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Table 6 HIGH clinical trial: Detection of treatmen-by-subset interaction when K=2

From: Enrichment Bayesian design for randomized clinical trials using categorical biomarkers and a binary outcome

  Interaction method \(\boldsymbol {\widehat {\theta }}\) global CI95% \(\boldsymbol {\widehat {\theta _{A}}}\) CI95% \(\boldsymbol {\widehat {\theta _{B}}}\) CI95% Decision nA nB Probability of interaction effect*
Age Partition Age≥65 Age<65     
1er interim analysis Millen   1.228[0.721-1.988] 0.913[0.548-1.412] Go with entire population 87 107 0.56
  Gail and Simon   1.228[0.721-1.988] 0.913[0.548-1.412] Go with entire population 87 107 0.02& 0.09
2nd interim analysis Millen   1.367[0.931-1.957] 0.868[0.586-1.241] Go with entire population 178 210 0.80
  Gail and Simon   1.367[0.931-1.957] 0.868[0.586-1.241] Go with entire population 178 210 0.02& 0.08
3th interim analysis Millen   1.184[0.879-1.568] 0.745[0.529-1.011] Go with entire population 265 320 0.85
  Gail and Simon   1.184[0.879-1.568] 0.745[0.529-1.011] Go with entire population 265 320 0.01& 0.00
Final analysis Millen 0.989[0.819-1.182] 1.245[0.956-1.597] 0.780[0.580-1.017] Go with entire population 360 416 0.9
  Gail and Simon 0.989[0.819-1.182] 1.245[0.956-1.597] 0.780[0.580-1.017] Go with entire population 360 416 0.01& 0.00
SOFA neurological Partition SOFA neuro≥1 SOFA neuro<1     
1er interim analysis Millen   0.799[0.391-1.349] 1.136[0.750-1.655] Go with entire population 27 167 0.66
  Gail and Simon   0.799[0.391-1.349] 1.136[0.750-1.655] Go with entire population 27 167 0.02& 0.02
2nd interim analysis Millen   0.633[0.341-1.026] 1.252[0.916-1.677] Enrichment in subset A 54 334 0.94
  Gail and Simon   0.633[0.341-1.026] 1.252[0.916-1.677] Enrichment in subset A 54 334 0.08& 0.00
3th interim analysis Millen   0.753[0.477-1.107] 1.252[0.916-1.679] Enrichment in subset A 77 334
  Gail and Simon   0.753[0.477-1.107] 1.252[0.916-1.679] Enrichment in subset A 77 334
Final analysis Millen 1.156[0.890-1.477] 0.858[0.350-1.688] 1.252[0.916-1.677] Enrichment in subset A 102 334
  Gail and Simon 1.156[0.890-1.477] 0.858[0.350-1.688] 1.252[0.916-1.677] Enrichment in subset A 102 334
PaO2/FiO2Partition PaO2/FiO2<100 PaO2/FiO2≥100     
1er interim analysis Millen   1.380[0.852-2.131] 0.848[0.498-1.342] Go with entire population 80 114 0.78
  Gail and Simon   1.380[0.852-2.131] 0.848[0.498-1.342] Go with entire population 80 114 0.07& 0.28
2nd interim analysis Millen   1.164[0.790-1.659] 1.050[0.717-1.475] Go with entire population 152 236 0.30
  Gail and Simon   1.164[0.790-1.659] 1.050[0.717-1.475] Go with entire population 152 236 0.00& 0.03
3th interim analysis Millen   0.973[0.694-1.319] 0.957[0.711-1.254] Go with entire population 219 366 0.16
  Gail and Simon   0.973[0.694-1.319] 0.957[0.711-1.254] Go with entire population 219 366 0.00& 0.00
Final analysis Millen 0.998[0.824-1.196] 0.983[0.731-1.292] 1.017[0.809-1.263] Go with entire population 278 498 0.09
  Gail and Simon 0.998[0.824-1.196] 0.983[0.731-1.292] 1.017[0.809-1.263] Go with entire population 278 498 0.00& 0.00
  1. The reported intervals are 95% credibility intervals, defined as [quantile(2.5%), quantile(97.5%)] of the posterior distribution.
  2. * In case of Millen’s criterion, this refers to the posterior probability that P2K (equation (2)). In case of Gail & Simon’s criterion, it refers to the posterior probabilities Pquali and Pquanti, respectively, as described in equations (5) & (6).