MCTtest {DoseFinding}

Performs multiple contrast test

Description

This function performs a multiple contrast test. The contrasts are either directly specified in ‘⁠contMat⁠’ or optimal contrasts derived from the ‘⁠models⁠’ argument. The directionality of the data (i.e. whether an increase or decrease in the response variable is beneficial is inferred from the ‘⁠models⁠’ object, see Mods).

For ‘⁠type = "normal"⁠’ an ANCOVA model based on a homoscedastic normality assumption (with additive covariates specified in ‘⁠addCovars⁠’) is fitted.

For ‘⁠type = "general"⁠’ it is assumed multivariate normally distributed estimates are specified in ‘⁠resp⁠’ with covariance given by ‘⁠S⁠’, and the contrast test statistic is calculated based on this assumption. Degrees of freedom specified in ‘⁠df⁠’.

Usage

MCTtest(dose, resp, data = NULL, models, S = NULL, type = c("normal", "general"),
        addCovars = ~1, placAdj = FALSE, alpha = 0.025, df = NULL,
        critV = NULL, pVal = TRUE,
        alternative = c("one.sided", "two.sided"), na.action = na.fail,
        mvtcontrol = mvtnorm.control(), contMat = NULL)

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"⁠’).

alpha

Significance level for the multiple contrast test

df

Specify the degrees of freedom to use in case ‘⁠type = "general"⁠’. If this argument is missing ‘⁠df = Inf⁠’ is used (which corresponds 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.

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.

contMat

Contrast matrix to apply to the ANCOVA dose-response estimates. The contrasts need to be in the columns of the matrix (i.e. the column sums need to be 0).

Details

Integrals over the multivariate t and multivariate normal distribution are calculated using the ‘⁠mvtnorm⁠’ package.

Value

An object of class MCTtest, a list containing the output.

Author(s)

Bjoern Bornkamp

References

Hothorn, T., Bretz, F., and Westfall, P. (2008). Simultaneous Inference in General Parametric Models, Biometrical Journal, 50, 346–363

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

See Also

powMCT, optContr

Examples

## example without covariates
data(biom)
## define shapes for which to calculate optimal contrasts
modlist <- Mods(emax = 0.05, linear = NULL, logistic = c(0.5, 0.1),
                linInt = c(0, 1, 1, 1), doses = c(0, 0.05, 0.2, 0.6, 1))
m1 <- MCTtest(dose, resp, biom, models=modlist)
## now calculate critical value (but not p-values)
m2 <- MCTtest(dose, resp, biom, models=modlist, critV = TRUE, pVal = FALSE)
## now hand over critical value
m3 <- MCTtest(dose, resp, biom, models=modlist, critV = 2.24)

## example with covariates
data(IBScovars)
modlist <- Mods(emax = 0.05, linear = NULL, logistic = c(0.5, 0.1),
                linInt = c(0, 1, 1, 1), doses = c(0, 1, 2, 3, 4))
MCTtest(dose, resp, IBScovars, models = modlist, addCovars = ~gender)

## example using general approach (fitted on placebo-adjusted scale)
ancMod <- lm(resp~factor(dose)+gender, data=IBScovars)
## extract estimates and information to feed into MCTtest
drEst <- coef(ancMod)[2:5]
vc <- vcov(ancMod)[2:5, 2:5]
doses <- 1:4
MCTtest(doses, drEst, S = vc, models = modlist, placAdj = TRUE,
        type = "general", df = Inf)

## example with general alternatives handed over
data(biom)
## calculate contrast matrix for the step-contrasts
## represent them as linInt models
models <- Mods(linInt=rbind(c(1,1,1,1),
                            c(0,1,1,1),
                            c(0,0,1,1),
                            c(0,0,0,1)),
                doses=c(0,0.05,0.2,0.6,1))
plot(models)
## now calculate optimal contrasts for these means
## use weights from actual sample sizes
weights <- as.numeric(table(biom$dose))
contMat <- optContr(models, w = weights)
## plot contrasts
plot(contMat)
## perform multiple contrast test
MCTtest(dose, resp, data=biom, contMat = contMat)

## example for using the Dunnett contrasts
## Dunnett contrasts
doses <- sort(unique(biom$dose))
contMat <- rbind(-1, diag(4))
rownames(contMat) <- doses
colnames(contMat) <- paste("D", doses[-1], sep="")
MCTtest(dose, resp, data=biom, contMat = contMat)