 (perc of max-effect at doses)
## linInt           0.5 1 0.7 0.5 (perc of max-effect at doses)

## for the linInt model one specifies the effect over placebo for
## each active dose.
## The fixed "scal" parameter of the betaMod is set to 1.2
## The fixed "off"  parameter of the linlog is set to 0.1
## These (standardized) candidate models can be specified as follows

models <- Mods(linear = NULL, linlog = NULL, emax = c(0.05, 0.3),
               exponential = 0.7, quadratic = -0.85,
               logistic = rbind(c(0.4, 0.09), c(0.3, 0.1)),
               betaMod = c(0.3, 1.3), sigEmax = c(0.5, 2),
               linInt = rbind(c(0.5, 0.75, 1, 1), c(0.5, 1, 0.7, 0.5)),
               doses = c(0, 0.05, 0.2, 0.6, 1),
               addArgs = list(scal=1.2, off=0.1))
## "models" now contains the candidate model set, as placEff, maxEff and
## direction were not specified a placebo effect of 0 and an effect of 1
## is assumed

## display of specified candidate set using default plot (based on lattice)
plot(models)
## display using ggplot2
plotMods(models)

## example for creating a candidate set with decreasing response
doses <- c(0, 10, 25, 50, 100, 150)
fmodels <- Mods(linear = NULL, emax = 25,
                   logistic = c(50, 10.88111), exponential = 85,
                   betaMod = rbind(c(0.33, 2.31), c(1.39, 1.39)),
                   linInt = rbind(c(0, 1, 1, 1, 1),
                                  c(0, 0, 1, 1, 0.8)),
                   doses=doses, placEff = 0.5, maxEff = -0.4,
                   addArgs=list(scal=200))
plot(fmodels)
plotMods(fmodels)
## some customizations (different model names, symbols, line-width)
plot(fmodels, lwd = 3, pch = 3, cex=1.2, col="red",
     modNams = paste("mod", 1:8, sep="-"))

## for a full-model object one can calculate the responses
## in a matrix
getResp(fmodels, doses=c(0, 20, 100, 150))

## calculate doses giving an improvement of 0.3 over placebo
TD(fmodels, Delta=0.3, direction = "decreasing")
## discrete version
TD(fmodels, Delta=0.3, TDtype = "discrete", doses=doses, direction = "decreasing")
## doses giving 50% of the maximum effect
ED(fmodels, p=0.5)
ED(fmodels, p=0.5, EDtype = "discrete", doses=doses)

plot(fmodels, plotTD = TRUE, Delta = 0.3)

## example for specifying all model parameters (fullMod=TRUE)
fmods <- Mods(emax = c(0, 1, 0.1), linear = cbind(c(-0.4,0), c(0.2,0.1)),
              sigEmax = c(0, 1.1, 0.5, 3),
              doses = 0:4, fullMod = TRUE)
getResp(fmods, doses=seq(0,4,length=11))
## calculate doses giving an improvement of 0.3 over placebo
TD(fmods, Delta=0.3)
## discrete version
TD(fmods, Delta=0.3, TDtype = "discrete", doses=0:4)
## doses giving 50% of the maximum effect
ED(fmods, p=0.5)
ED(fmods, p=0.5, EDtype = "discrete", doses=0:4)
plot(fmods)

DoseFinding documentation built on Sept. 11, 2024, 9:04 p.m.