DoseFinding (version 0.9-16)

Mods: 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.

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 by the code, they need to be specified via the addArgs argument.

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.

Usage

Mods(..., doses, placEff = 0, maxEff,
     direction = c("increasing", "decreasing"), addArgs=NULL,
     fullMod = FALSE)
getResp(fmodels, doses)
# S3 method for 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.

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.

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.

fmodels

An object of class Mods

Delta

Delta: The target effect size use for the target dose (TD) (Delta should be > 0).

x

Object of class Mods with type 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.

plotTD

plotTD is a logical determining, whether the TD should be plotted. Delta is the target effect to estimate for the TD.

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.

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

# NOT RUN {
## 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
plot(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)
## 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)
# }