Dunnett's Test for Comparing Several Treatments With a Common Control

Performs Dunnett's parametric post hoc test for comparing multiple treatment groups with a control group while controlling the familywise error rate.

Usage

dunnettTest(x, ...)

# S3 method for class 'formula'
dunnettTest(formula, data, subset, na.action, ...)

# Default S3 method
dunnettTest(x, g, control = NULL, conf.level = 0.95, ...)

Arguments

x: a numeric vector of data values or a list of numeric vectors.
...: further arguments passed to or from methods.
formula: a formula of the form lhs ~ rhs, where lhs contains the data values and rhs defines the corresponding groups.
data: an optional matrix or data frame (or a similar object; see model.frame()) containing the variables in formula. By default, the variables are taken from environment(formula).
subset: an optional vector specifying a subset of observations to be used.
na.action: a function indicating how missing values should be handled. Defaults to getOption("na.action").
g: a vector or factor identifying the group of each element of x; ignored if x is a list.
control: a character vector identifying one or more control levels. Each specified control is compared separately with all remaining groups. Defaults to the first group.
conf.level: the confidence level for the simultaneous confidence intervals. Defaults to 0.95.

Value

An object of class "PostHocTest": a list containing one matrix for each control level. Each matrix has columns diff for the observed mean difference (treatment minus control), lci and uci for the simultaneous confidence limits, and pval for the multiplicity-adjusted p-value.

Print and plot methods are available for class "PostHocTest". The plot method supplies its own axis labels and title and therefore does not accept xlab, ylab, or main.

Details

If x is a list, its elements are taken as the samples to be compared and must therefore be numeric vectors. In this case, g is ignored. The test can be performed with dunnettTest(x) or, if the samples are stored in separate objects, with dunnettTest(list(x, ...)).

Otherwise, x must be a numeric vector and g a vector or factor of the same length that identifies the group of each observation.

The adjusted p-values and simultaneous confidence intervals are two-sided. The confidence limits use the equicoordinate quantile of \(\max_j |T_j|\) (tail = "both.tails" in mvtnorm::qmvt()), in accordance with the adjusted p-values \(1 - P(\max_j |T_j| \le |t_i|)\). Multivariate t probabilities are evaluated by randomized quasi-Monte Carlo integration using mvtnorm. A fixed seed ensures that repeated calls produce identical results up to the numerical integration accuracy.

References

Dunnett, C. W. (1955). A multiple comparison procedure for comparing several treatments with a control. Journal of the American Statistical Association, 50, 1096–1121.

Examples

## Hollander and Wolfe (1973, p. 116)
## Mucociliary efficiency from the rate of removal of dust in normal
##  subjects, subjects with obstructive airway disease, and subjects
##  with asbestosis.
x <- c(2.9, 3.0, 2.5, 2.6, 3.2) # normal subjects
y <- c(3.8, 2.7, 4.0, 2.4)      # with obstructive airway disease
z <- c(2.8, 3.4, 3.7, 2.2, 2.0) # with asbestosis

dunnettTest(list(x, y, z))
#> 
#>   Dunnett's test for comparing several treatments with a control : Dunnett
#>     95% family-wise confidence level
#> 
#> $`1`
#>       diff        lci       uci  pval signif
#> 2-1  0.385 -0.6898153 1.4598153 0.583       
#> 3-1 -0.020 -1.0333456 0.9933456 0.998       
#> 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 

## Equivalent vector-and-group interface
x <- c(x, y, z)
g <- factor(rep(1:3, c(5, 4, 5)),
            labels = c("Normal subjects",
                       "Subjects with obstructive airway disease",
                       "Subjects with asbestosis"))

dunnettTest(x, g)
#> 
#>   Dunnett's test for comparing several treatments with a control : Dunnett
#>     95% family-wise confidence level
#> 
#> $`Normal subjects`
#>                                                            diff        lci
#> Subjects with obstructive airway disease-Normal subjects  0.385 -0.6898153
#> Subjects with asbestosis-Normal subjects                 -0.020 -1.0333456
#>                                                                uci  pval signif
#> Subjects with obstructive airway disease-Normal subjects 1.4598153 0.583       
#> Subjects with asbestosis-Normal subjects                 0.9933456 0.998       
#> 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 

## Formula interface
boxplot(Ozone ~ factor(Month), data = airquality)

dunnettTest(Ozone ~ factor(Month), data = airquality)
#> 
#>   Dunnett's test for comparing several treatments with a control : Dunnett
#>     95% family-wise confidence level
#> 
#> $`5`
#>          diff       lci      uci    pval signif
#> 6-5  5.829060 -22.43036 34.08848   0.965       
#> 7-5 35.500000  15.23412 55.76588 < 0.001    ***
#> 8-5 36.346154  16.08027 56.61204 < 0.001    ***
#> 9-5  7.832891 -11.90191 27.56770   0.735       
#> 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 

## Single control level with a 90% simultaneous confidence level
dunnettTest(Ozone ~ factor(Month), data = airquality,
            control = "8", conf.level = 0.9)
#> 
#>   Dunnett's test for comparing several treatments with a control : Dunnett
#>     90% family-wise confidence level
#> 
#> $`8`
#>            diff       lci        uci    pval signif
#> 5-8 -36.3461538 -54.26325 -18.429061 < 0.001    ***
#> 6-8 -30.5170940 -55.50129  -5.532901   0.030    *  
#> 7-8  -0.8461538 -18.76325  17.070939   1.000       
#> 9-8 -28.5132626 -45.96083 -11.065695   0.002    ** 
#> 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 

## Multiple control levels
dunnettTest(Ozone ~ factor(Month), data = airquality,
            control = c("5", "8"))
#> 
#>   Dunnett's test for comparing several treatments with a control : Dunnett
#>     95% family-wise confidence level
#> 
#> $`5`
#>          diff       lci      uci    pval signif
#> 6-5  5.829060 -22.43036 34.08848   0.965       
#> 7-5 35.500000  15.23412 55.76588 < 0.001    ***
#> 8-5 36.346154  16.08027 56.61204 < 0.001    ***
#> 9-5  7.832891 -11.90191 27.56770   0.735       
#> 
#> $`8`
#>            diff       lci        uci    pval signif
#> 5-8 -36.3461538 -56.61204 -16.080272 < 0.001    ***
#> 6-8 -30.5170940 -58.77652  -2.257672   0.030    *  
#> 7-8  -0.8461538 -21.11204  19.419728   1.000       
#> 9-8 -28.5132626 -48.24807  -8.778457   0.002    ** 
#> 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>