Performs multiple contrast test

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.

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

Author

Bjoern Bornkamp

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)
#> Multiple Contrast Test
#> 
#> Contrasts:
#>     emax linear logistic linInt
#> 0 -0.894 -0.616   -0.894 -0.521
#> 1  0.207 -0.338    0.228 -0.573
#> 2  0.226  0.002    0.227  0.373
#> 3  0.225  0.315    0.217  0.357
#> 4  0.236  0.638    0.222  0.365
#> 
#> Contrast Correlation:
#>           emax linear logistic linInt
#> emax     1.000  0.715    1.000  0.617
#> linear   0.715  1.000    0.698  0.863
#> logistic 1.000  0.698    1.000  0.598
#> linInt   0.617  0.863    0.598  1.000
#> 
#> Multiple Contrast Test:
#>          t-Stat   adj-p
#> emax      3.178 0.00187
#> logistic  3.164 0.00210
#> linear    2.640 0.01035
#> linInt    2.247 0.02764

## 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)
#> Multiple Contrast Test
#> 
#> Contrasts:
#>    emax linear logistic linInt
#> 1 0.462 -0.429    0.511 -0.672
#> 2 0.505  0.002    0.507  0.437
#> 3 0.504  0.400    0.485  0.418
#> 4 0.527  0.810    0.497  0.428
#> 
#> Contrast Correlation:
#>           emax linear logistic linInt
#> emax     1.000  0.715    1.000  0.617
#> linear   0.715  1.000    0.698  0.863
#> logistic 1.000  0.698    1.000  0.598
#> linInt   0.617  0.863    0.598  1.000
#> 
#> Multiple Contrast Test:
#>          t-Stat   adj-p
#> emax      3.178 0.00187
#> logistic  3.164 0.00203
#> linear    2.640 0.00988
#> linInt    2.247 0.02681

## 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)
#> Multiple Contrast Test
#> 
#> Contrasts:
#>      linInt1 linInt2 linInt3 linInt4
#> 0     -0.894  -0.548  -0.365  -0.224
#> 0.05   0.224  -0.548  -0.365  -0.224
#> 0.2    0.224   0.365  -0.365  -0.224
#> 0.6    0.224   0.365   0.548  -0.224
#> 1      0.224   0.365   0.548   0.894
#> 
#> Contrast Correlation:
#>         linInt1 linInt2 linInt3 linInt4
#> linInt1   1.000   0.612   0.408   0.250
#> linInt2   0.612   1.000   0.667   0.408
#> linInt3   0.408   0.667   1.000   0.612
#> linInt4   0.250   0.408   0.612   1.000
#> 
#> Multiple Contrast Test:
#>         t-Stat   adj-p
#> linInt2  3.418 0.00179
#> linInt3  2.780 0.01098
#> linInt1  2.486 0.02423
#> linInt4  1.753 0.11949

## 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)
#> Multiple Contrast Test
#> 
#> Contrasts:
#>      D0.05 D0.2 D0.6 D1
#> 0       -1   -1   -1 -1
#> 0.05     1    0    0  0
#> 0.2      0    1    0  0
#> 0.6      0    0    1  0
#> 1        0    0    0  1
#> 
#> Contrast Correlation:
#>       D0.05 D0.2 D0.6  D1
#> D0.05   1.0  0.5  0.5 0.5
#> D0.2    0.5  1.0  0.5 0.5
#> D0.6    0.5  0.5  1.0 0.5
#> D1      0.5  0.5  0.5 1.0
#> 
#> Multiple Contrast Test:
#>       t-Stat  adj-p
#> D1     2.680 0.0151
#> D0.6   2.617 0.0178
#> D0.2   2.066 0.0654
#> D0.05  0.497 0.6034