Case study 1
Summary
This case study deals with a Phase III clinical trial in patients with mild or moderate asthma (it is based on a clinical trial example from Millen et al., 2014, Section 2.2). The trial is intended to support a tailoring strategy. In particular, the treatment effect of a single dose of a new treatment will be compared to that of placebo in the overall population of patients as well as a prespecified subpopulation of patients with a markerpositive status at baseline (for compactness, the overall population is denoted by OP, markerpositive subpopulation is denoted by M+ and markernegative subpopulation is denoted by M−).
Markerpositive patients are more likely to receive benefit from the experimental treatment. The overall objective of the clinical trial accounts for the fact that the treatment’s effect may, in fact, be limited to the markerpositive subpopulation. The trial will be declared successful if the treatment’s beneficial effect is established in the overall population of patients or, alternatively, the effect is established only in the subpopulation. The primary endpoint in the clinical trial is defined as an increase from baseline in the forced expiratory volume in one second (FEV1). This endpoint is normally distributed and improvement is associated with a larger change in FEV1.
Define a Data Model
A data model specifies a scheme for generating individual patients’ data in the set of predefined samples, i.e., nonoverlapping homogeneous groups of patients, in a clinical trial. In this case study, the overall population of patients is naturally split into four samples that are defined as follows:

Sample 1 (
Placebo BioNeg
) includes biomarkernegative patients in the placebo arm. 
Sample 2 (
Placebo BioPos
) includes biomarkerpositive patients in the placebo arm. 
Sample 3 (
Treatment BioNeg
) includes biomarkernegative patients in the treatment arm. 
Sample 4 (
Treatment BioPos
) includes biomarkerpositive patients in the treatment arm.
Using this definition of samples, the trial’s sponsor can model the fact that the treatment’s effect is most pronounced in patients with a biomarkerpositive status.
For each sample in the data model, the parameters of the outcome distribution (i.e., mean and common standard deviation) defined in the following Table are listed in a single set of outcome parameters.
Sample  Mean  Standard deviation 

Placebo BioNeg  0.12  0.45 
Placebo BioPos  0.12  0.45 
Treatment BioNeg  0.21  0.45 
Treatment BioPos  0.345  0.45 
The outcome parameters are specified using the following R code.
Consider, for the sake of illustration, a data model with a single set of samplespecific patient counts that corresponds to the total sample size of 310 patients. The number of patients in each individual samples is computed based on the expected prevalence of biomarkerpositive patients (40% of patients in the population of interest are expected to have a biomarkerpositive status).
Finally, the data model can be set up by initializing the DataModel
object
and adding each component to it. The outcome distribution is defined using
the OutcomeDist
object with the NormalDist
distribution. The data model
is shown below.
Define an Analysis Model
The analysis model, shown below, defines the two individual
tests that will be carried out to compare the treatment to placebo in the
overall population (OP test
) and in the subset of biomarkerpositive patients
(BioPos test
). Each comparison will be carried out based on a onesided
twosample ttest (TTest
method defined in each Test
object). A key feature
of the analysis strategy in this case study is that the samples defined in the
data model are different from the samples used in the analysis of the primary
endpoint. As shown in above, four samples were included in the data
model. However, from the analysis perspective, the sponsor is interested in
examining the treatment effect within two samples, namely, the placebo and
treatment samples within the overall population and within the biomarkerpositive
subpopulation. As shown below, to perform a comparison in the
overall population (OP test
), the ttest needs to applied to the following
analysis samples:

Placebo arm is defined by merging the samples
Placebo BioNeg
andPlacebo BioPos
. 
Treatment arm is defined by merging the samples
Treatment BioNeg
andTreatment BioPos
.
Further, the treatment effect test in the subpopulation of biomarkerpositive patients (BioPos test) is carried out based on these analysis samples:

Placebo arm is defined directly based on the sample
Placebo BioPos
. 
Treatment armis defined directly based on the sample
Treatment BioPos
.
In addition, the weighted Bonferroni and Hochberg procedures are requested
using the MultAdjProc
objects. For the purpose of illustration, the
initial weight of the overall population test has been set to 0.8 and thus the
weight of the subpopulation test equals 0.2.
Define an Evaluation Model
The evaluation model specifies clinically relevant criteria for assessing the
performance of the selected test and multiplicity adjustment defined in the
analysis model. As a starting point, it is of interest to compute the probability
of achieving a significant outcome in each individual test, e.g., the
probability of a significant difference between the treatment and placebo in
the overall population and subpopulation of biomarkerpositive patents. This
is accomplished by requesting a Criterion
object with the MarginalPower
method. The method is applied to the two tests defined in the analysis model,
i.e., to OP test
and BioPos test
.
Further, considering more advanced evaluation criteria, the first criterion is based on disjunctive power which corresponds to
the probability of demonstrating a statistically significant treatment effect in
at least one population. This criterion is defined using the DisjunctivePower
method.
The second evaluation criterion corresponds to weighted power based on combining the probabilities of broad and restricted claims, defined as shown below:

Broad claim of treatment effectiveness in the overall population is made if the null hypothesis assciated with the overall population (H0) is rejected.

Restricted claim of treatment effectiveness in the subpopulation is made if the null hypothesis assciated with the biomarkerpositive subpopulation (H+) is rejected but H0 is not rejected.
This criterion is not included in the Mediana package but can be implemented as a custom
criterion. The user can define this criterion by creating a custom function as
described below. The function’s first argument (test.result
) is a matrix of
pvalues corresponding to the test ID defined in the tests
argument of the
Criterion
object and produced by the Test
objects defined in the analysis
model. Similarly, the second argument (statistic.result
) is a matrix of
results corresponding to the statistic ID defined in the statistics
argument
of the Criterion
objects produced by the Statistic
objects defined in the
analysis model. In this example, the criteria will only use the test.result
argument, which will contain the pvalues produced by the tests associated
with the two treatmentplacebo comparisons in each population. The last
argument (parameter
) contains the optional parameter(s) defined by the user
in the Criterion
object. In this example, the par
argument contains the
overall alpha level (alpha
) as well as the importance values assigned to the
broad and restricted claims (v1
and v2
). The subgroup.cs1.WeightedPower
function, defined below, computes
the probability of broad and restricted claims and then a weighted sum
of the two probabilities is calculated. The order in which the tests are included
in the evaluation model is important as the first one must correspond to the
test in the overall population.
A similar approach can be applied to create a custom function for computing the marginal probability of a restricted claim. This function is defined below.
The evaluation model based on the two builtin evaluation criteria (marginal power and disjunctive power) as well as two custom evaluation criteria (weighted power and marginal probability of a restricted claim) is defined in the following evaluation model.
Perform Clinical Scenario Evaluation
Using the data, analysis and evaluation models, simulationbased Clinical Scenario Evaluation is performed by calling the CSE
function:
Download
Click on the icons below to download the R code used in this case study and report that summarizes the results of Clinical Scenario Evaluation: