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Correct and logical inference on efficacy in subgroups and their mixture for binary outcomes
Hui-Min Lin1, Haiyan Xu2, Ying Ding3
1Takeda Oncology, Cambridge, Massachusetts, USA.
Abstract:
Targeted therapies are becoming more common. In targeted therapy development, suppose its companion diagnostic test divides patients into a marker-positive subgroup and its complementary marker-negative subgroup. To find the right patient population for the therapy to target, inference on efficacy in the marker-positive and marker-negative subgroups as well as efficacy in the overall mixture population are all of interest. Depending on the type of clinical endpoints, inference on mixture population can be nontrivial and commonly used efficacy measures may not be suitable for a mixture population. Correlations among estimates of efficacy in the marker-positive, marker-negative, and overall mixture population play a crucial role in using an earlier phase study to inform on the design of a confirmatory study (e.g., determination of sample size). This article first shows that when the clinical endpoint is binary (such as respond or not), odds ratio is inappropriate as an efficacy measure in this setting, but relative response (RR) is appropriate. We show a safe way of calculating estimated correlations is to consider mixing subgroup response probabilities within each treatment arm first, and then derive the joint distribution of RR estimates. We also show, if one calculates RR within each subgroup first, how wrong the correlations can be if the Delta method derivation fails to take randomness of estimating the mixing coefficient into account.
Insights
Relative response (RR) is appropriate for assessing targeted therapy efficacy in binary outcomes, unlike odds ratios. Calculating correlations requires careful consideration of subgroup response probabilities to avoid errors in study design.
Area of Science:
- Clinical trial design
- Biostatistics
- Pharmacology
Background:
- Targeted therapies require precise patient stratification using companion diagnostics.
- Evaluating efficacy across marker-positive, marker-negative, and overall patient populations is crucial.
- Standard efficacy measures may be unsuitable for mixture populations with binary endpoints.
Purpose of the Study:
- To identify appropriate efficacy measures for targeted therapy trials with binary endpoints.
- To develop a reliable method for calculating correlations between subgroup and overall efficacy estimates.
- To inform the design of confirmatory studies using data from earlier phases.
Main Methods:
- Demonstrated the inappropriateness of odds ratios for binary endpoints in mixture populations.
- Proposed relative response (RR) as a suitable efficacy measure.
- Developed a method for calculating correlations by first mixing subgroup response probabilities within treatment arms.
Main Results:
- Relative response (RR) is an appropriate efficacy measure for binary endpoints in targeted therapy trials.
- A safe method for calculating estimated correlations involves mixing subgroup response probabilities.
- Ignoring the randomness of the mixing coefficient in correlation calculations can lead to significant errors.
Conclusions:
- Relative response is recommended for evaluating targeted therapy efficacy with binary outcomes.
- Accurate correlation estimation is vital for informing subsequent clinical trial designs.
- Methodological rigor in statistical analysis ensures reliable interpretation of targeted therapy effectiveness.
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