![\"\"](\"https:\/\/cytel.agencyukdev.com\/wp-content\/uploads\/2024\/06\/image-png-Jun-11-2024-09-46-55-5720-AM.webp\")
<\/p>\nSubpopulations are often of key interest in clinical trials. For example, an investigational drug may be targeted to have efficacy on a particular subpopulation of patients who test positive for a specific biomarker. That drug may also be thought to have some degree of benefit, though lesser, on the opposite subpopulation\u2014those who test negative for that biomarker.<\/p>\n
This leads to consideration of at least three key hypotheses for the trial:<\/p>\n
1. \u00a0 \u00a0efficacy in the biomarker-positive subpopulation;
\n2. \u00a0 \u00a0efficacy in the full population; and
\n3. \u00a0 \u00a0efficacy in the biomarker-negative population.<\/p>\n
<\/p>\n
These three efficacy hypotheses can be tested sequentially at the type-1 error level set for the trial, or the type-1 error can be divided among them. This leads to many potential approaches to set up the key hypotheses for the trial.<\/p>\n
<\/p>\n
![\"\"](\"https:\/\/cytel.agencyukdev.com\/wp-content\/uploads\/2024\/06\/image-png-Jun-11-2024-09-46-55-5720-AM-1.webp\")
<\/p>\n
<\/p>\n
Schematic 1:\u00a0<\/strong>Sequential testing: first test full population, and only if statistically significant, then test biomarker positive subpopulation, and only if statistically significant, then test biomarker negative subpopulation.<\/p>\n <\/p>\n Schematic 2:\u00a0<\/strong>Sequential testing: first test biomarker positive subpopulation, and only if statistically significant, then test full population, and only if statistically significant, then test biomarker negative subpopulation.<\/p>\n <\/p>\n <\/p>\n Schematic 3:\u00a0<\/strong>Divide alpha=0.05 as follows and pass to other tests as indicated. Test Biomarker positive subpopulation and full population at alpha=0.01, and test biomarker negative subpopulation at alpha=0.005. \u00a0For each statistically significant test of those\u00a0three, pass half that alpha to the other\u00a0two\u00a0tests if they were not first statistically significant at their respective original alpha level, then combine the original alpha and passed alpha\u00a0and\u00a0retest.<\/p>\n<\/h3>\n
Sequential testing first in\u00a0biomarker-positive subpopulations<\/strong><\/h3>\n
![\"\"](\"https:\/\/cytel.agencyukdev.com\/wp-content\/uploads\/2024\/06\/image-png-Jun-11-2024-09-48-40-1972-AM.webp\")
<\/p>\nTesting with divided alpha<\/h3>\n
![\"\"](\"https:\/\/cytel.agencyukdev.com\/wp-content\/uploads\/2024\/06\/image-png-Jun-11-2024-09-53-00-4719-AM.webp\")
<\/p>\n