# Overview DoseFinding package

The DoseFinding package provides functions for the design and analysis of dose-finding experiments (for example pharmaceutical Phase II clinical trials). It provides functions for: multiple contrast tests (`MCTtest` for analysis and `powMCT`, `sampSizeMCT` for sample size calculation), fitting non-linear dose-response models (`fitMod` for ML estimation and `bFitMod` for Bayesian and bootstrap/bagging ML estimation), calculating optimal designs (`optDesign` or `calcCrit` for evaluation of given designs), both for normal and general response variable. In addition the package can be used to implement the MCP-Mod procedure, a combination of testing and dose-response modelling (`MCPMod`) (Bretz et al. (2005), Pinheiro et al. (2014)). A number of vignettes cover practical aspects on how MCP-Mod can be implemented using the DoseFinding package. For example a FAQ document for MCP-Mod, analysis approaches for normal and binary data, sample size and power calculations as well as handling data from more than one dosing regimen in certain scenarios.

Below a short overview of the main functions.

## Perform multiple contrast test

    library(DoseFinding)
    data(IBScovars)
    head(IBScovars)

      gender      resp dose
    1      1 1.5769231    1
    2      1 0.6833333    3
    3      1 0.2857143    0
    4      1 0.6307692    3
    5      1 0.1428571    2
    6      1 0.1571429    1

    ## perform (model based) multiple contrast test
    ## define candidate dose-response shapes
    models <- Mods(linear = NULL, emax = 0.2, quadratic = -0.17,
                   doses = c(0, 1, 2, 3, 4))
    ## plot models
    plot(models)

    ## perform multiple contrast test
    ## functions powMCT and sampSizeMCT provide tools for sample size
    ## calculation for multiple contrast tests
    test <- MCTtest(dose, resp, IBScovars, models=models,
                    addCovars = ~ gender)
    test

    Multiple Contrast Test

    Contrasts:
      linear   emax quadratic
    0 -0.616 -0.889    -0.815
    1 -0.338  0.135    -0.140
    2  0.002  0.226     0.294
    3  0.315  0.252     0.407
    4  0.638  0.276     0.254

    Contrast Correlation:
              linear  emax quadratic
    linear     1.000 0.768     0.843
    emax       0.768 1.000     0.948
    quadratic  0.843 0.948     1.000

    Multiple Contrast Test:
              t-Stat   adj-p
    emax       3.208 0.00160
    quadratic  3.083 0.00231
    linear     2.640 0.00844

## Fit non-linear dose-response models here illustrated with Emax model

    fitemax <- fitMod(dose, resp, data=IBScovars, model="emax",
                      bnds = c(0.01,5))
    ## display fitted dose-effect curve
    plot(fitemax, CI=TRUE, plotData="meansCI")

## Calculate optimal designs, here illustrated for target dose (TD) estimation

    ## optimal design for estimation of the smallest dose that gives an
    ## improvement of 0.2 over placebo, a model-averaged design criterion
    ## is used (over the models defined in Mods)
    doses <- c(0, 10, 25, 50, 100, 150)
    fmodels <- Mods(linear = NULL, emax = 25, exponential = 85,
                    logistic = c(50, 10.8811),
                    doses = doses, placEff=0, maxEff=0.4)
    plot(fmodels, plotTD = TRUE, Delta = 0.2)

    weights <- rep(1/4, 4)
    desTD <- optDesign(fmodels, weights, Delta=0.2, designCrit="TD")
    desTD

    Calculated TD - optimal design:
          0      10      25      50     100     150
    0.34960 0.09252 0.00366 0.26760 0.13342 0.15319

    plot(desTD, fmodels)

## References

Bretz, F., Pinheiro, J. C., and Branson, M. (2005), “Combining multiple comparisons and modeling techniques in dose-response studies,” Biometrics, Wiley Online Library, 61, 738–748. https://doi.org/10.1111/j.1541-0420.2005.00344.x.

Pinheiro, J., Bornkamp, B., Glimm, E., and Bretz, F. (2014), “Model-based dose finding under model uncertainty using general parametric models,” Statistics in Medicine, 33, 1646–1661. https://doi.org/10.1002/sim.6052.