optContr {DoseFinding}  R Documentation 
Calculate optimal contrasts
Description
This function calculates a contrast vectors that are optimal for detecting certain alternatives. The contrast is optimal in the sense of maximizing the noncentrality parameter of the underlying contrast test statistic:
\frac{c'\mu}{\sqrt{c'Sc}}
Here \mu
is the mean vector under the alternative and S
the
covariance matrix associated with the estimate of \mu
.
The optimal contrast is given by
c^{opt} \propto S^{1}\left(\mu  \frac{\mu^{\prime}S^{1}
1}{1^\prime S^{1} 1}\right),
see Pinheiro et al. (2014).
Note that the directionality (i.e. whether in "increase" in the
response variable is beneficial or a "decrease", is inferred from the
specified ‘models’ object, see Mods
for details).
Constrained contrasts (type = "constrained") add the additional constraint in the optimization that the sign of the contrast coefficient for control and active treatments need to be different. The quadratic programming algorithm from the quadprog package is used to calculate the contrasts.
Usage
optContr(models, doses, w, S, placAdj = FALSE,
type = c("unconstrained", "constrained"))
## S3 method for class 'optContr'
plot(x, superpose = TRUE, xlab = "Dose",
ylab = NULL, plotType = c("contrasts", "means"), ...)
plotContr(optContrObj, xlab = "Dose",
ylab = "Contrast coefficients")
Arguments
models 
An object of class ‘Mods’ defining the doseresponse shapes for which to calculate optimal contrasts. 
doses 
Optional argument. If this argument is missing the doses attribute in the ‘Mods’ object specified in ‘models’ is used. 
w , S 
Arguments determining the matrix S used in the formula for the optimal
contrasts. Exactly one of ‘w’ and ‘S’ has
to be specified. Note that ‘w’ and ‘S’ only have to be
specified up to proportionality

placAdj 
Logical determining, whether the contrasts should be applied to placeboadjusted estimates. If yes the returned coefficients are no longer contrasts (i.e. do not sum to 0). However, the result of multiplying of this "contrast" matrix with the placebo adjusted estimates, will give the same results as multiplying the original contrast matrix to the unadjusted estimates. 
type 
For ‘type = "constrained"’ the contrast coefficients of the zero dose group are constrained to be different from the coefficients of the active treatment groups. So that a weighted sum of the active treatments is compared against the zero dose group. For an increasing trend the coefficient of the zero dose group is negative and all other coefficients have to be positive (for a decreasing trend the other way round). 
x , superpose , xlab , ylab , plotType 
Arguments for the plot method for optContr objects. plotType determines, whether the contrasts or the underlying (standardized) mean matrix should be plotted. 
optContrObj 
For function ‘plotContr’ the ‘optContrObj’ should contain an object of class ‘optContr’. 
... 
Additional arguments for plot method 
Value
Object of class ‘optContr’. A list containing entries contMat and muMat (i.e. contrast, mean and correlation matrix).
Author(s)
Bjoern Bornkamp
References
Bretz, F., Pinheiro, J. C., and Branson, M. (2005), Combining multiple comparisons and modeling techniques in doseresponse studies, Biometrics, 61, 738–748
Pinheiro, J. C., Bornkamp, B., Glimm, E. and Bretz, F. (2014) Modelbased dose finding under model uncertainty using general parametric models, Statistics in Medicine, 33, 1646–1661
See Also
Examples
doses < c(0,10,25,50,100,150)
models < Mods(linear = NULL, emax = 25,
logistic = c(50, 10.88111), exponential= 85,
betaMod=rbind(c(0.33,2.31), c(1.39,1.39)),
doses = doses, addArgs = list(scal = 200))
contMat < optContr(models, w = rep(50,6))
plot(contMat)
plotContr(contMat) # display contrasts using ggplot2
## now we would like the "contrasts" for placebo adjusted estimates
dosPlac < doses[1]
## matrix proportional to covmatrix of plac. adj. estimates for balanced data
S < diag(5)+matrix(1, 5,5)
## note that we explicitly hand over the doses here
contMat0 < optContr(models, doses=dosPlac, S = S, placAdj = TRUE)
## > contMat0 is no longer a contrast matrix (columns do not sum to 0)
colSums(contMat0$contMat)
## calculate contrast matrix for unadjusted estimates from this matrix
## (should be same as above)
aux < rbind(colSums(contMat0$contMat), contMat0$contMat)
t(t(aux)/sqrt(colSums(aux^2))) ## compare to contMat$contMat
## now calculate constrained contrasts
optContr(models, w = rep(50,6), type = "constrained")
optContr(models, doses=dosPlac, S = S, placAdj = TRUE,
type = "constrained")