S4BuyseTestconfint {BuyseTest}  R Documentation 
Extract Confidence Interval from GPC
Description
Extract confidence intervals for summary statistics (net benefit, win ratio, ...) estimated by GPC.
Usage
## S4 method for signature 'S4BuyseTest'
confint(
object,
endpoint = NULL,
statistic = NULL,
strata = FALSE,
cumulative = TRUE,
null = NULL,
conf.level = NULL,
alternative = NULL,
method.ci.resampling = NULL,
order.Hprojection = NULL,
transformation = NULL,
cluster = NULL,
sep = "."
)
Arguments
object 
an R object of class 
endpoint 
[character] for which endpoint(s) the confidence intervals should be output?
If 
statistic 
[character] the statistic summarizing the pairwise comparison:

strata 
[character] the strata relative to which the statistic should be output.
Can also be 
cumulative 
[logical] should the summary statistic be cumulated over endpoints? Otherwise display the contribution of each endpoint. 
null 
[numeric] right hand side of the null hypothesis (used for the computation of the pvalue). 
conf.level 
[numeric] confidence level for the confidence intervals.
Default value read from 
alternative 
[character] the type of alternative hypothesis: 
method.ci.resampling 
[character] the method used to compute the confidence intervals and pvalues when using bootstrap or permutation ( 
order.Hprojection 
[integer, 12] order of the Hdecomposition used to compute the variance. 
transformation 
[logical] should the CI be computed on the inverse hyperbolic tangent scale / log scale for the net benefit / win ratio and backtransformed.
Otherwise they are computed without any transformation.
Default value read from 
cluster 
[numeric vector] Group of observations for which the iid assumption holds . 
sep 
[character] character string used to separate the endpoint and the strata when naming the statistics. 
Details
statistic: when considering a single endpoint and denoting
Y
the endpoint in the treatment group,
X
the endpoint in the control group,
and \tau
the threshold of clinical relevance,
the net benefit is P[Y \ge X + \tau]  P[X \ge Y + \tau]
,
the win ratio is \frac{P[Y \ge X + \tau]}{P[X \ge Y + \tau]}
,
the proportion in favor of treatment is P[Y \ge X + \tau]
,
the proportion in favor of control is P[X \ge Y + \tau]
.
method.ci.resampling: when using bootstrap/permutation, pvalues and confidence intervals are computing as follow:

percentile
(bootstrap): compute the confidence interval using the quantiles of the bootstrap estimates. Compute the pvalue by finding the confidence level at which a bound of the confidence interval equals the null hypothesis. 
percentile
(permutation): apply the selected transformation to the estimate and permutation estimates. Compute the confidence interval by (i) shfiting the estimate by the quantiles of the centered permutation estimates and (ii) backtransforming . Compute the pvalue as the relative frequency at which the estimate are less extreme than the permutation estimates. 
gaussian
(bootstrap and permutation): apply the selected transformation to the estimate and bootstrap/permutation estimates. Estimate the variance of the estimator using the empirical variance of the transformed boostrap/permutation estimates. Compute confidence intervals and pvalues under the normality assumption and backtransform the confidence intervals. 
student
(bootstrap): apply the selected transformation to the estimate, its standard error, the bootstrap estimates, and their standard error. Compute the studentized bootstrap estimates by dividing the centered bootstrap estimates by their standard error. Compute the confidence interval based on the standard error of the estimate and the quantiles of the studentized bootstrap estimates, and backtransform. Compute the pvalue by finding the confidence level at which a bound of the confidence interval equals the null hypothesis. 
student
(permutation): apply the selected transformation to the estimate, its standard error, the permutation estimates, and their standard error. Compute the studentized permutation estimates by dividing the centered permutation estimates by their standard error. Compute the confidence interval based on the standard error of the estimate and the quantiles of the studentized permutation estimates, and backtransform. Compute the pvalue as the relative frequency at which the studentized estimate are less extreme than the permutation studentized estimates.
WARNING: when using a permutation test, the uncertainty associated with the estimator is computed under the null hypothesis.
Thus the confidence interval may not be valid if the null hypothesis is false.
Value
A matrix containing a column for the estimated statistic (over all strata), the lower bound and upper bound of the confidence intervals, and the associated pvalues. When using resampling methods:
an attribute
n.resampling
specified how many samples have been used to compute the confidence intervals and the pvalues.an attribute
method.ci.resampling
method used to compute the confidence intervals and pvalues.
Author(s)
Brice Ozenne
References
On the GPC procedure: Marc Buyse (2010). Generalized pairwise comparisons of prioritized endpoints in the twosample problem. Statistics in Medicine 29:32453257
On the win ratio: D. Wang, S. Pocock (2016). A win ratio approach to comparing continuous nonnormal outcomes in clinical trials. Pharmaceutical Statistics 15:238245
On the MannWhitney parameter: Fay, Michael P. et al (2018). Causal estimands and confidence intervals asscoaited with WilcoxonMannWhitney tests in randomized experiments. Statistics in Medicine 37:29232937
See Also
BuyseTest
for performing a generalized pairwise comparison.
S4BuyseTestsummary
for a more detailed presentation of the S4BuyseTest
object.