Case study 3
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 marker negative 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
To set up a data model for this clinical trial, it is natural to define samples (mutually exclusive groups of patients) as follows:

Sample 1: Markernegative patients in the placebo arm.

Sample 2: Markerpositive patients in the placebo arm.

Sample 3: Markernegative patients in the treatment arm.

Sample 4: Markerpositive 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 markerpositive status.
The treatment effect assumptions in the four samples are summarized in the next table (expiratory volume in FEV1 is measured in liters). As shown in the table, the mean change in FEV1 is constant across the markernegative and markerpositive subpopulations in the placebo arm (Samples 1 and 2). A positive treatment effect is expected in both subpopulations in the treatment arm but markerpositive patients will experience most of the beneficial effect (Sample 4).
Sample  Mean  Standard deviation 

Placebo M  0.12  0.45 
Placebo M+  0.12  0.45 
Treatment M  0.24  0.45 
Treatment M+  0.30  0.45 
The following data model incorporates the assumptions listed above by defining a single set of outcome parameters. The data model includes three sample size sets (total sample size is set to 330, 340 and 350 patients). The sizes of the individual samples are computed based on historic information (40% of patients in the population of interest are expected to have a markerpositive status). In order to define specific sample size for each sample, they will be specified within each Sample
object.
Define an Analysis Model
The analysis model in this clinical trial example is generally similar to that used in Case study 2 but there is an important difference which is described below.
As in Case study 2, the primary endpoint follows a normal distribution and thus the treatment effect will be assessed using the twosample ttest.
Since two null hypotheses are tested in this trial (null hypotheses of no effect in the overall population of patients and subpopulation of markerpositive patients), a multiplicity adjustment needs to be applied. The Hochberg procedure with equally weighted null hypotheses will be used for this purpose.
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 the Table, four samples are included in the data model. However, from the analysis perspective, the sponsor in interested in examining the treatment effect in two samples, namely, the overall population and markerpositive subpopulation. As shown below, to perform a comparison in the overall population, the ttest is applied to the following analysis samples:

Placebo arm: Samples 1 and 2 (
Placebo M
andPlacebo M+
) are merged. 
Treatment arm: Samples 3 and 4 (
Treatment M
andTreatment M+
) are merged.
Further, the treatment effect test in the subpopulation of markerpositive patients is carried out based on these analysis samples:

Placebo arm: Sample 2 (
Placebo M+
). 
Treatment arm: Sample 4 (
Treatment M+
).
These analysis samples are specified in the analysis model below. The samples defined in the data model are merged using c()
or list()
function, e.g., c("Placebo M", "Placebo M+")
defines the placebo arm and c("Treatment M", "Treatment M+")
defines the experimental treatment arm in the overall population test.
Define an Evaluation Model
It is reasonable to consider the following success criteria in this case study:

Marginal power: Probability of a significant outcome in each patient population.

Disjunctive power: Probability of a significant treatment effect in the overall population (OP) or markerpositive subpopulation (M+). This metric defines the overall probability of success in this clinical trial.

Conjunctive power: Probability of simultaneously achieving significance in the overall population and markerpositive subpopulation. This criterion will be useful if the trial’s sponsor is interested in pursuing an enhanced efficacy claim (Millen et al., 2012).
The following evaluation model applies the three criteria to the two tests listed in the analysis model:
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: