DoseFinding (version 0.9-9)

optContr: 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 non-centrality 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. (2013).

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 iterative algorithm for calculating the constrained contrasts was derived by E. Glimm).

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"), ...)

Arguments

models

An object of class Mods defining the dose-response 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

Value

• Object of class optContr. A list containing entries contMat and muMat (i.e. contrast, mean and correlation matrix).

item

• placAdj
• type
• x, superpose, xlab, ylab, plotType
• ...

samp

type = "constrained"

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., Glimm, E. and Bretz, F. (2013) Model-based dose finding under model uncertainty using general parametric models, Technical report, preprint available under http://arxiv.org/abs/1305.0889

See Also

MCTtest

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)

## now we would like the "contrasts" for placebo adjusted estimates
dosPlac <- doses[-1]
## matrix proportional to cov-matrix 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")