Adjusted pvalues and onesided simultaneous confidence limits
AdjustPvalues
function
The AdjustPvalues
function can be used to get adjusted pvalues for commonly used multiple testing procedures based on univariate pvalues (Bonferroni, Holm, Hommel, Hochberg, fixedsequence procedures), commonly used parametric multiple testing procedures (singlestep and stepdown Dunnett procedures) and multistage gatepeeking procedure.
Description
Inputs
The AdjustPvalues
function requires the input of two prespecified objects defined in the following two arguments:

pval
defines the raw pvalues. proc
defines the multiple testing procedure. Several procedures are already implemented in the Mediana package (listed below, along with the required or optional parameters to specify in the par argument):BonferroniAdj
: Bonferroni procedure. Optional parameter:weight
.HolmAdj
: Holm procedure. Optional parameter:weight
.HochbergAdj
: Hochberg procedure. Optional parameter:weight
.HommelAdj
: Hommel procedure. Optional parameter:weight
.FixedSeqAdj
: Fixedsequence procedure.FallbackAdj
: Fallback procedure. Required parameters:weight
.DunnettAdj
: Singlestep Dunnett procedure. Required parameters:n
.StepDownDunnettAdj
: Stepdown Dunnett procedure. Required parameters:n
.ChainAdj
: Family of chain procedures. Required parameters:weight
andtransition
.NormalParamAdj
: Parametric multiple testing procedure derived from a multivariate normal distribution. Required parameter:corr
. Optional parameter:weight
.ParallelGatekeepingAdj
: Family of parallel gatekeeping procedures. Required parameters:family
,proc
,gamma
.MultipleSequenceGatekeepingAdj
: Family of multiplesequence gatekeeping procedures. Required parameters:family
,proc
,gamma
.MixtureGatekeepingAdj
: Family of mixturebased gatekeeping procedures. Required parameters:family
,proc
,gamma
,serial
,parallel
.
par
defines the parameters associated to the multiple testing procedure.
Outputs
The AdjustPvalues
function returns a vector of adjusted pvalues.
Example
The following example illustrates the use of the AdjustedPvalues
function to get adjusted pvalues for traditional nonparametric, semiparametric and parametric procedures, as well as more complex multiple testing procedures.
Traditional nonparametric and semiparametric procedures
For the illustration of adjustedment of raw pvalues with the traditional nonparametric and semiparametric procedures, we will consider the following three raw pvalues:
These pvalues will be adjusted with several multiple testing procedures as specified below:
In order to obtain the adjusted pvalues for all these procedures, the sapply
function can be used as follows. Note that as no weight
parameter is defined, the equally weighted procedures are used to adjust the pvalues. Finally, for the fixedsequence procedure (FixedSeqAdj
), the order of the testing sequence is based on the order of the pvalues in the vector.
The output is as follows:
In order to specify unequal weights for the three raw pvalues, the weight
parameter can be defined as follows. Note that this parameter has no effect on the adjustment with the fixedsequence procedure.
The output is as follows:
Traditional parametric procedures
Consider a clinical trials comparing three doses with a Placebo based on a normally distributed endpoints. Let H1, H2 and H3 be the three null hypotheses of no effect tested in the trial:

H1: No difference between Dose 1 and Placebo

H2: No difference between Dose 2 and Placebo

H3: No difference between Dose 3 and Placebo
The treatment effect estimates, corresponding to the mean doseplacebo difference are specified below, as well as the pooled standard deviation, the sample size, the standard errors and the Tstatistics associated with the three doseplacebo tests
Based on the Tstatistics, the raw pvalues can be easily obtained:
The adjusted pvalues based on the single step Dunnett and stepdown Dunnett procedures are obtained as follows.
The outputs are presented below.
Gatekeeping procedures
For illustration, we will consider a clinical trial with two families of null hypotheses. The first family contains the null hypotheses associated with the Endpoints 1 and 2, that are considered as primary endpoints, and the second family the null hypotheses associated with the Endpoints 3 and 4 (key secondary endpoints). The null hypotheses of the secondary family will be tested if and only if at least one null hypothesis from the first family is rejected. Let H1, H2, H3 and H4 be the four null hypotheses of no effect on Endpoint 1, 2, 3 and 4 respectively tested in the trial:

H1: No difference between Drug and Placebo on Endpoint 1 (Family 1)

H2: No difference between Drug and Placebo on Endpoint 2 (Family 1)

H3: No difference between Drug and Placebo on Endpoint 3 (Family 2)

H4: No difference between Drug and Placebo on Endpoint 4 (Family 2)
The raw pvalues are specified below:
The parameters of the parallel gatekeeping procedure are specified using the three arguments family
which specifies the hypotheses included in each family, proc
which specifies the component procedure associated with each family and gamma
which specifies the truncation parameter of each family.
The adjusted pvalues are obtained using the AdjustedPvalues
function as specified below:
AdjustCIs
function
The AdjustCIs
function can be used to get simultaneous confidence intervals for selected multiple testing procedures based on univariate pvalues (Bonferroni, Holm and fixedsequence procedures) and commonly used parametric multiple testing procedures (singlestep and stepdown Dunnett procedures).
Description
Inputs
The AdjustPvalues
function requires the input of two prespecified objects defined in the following two arguments:

est
defines the point estimates. proc
defines the multiple testing procedure. Several procedures are already implemented in the Mediana package (listed below, along with the required or optional parameters to specify in the par argument):BonferroniAdj
: Bonferroni procedure. Required parameters:n
,sd
andcovprob
. Optional parameter:weight
.HolmAdj
: Holm procedure. Required parameters:n
,sd
andcovprob
. Optional parameter:weight
.FixedSeqAdj
: Fixedsequence procedure. Required parameters:n
,sd
andcovprob
.DunnettAdj
: Singlestep Dunnett procedure. Required parameters:n
,sd
andcovprob
.StepDownDunnettAdj
: Stepdown Dunnett procedure. Required parameters:n
,sd
andcovprob
.
par
defines the parameters associated to the multiple testing procedure.
Outputs
The AdjustCIs
function returns a vector lower simultaneous confidence limits.
Example
Consider a clinical trials comparing three doses with a Placebo based on a normally distributed endpoints. Let H1, H2 and H3 be the three null hypotheses of no effect tested in the trial:

H1: No difference between Dose 1 and Placebo

H2: No difference between Dose 2 and Placebo

H3: No difference between Dose 3 and Placebo
The treatment effect estimates, corresponding to the mean doseplacebo difference are specified below, as well as the pooled standard deviation, the sample size.
The onesided simultaneous confidence limits for several multiple testing procedures are obtained using the AdjustCIs
function wrapped in a sapply
function.
The output obtained is presented below: