R: Define dose-response models

Mods {DoseFinding} | R Documentation

## 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) = theta0+theta1 f0(d,theta2)

where the parameter theta2 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 theta0,theta1 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 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 theta2 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.

### 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
    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)

[Package DoseFinding version 0.9-17 Index]