MCPMod - Multiple Comparisons and Modeling

Tests for a dose-response effect using a model-based multiple contrast test (see MCTtest), selects one (or several) model(s) from the significant shapes, fits them using fitMod. For details on the method see Bretz et al. (2005).

Usage

MCPMod(dose, resp, data, models, S = NULL, type = c("normal", "general"),
       addCovars = ~1, placAdj = FALSE, selModel = c("AIC", "maxT", "aveAIC"),
       alpha = 0.025, df = NULL, critV = NULL, doseType = c("TD", "ED"),
       Delta, p, pVal = TRUE, alternative = c("one.sided", "two.sided"),
       na.action = na.fail, mvtcontrol = mvtnorm.control(),
       bnds, control = NULL)

# S3 method for class 'MCPMod'
predict(object,
        predType = c("full-model", "ls-means", "effect-curve"),
        newdata = NULL, doseSeq = NULL, se.fit = FALSE, ...)



# S3 method for class 'MCPMod'
plot(x, CI = FALSE, level = 0.95,
       plotData = c("means", "meansCI", "raw", "none"),
       plotGrid = TRUE, colMn = 1, colFit = 1, ...)

Arguments

dose, resp

Either vectors of equal length specifying dose and response values, or names of variables in the data frame specified in data.

data

Data frame containing the variables referenced in dose and resp if data is not specified it is assumed that dose and resp are variables referenced from data (and no vectors)

models

An object of class "Mods", see Mods for details

S

The covariance matrix of resp when type = "general", see Description.

type

Determines whether inference is based on an ANCOVA model under a homoscedastic normality assumption (when type = "normal"), or estimates at the doses and their covariance matrix and degrees of freedom are specified directly in resp, S and df. See also fitMod and Pinheiro et al. (2014).

addCovars

Formula specifying additive linear covariates (for type = "normal")

placAdj

Logical, if true, it is assumed that placebo-adjusted estimates are specified in resp (only possible for type = "general").

selModel

Optional character vector specifying the model selection criterion for dose estimation. Possible values are

AIC: Selects model with smallest AIC (this is the default)
maxT: Selects the model corresponding to the largest t-statistic.
aveAIC: Uses a weighted average of the models corresponding to the significant contrasts. The model weights are chosen by the formula: \(w_i = \exp(-0.5AIC_i)/\sum_i(\exp(-0.5AIC_i))\) See Buckland et al. (1997) for details.

For type = "general" the "gAIC" is used.

alpha

Significance level for the multiple contrast test

df

Specify the degrees of freedom to use in case type = "general", for the call to MCTtest and fitMod. Infinite degrees of (df=Inf) correspond to the multivariate normal distribution. For type = "normal" the degrees of freedom deduced from the AN(C)OVA fit are used and this argument is ignored.

critV

Supply a pre-calculated critical value. If this argument is NULL, no critical value will be calculated and the test decision is based on the p-values. If critV = TRUE the critical value will be calculated.

doseType, Delta, p

doseType determines the dose to estimate, ED or TD (see also Mods), and Delta and p need to be specified depending on whether TD or ED is to be estimated. See TD and ED for details.

pVal

Logical determining, whether p-values should be calculated.

alternative

Character determining the alternative for the multiple contrast trend test.

na.action

A function which indicates what should happen when the data contain NAs.

mvtcontrol

A list specifying additional control parameters for the qmvt and pmvt calls in the code, see also mvtnorm.control for details.

bnds

Bounds for non-linear parameters. This needs to be a list with list entries corresponding to the selected bounds. The names of the list entries need to correspond to the model names. The defBnds function provides the default selection.

control

Control list for the optimization.
A list with entries: "nlminbcontrol", "optimizetol" and "gridSize".

The entry nlminbcontrol needs to be a list and is passed directly to control argument in the nlminb function, that is used internally for models with 2 nonlinear parameters (e.g. sigmoid Emax or beta model).

The entry optimizetol is passed directly to the tol argument of the optimize function, which is used for models with 1 nonlinear parameters (e.g. Emax or exponential model).

The entry gridSize needs to be a list with entries dim1 and dim2 giving the size of the grid for the gridsearch in 1d or 2d models.

object, x

MCPMod object

predType, newdata, doseSeq, se.fit, ...

predType determines whether predictions are returned for the full model (including potential covariates), the ls-means (SAS type) or the effect curve (difference to placebo).

newdata gives the covariates to use in producing the predictions (for predType = "full-model"), if missing the covariates used for fitting are used.

doseSeq dose-sequence on where to produce predictions (for predType = "effect-curve" and predType = "ls-means"). If missing the doses used for fitting are used.

se.fit: logical determining, whether the standard error should be calculated.

...: Additional arguments, for plot.MCPMod these are passed to plot.DRMod.

CI, level, plotData, plotGrid, colMn, colFit

Arguments for plot method: CI determines whether confidence intervals should be plotted. level determines the level of the confidence intervals. plotData determines how the data are plotted: Either as means or as means with CI, raw data or none. In case of type = "normal" and covariates the ls-means are displayed, when type = "general" the option "raw" is not available. colMn and colFit determine the colors of fitted model and the raw means.

Value

An object of class MCPMod, which contains the fitted MCTtest object as well as the DRMod objects and additional information (model selection criteria, dose estimates, selected models).

References

Bretz, F., Pinheiro, J. C., and Branson, M. (2005), Combining multiple comparisons and modeling techniques in dose-response studies, Biometrics, 61, 738–748

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

Pinheiro, J. C., Bretz, F., and Branson, M. (2006). Analysis of dose-response studies - modeling approaches, in N. Ting (ed.). Dose Finding in Drug Development, Springer, New York, pp. 146–171

Pinheiro, J. C., 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

Schorning, K., Bornkamp, B., Bretz, F., & Dette, H. (2016). Model selection versus model averaging in dose finding studies. Statistics in Medicine, 35, 4021–4040

Xun, X. and Bretz, F. (2017) The MCP-Mod methodology: Practical Considerations and The DoseFinding R package, in O'Quigley, J., Iasonos, A. and Bornkamp, B. (eds) Handbook of methods for designing, monitoring, and analyzing dose-finding trials, CRC press

Buckland, S. T., Burnham, K. P. and Augustin, N. H. (1997). Model selection an integral part of inference, Biometrics, 53, 603–618

Seber, G.A.F. and Wild, C.J. (2003). Nonlinear Regression, Wiley.

Author

Bjoern Bornkamp

Examples

data(biom)
## first define candidate model set (only need "standardized" models)
models <- Mods(linear = NULL, emax=c(0.05,0.2), linInt=c(1, 1, 1, 1),
               doses=c(0,0.05,0.2,0.6,1))
plot(models)

## perform MCPMod procedure
MM <- MCPMod(dose, resp, biom, models, Delta=0.5)
## a number of things can be done with an MCPMod object
MM # print method provides basic information
#> MCPMod
#> 
#> Multiple Contrast Test:
#>        t-Stat   adj-p
#> emax2   3.464 < 0.001
#> emax1   3.339 0.00150
#> linear  2.972 0.00402
#> linInt  2.486 0.01632
#> 
#> Estimated Dose Response Models:
#> linear model
#>    e0 delta 
#> 0.492 0.559 
#> 
#> emax model
#>    e0  eMax  ed50 
#> 0.322 0.746 0.142 
#> 
#> linInt model
#>    d0 d0.05  d0.2  d0.6    d1 
#> 0.345 0.457 0.810 0.934 0.949 
#> 
#> Selected model (AIC): emax
#> 
#> Estimated TD, Delta=0.5
#> linear   emax linInt 
#> 0.8951 0.2886 0.3115 
summary(MM) # more information
#> MCPMod
#> 
#> ***************************************
#> MCP part 
#> ***************************************
#> Multiple Contrast Test
#> 
#> Contrasts:
#>      linear  emax1  emax2 linInt
#> 0    -0.437 -0.799 -0.643 -0.894
#> 0.05 -0.378 -0.170 -0.361  0.224
#> 0.2  -0.201  0.207  0.061  0.224
#> 0.6   0.271  0.362  0.413  0.224
#> 1     0.743  0.399  0.530  0.224
#> 
#> Contrast Correlation:
#>        linear emax1 emax2 linInt
#> linear  1.000 0.766 0.912  0.488
#> emax1   0.766 1.000 0.949  0.893
#> emax2   0.912 0.949 1.000  0.719
#> linInt  0.488 0.893 0.719  1.000
#> 
#> Multiple Contrast Test:
#>        t-Stat   adj-p
#> emax2   3.464 < 0.001
#> emax1   3.339 0.00150
#> linear  2.972 0.00402
#> linInt  2.486 0.01632
#> 
#> ***************************************
#> Mod part 
#> ***************************************
#> ** Fitted model 1 
#> Dose Response Model
#> 
#> Model: linear 
#> Fit-type: normal 
#> 
#> Residuals:
#>    Min     1Q Median     3Q    Max 
#> -2.097 -0.445  0.136  0.512  2.164 
#> 
#> Coefficients with approx. stand. error:
#>       Estimate Std. Error
#> e0       0.492     0.0998
#> delta    0.559     0.1885
#> 
#> Residual standard error: 0.714 
#> Degrees of freedom: 98 
#> 
#> ** Fitted model 2 
#> Dose Response Model
#> 
#> Model: emax 
#> Fit-type: normal 
#> 
#> Residuals:
#>    Min     1Q Median     3Q    Max 
#> -2.000 -0.442  0.130  0.429  2.088 
#> 
#> Coefficients with approx. stand. error:
#>      Estimate Std. Error
#> e0      0.322      0.152
#> eMax    0.746      0.236
#> ed50    0.142      0.180
#> 
#> Residual standard error: 0.706 
#> Degrees of freedom: 97 
#> 
#> ** Fitted model 3 
#> Dose Response Model
#> 
#> Model: linInt 
#> Fit-type: normal 
#> 
#> Residuals:
#>    Min     1Q Median     3Q    Max 
#> -1.990 -0.397  0.079  0.456  2.062 
#> 
#> Coefficients with approx. stand. error:
#>       Estimate Std. Error
#> d0       0.345      0.159
#> d0.05    0.457      0.159
#> d0.2     0.810      0.159
#> d0.6     0.934      0.159
#> d1       0.949      0.159
#> 
#> Residual standard error: 0.712 
#> Degrees of freedom: 95 
#> 
#> ***************************************
#> Model selection criteria (AIC):
#> ***************************************
#>   linear     emax   linInt 
#> 220.4986 219.1383 222.8249 
#> 
#> Selected model: emax 
#> 
#> ***************************************
#> Estimated TD, Delta=0.5
#> ***************************************
#> linear   emax linInt 
#> 0.8951 0.2886 0.3115 
## predict all significant dose-response models
predict(MM, se.fit=TRUE, doseSeq=c(0,0.2,0.4, 0.9, 1),
        predType="ls-means")
#> $linear
#> $linear$fit
#> [1] 0.4923408 0.6040619 0.7157829 0.9950856 1.0509461
#> 
#> $linear$se.fit
#> [1] 0.09984282 0.07829697 0.07166124 0.12282570 0.13859522
#> 
#> 
#> $emax
#> $emax$fit
#> [1] 0.3216107 0.7578039 0.8721944 0.9660905 0.9750049
#> 
#> $emax$se.fit
#> [1] 0.15211417 0.11528764 0.09035778 0.11855885 0.12504802
#> 
#> 
#> $linInt
#> $linInt$fit
#> [1] 0.3449054 0.8103158 0.8723763 0.9451428 0.9487114
#> 
#> $linInt$se.fit
#> [1] 0.1592893 0.1592893 0.1126345 0.1259292 0.1592893
#> 
#> 
## display all model functions 
plot(MM, plotData="meansCI", CI=TRUE)


## now perform model-averaging
MM2 <- MCPMod(dose, resp, biom, models, Delta=0.5, selModel = "aveAIC")
sq <- seq(0,1,length=11)
pred <- predict(MM, doseSeq=sq, predType="ls-means")
modWeights <- MM2$selMod
## model averaged predictions
pred <- do.call("cbind", pred)%*%modWeights
## model averaged dose-estimate
TDEst <- MM2$doseEst%*%modWeights

## now an example using a general fit and fitting based on placebo
## adjusted first-stage estimates
data(IBScovars)
## ANCOVA fit model including covariates
anovaMod <- lm(resp~factor(dose)+gender, data=IBScovars)
drFit <- coef(anovaMod)[2:5] # placebo adjusted estimates at doses
vCov <- vcov(anovaMod)[2:5,2:5]
dose <- sort(unique(IBScovars$dose))[-1] # no estimate for placebo
## candidate models
models <- Mods(emax = c(0.5, 1), betaMod=c(1,1), doses=c(0,4))
plot(models)

## hand over placebo-adjusted estimates drFit to MCPMod
MM3 <- MCPMod(dose, drFit, S=vCov, models = models, type = "general",
              placAdj = TRUE, Delta=0.2)
plot(MM3, plotData="meansCI")


## The first example, but with critical value handed over
## this is useful, e.g. in simulation studies
MM4 <- MCPMod(dose, resp, biom, models, Delta=0.5, critV = 2.31)