Case study 2
Summary
The clinical trial example used in this case study is the same as in Case study 1. For a detailed description of this clinical trial, see Case study 1. The difference resides in the decision strategy in a clinical trial with two potential regulatory claims, namely, the broad claim of treatment effectiveness in the overall population and restricted claim that pertains to a subpopulation of markerpositive patients.
The influence condition presented in Section 3.2.3 of the Clinical Trial Optimization Using R serves as a tool for facilitating the decisionmaking process in clinical trials with two patient populations. The condition states that the broad claim of treatment effectiveness in the overall patient population can be supported only if there is sufficient evidence of a beneficial treatment effect in the biomarkernegative subset and thus a significant treatment effect in the overall population is not directly driven by a strong effect in the biomarkerpositive subpopulation. If the influence condition is met, the trialâ€™s sponsor can rule out the possibility of incorrectly characterizing the efficacy profile in the overall population. When the influence condition is taken into account, it is no longer correct to use the simple rules for making the broad and restricted claims used in Case study 1:

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.
The modified decision rules are displayed in the following figure and can be summarized as follows:

Broad claim is made if (1) H0 is rejected and H+ is not rejected or (2) H0 and H+ are both rejected and the influence condition is met.

Restricted claim is made if at least one of the two conditions is met: (1) H+ is rejected but H0 is not rejected or (2) H0 and H+ are both rejected but the influence condition is not satisfied.
A straightforward frequentist formulation of the influence condition will be utilized in this case study. The influence condition is said to be met if the estimated effect size in the biomarkernegative subgroup is above a prespecified nonnegative quantity that serves as a threshold for defining a minimal clinically important effect in the biomarkernegative subpopulation. This parameter will be referred to as the influence threshold. This inequality shows that a sufficiently large treatment effect is present in the subset of patients with a biomarkernegative status.
Define a Data Model
As the data model is exactly the same as the one specified in Case study 1, see Case Study 1 for a detailed description of the data model.
Define an Analysis Model
The analysis model includes the same four statistical tests as in Case Study 1 and the weighted Hochberg procedure. The statistical tests are defined in exactly the same way as in Case study 1.
The computation of the effect size in the biomarkernegative subpopulation is
performed by including the Statistic
object with the EffectSizeContStat
method in the analysis model. This method computes the effect size for normally
distributed endpoints.
Define an Evaluation Model
A custom function needs to be defined in the evaluation model to implement
the criterion based on weighted power using the general approach used in Case Study 1. The only difference is that, in this case, the statistic.result
argument of the function will be used to specify the matrix of effect sizes in the
biomarkernegative subpopulation. This custom function computes weighted
power based on the modified broad and restricted claims with the influence
condition.
Custom functions can be written to compute the probabilities of broad and
restricted claims (subgroup.cs2.BroadClaimPower
and subgroup.cs2.RestrictedClaimPower
)
in a similar way.
The resulting evaluation model is presented below. For the purpose of illustration,
the influence threshold (i.e., influence_threshold
) is set to 0.186
in the par
argument of the functions for computing weighted power and probabilities
of broad and restricted claims.
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: