Background
Methods: two-stage Bayesian hierarchical models
Stage 1: Bayesian blinded safety monitoring
Beta-binomial model
Bayesian hierarchical blinded model
Stage 2: Bayesian Unblinded safety monitoring
Conduct of the trial
Case study
Eight Arms | Dose (Oxygen Toxicity Units) | Sample Size (N = 53) | |
---|---|---|---|
1 | Control (1.0 ATA) | 0.0 | 11 |
2 | 1.5 ATA | 2.60 | 6 |
3 | 2 ATA | 4.17 | 6 |
4 | NBH (100% FiO2 at 1.0 ATA) | 5.40 | 6 |
5 | 2.5 ATA | 5.92 | 6 |
6 | 1.5 ATA + NBH | 6.20 | 6 |
7 | 2 ATA + NBH | 7.76 | 6 |
8 | 2.5 ATA + NBH | 9.52 | 6 |
Adverse event of special interest
Adverse Event | Clinical Relevance | Expected Event Rate (πM) |
---|---|---|
Pneumothorax Induced by HBO therapy | Abnormal collection of air in the pleural space between the lung and the chest wall, can result in steadily worsening oxygen supply. This is a pressure related phenomenon that can also be caused by major trauma or medical procedure. As an AE it is expected to increase as a function of dose atmospheres, but not duration of exposure or number of days treatment. This is expected to occur during the dive and would result in aborting the treatment. | 2% |
Signs of Pulmonary Dysfunction | Signs of pulmonary dysfunction, including PaO2/FiO2 ≤ 200 or requiring PEEP > 10 cm of water to maintain a PaO2/FiO2 ratio of > 200. This is an adverse event which may be related to total oxygen toxicity exposure and as such should increase with dose and number of treatments. Symptoms are expected to progressively worsen over subsequent dives. | 25% |
Pneumonia | This is an adverse event which is related to total oxygen toxicity exposure and as such should increase with dose and number of treatments. Symptoms are expected to progressively worsen over subsequent dives. | 40% |
Critical decreased CPP (< 60 mmHg) | This AE is not specific to HBO therapy, but is associated with poor outcome (reperfusion). It is expected to be the same in all groups but could demonstrate differences if the process of transferring to the dive chamber causes increased AEs. This should be analyzed as active vs. control. | 75% |
Critical hypotension (MAP< 70 mmHg) | This AE is not specific to HBO therapy, but can be related to transfer from critical care unit (e.g. disconnecting and reconnecting of lines). It is expected to be the same in all groups but could demonstrate differences if the process of transferring to the dive chamber causes increased AEs. This should be analyzed as active vs. control. | 75% |
Seizures during HBO treatment | These are expected to occur immediately proximal to treatment as a function of dose oxygen toxicity (rather than cumulative exposure). It is possible to have multiple episodes of AE. Subjects with a baseline propensity to seize may elevate the numerator for this AE. | 1% |
Hypercarbia during transportation (PaCO2 > 45 mmHg) | This AE is not specific to HBO therapy, but related to transfer from critical care unit (e.g. disconnecting and reconnecting of lines). It is expected to be the same in all groups but could demonstrate differences if the process of transferring to the dive chamber causes increased AEs. This should be analyzed as active vs. control. | 10% |
Simulation study
Two-stage Bayesian hierarchical safety monitoring models
Example AEs | Expected Event Rate (πM) | True Proportion (π0) | Proportion of Flagged Trials After N = 53 Subjects Treated | |
---|---|---|---|---|
Beta-Binomial Independent Model \( \left({P}_{cri{t}_{Ind}}=0.9\right) \) | Bayesian Blinded Hierarchical Model \( \left({P}_{crit_I}=0.9\right) \) | |||
Pneumothorax Induced by HBO therapy | 2% | 2% | 0.14 | 0.02 |
2% | 12% | 1.00 | 0.98 | |
2% | 17% | 1.00 | 1.00 | |
Signs of Pulmonary Dysfunction | 25% | 25% | 0.10 | 0.05 |
25% | 35% | 0.83 | 0.75 | |
25% | 40% | 0.97 | 0.91 | |
Pneumonia | 40% | 40% | 0.09 | 0.06 |
40% | 50% | 0.76 | 0.72 | |
40% | 55% | 0.96 | 0.90 | |
Critical decreased CPP (< 60 mmHg) | 75% | 75% | 0.10 | 0.07 |
75% | 85% | 0.89 | 0.87 | |
75% | 90% | 1.00 | 0.99 | |
Critical hypotension (MAP< 70 mmHg) | 75% | 75% | 0.10 | 0.06 |
75% | 85% | 0.89 | 0.88 | |
75% | 90% | 1.00 | 0.99 | |
Seizures during HBO treatment | 1% | 1% | 0.27 | 0.01 |
1% | 11% | 1.00 | 0.99 | |
1% | 16% | 1.00 | 1.00 | |
Hypercarbia during transportation (PaCO2 > 45 mmHg) | 10% | 10% | 0.12 | 0.04 |
10% | 20% | 0.95 | 0.86 | |
10% | 25% | 1.00 | 0.97 | |
No Signal Pattern | Family-Wise Error Rate (FWER) | |||
Overall Adverse Events | Safe: π0 = πM | 0.62 | 0.19 |
Results
Example AEs (True Proportion; Expected Event Rate) | Blinded: Proportion with signal for early termination Unblinded: Termination Proportion with confirmed by unblinded data | (Pcrit1, Pcrit2) | ||
---|---|---|---|---|
(0.9, 0.7) | (0.9, 0.8) | (0.9, 0.9) | ||
Pneumothorax Induced by HBO therapy (π = 2%; πM = 2%) | Blinded | 0.02 | 0.02 | 0.01 |
Unblinded | 0.58 | 0.40 | 0.16 | |
Overall Rate | 0.01 | 0.01 | 0.00 | |
Signs of Pulmonary Dysfunction (π = 25%; πM = 25%) | Blinded | 0.05 | 0.05 | 0.06 |
Unblinded | 0.40 | 0.26 | 0.16 | |
Overall Rate | 0.02 | 0.01 | 0.01 | |
Pneumonia (π = 40%; πM = 40%) | Blinded | 0.06 | 0.06 | 0.06 |
Unblinded | 0.41 | 0.24 | 0.13 | |
Overall Rate | 0.03 | 0.02 | 0.01 | |
Critical decreased CPP (< 60 mmHg) (π = 75%; πM = 75%) | Blinded | 0.06 | 0.06 | 0.07 |
Unblinded | 0.45 | 0.30 | 0.16 | |
Overall Rate | 0.03 | 0.02 | 0.01 | |
Critical hypotension (MAP< 70 mmHg) (π = 75%; πM = 75%) | Blinded | 0.06 | 0.07 | 0.06 |
Unblinded | 0.44 | 0.31 | 0.16 | |
Overall Rate | 0.03 | 0.02 | 0.01 | |
Seizures during HBO treatment (π = 1%; πM = 1%) | Blinded | 0.01 | 0.01 | 0.01 |
Unblinded | 0.53 | 0.40 | 0.11 | |
Overall Rate | 0.00 | 0.00 | 0.00 | |
Hypercarbia during transportation (PaCO2 > 45 mmHg) (π = 10%; πM = 10%) | Blinded | 0.04 | 0.04 | 0.04 |
Unblinded | 0.41 | 0.27 | 0.14 | |
Overall Rate | 0.01 | 0.01 | 0.01 | |
Family-Wise Error Rate (FWER) | ||||
Overall Adverse Events | Blinded | 0.18 | 0.17 | 0.19 |
Unblinded | 0.57 | 0.44 | 0.25 | |
Overall Rate | 0.10 | 0.08 | 0.05 |
Example AEs (True Proportion; Expected Event Rate) | Blinded: Proportion with signal for early termination Unblinded: Termination Proportion with confirmed by unblinded data | (Pcrit1, Pcrit2) | ||
---|---|---|---|---|
(0.9, 0.7) | (0.9, 0.8) | (0.9, 0.9) | ||
Pneumothorax Induced by HBO therapya (π = 3%; πM = 2%) | Blinded | 0.28 | 0.27 | 0.28 |
Unblinded | 0.79 | 0.62 | 0.33 | |
Overall Rate | 0.23 | 0.17 | 0.09 | |
Signs of Pulmonary Dysfunctiona (π = 31%; πM = 25%) | Blinded | 0.55 | 0.54 | 0.54 |
Unblinded | 0.76 | 0.63 | 0.42 | |
Overall Rate | 0.42 | 0.34 | 0.23 | |
Pneumoniaa (π = 48%; πM = 40%) | Blinded | 0.58 | 0.59 | 0.59 |
Unblinded | 0.75 | 0.65 | 0.44 | |
Overall Rate | 0.44 | 0.39 | 0.26 | |
Critical decreased CPPa (< 60 mmHg) (π = 80%; πM = 75%) | Blinded | 0.55 | 0.55 | 0.56 |
Unblinded | 0.76 | 0.60 | 0.39 | |
Overall Rate | 0.42 | 0.33 | 0.22 | |
Critical hypotensiona (MAP< 70 mmHg) (π = 80%; πM = 75%) | Blinded | 0.56 | 0.56 | 0.54 |
Unblinded | 0.77 | 0.61 | 0.39 | |
Overall Rate | 0.43 | 0.34 | 0.21 | |
Seizures during HBO treatmenta (π = 1%; πM = 1%) | Blinded | 0.23 | 0.23 | 0.23 |
Unblinded | 0.79 | 0.61 | 0.31 | |
Overall Rate | 0.19 | 0.14 | 0.07 | |
Hypercarbia during transportationa (PaCO2 > 45 mmHg) (π = 13%; πM = 10%) | Blinded | 0.44 | 0.43 | 0.43 |
Unblinded | 0.77 | 0.62 | 0.40 | |
Overall Rate | 0.33 | 0.26 | 0.17 |
Example AEs (True Proportion; Expected Event Rate) | Blinded: Proportion with signal for early termination Unblinded: Termination Proportion with confirmed by unblinded data | (Pcrit1, Pcrit2) | ||
---|---|---|---|---|
(0.9, 0.7) | (0.9, 0.8) | (0.9, 0.9) | ||
Pneumothorax Induced by HBO therapya (π = 3%; πM = 2%) | Blinded | 0.10 | 0.10 | 0.11 |
Unblinded | 0.68 | 0.48 | 0.27 | |
Overall Rate | 0.07 | 0.05 | 0.03 | |
Signs of Pulmonary Dysfunctiona (π = 31%; πM = 25%) | Blinded | 0.36 | 0.36 | 0.36 |
Unblinded | 0.70 | 0.55 | 0.36 | |
Overall Rate | 0.25 | 0.20 | 0.13 | |
Pneumoniaa (π = 48%; πM = 40%) | Blinded | 0.41 | 0.40 | 0.41 |
Unblinded | 0.68 | 0.57 | 0.37 | |
Overall Rate | 0.28 | 0.23 | 0.15 | |
Critical decreased CPP (< 60 mmHg) (π = 75%; πM = 75%) | Blinded | 0.15 | 0.16 | 0.15 |
Unblinded | 0.49 | 0.34 | 0.17 | |
Overall Rate | 0.07 | 0.05 | 0.02 | |
Critical hypotension (MAP< 70 mmHg) (π = 75%; πM = 75%) | Blinded | 0.15 | 0.16 | 0.16 |
Unblinded | 0.48 | 0.31 | 0.16 | |
Overall Rate | 0.07 | 0.05 | 0.03 | |
Seizures during HBO treatment (π = 1%; πM = 1%) | Blinded | 0.05 | 0.05 | 0.05 |
Unblinded | 0.59 | 0.39 | 0.20 | |
Overall Rate | 0.03 | 0.02 | 0.01 | |
Hypercarbia during transportation (PaCO2 > 45 mmHg) (π = 10%; πM = 10%) | Blinded | 0.10 | 0.11 | 0.10 |
Unblinded | 0.47 | 0.36 | 0.15 | |
Overall Rate | 0.05 | 0.04 | 0.02 |
Example AEs (True Proportion; Expected Event Rate) | Blinded: Proportion with signal for early termination Unblinded: Termination Proportion with confirmed by unblinded data | (Pcrit1, Pcrit2) | ||
---|---|---|---|---|
(0.9, 0.7) | (0.9, 0.8) | (0.9, 0.9) | ||
Pneumothorax Induced by HBO therapya (π = 3%; πM = 2%) | Blinded | 0.25 | 0.26 | 0.26 |
Unblinded | 0.74 | 0.57 | 0.28 | |
Overall Rate | 0.19 | 0.15 | 0.07 | |
Signs of Pulmonary Dysfunctiona (π = 31%; πM = 25%) | Blinded | 0.53 | 0.53 | 0.53 |
Unblinded | 0.74 | 0.60 | 0.39 | |
Overall Rate | 0.39 | 0.31 | 0.21 | |
Pneumoniaa (π = 48%; πM = 40%) | Blinded | 0.56 | 0.57 | 0.58 |
Unblinded | 0.75 | 0.61 | 0.41 | |
Overall Rate | 0.43 | 0.35 | 0.24 | |
Critical decreased CPPa (< 60 mmHg) (π = 80%; πM = 75%) | Blinded | 0.50 | 0.49 | 0.51 |
Unblinded | 0.66 | 0.51 | 0.30 | |
Overall Rate | 0.33 | 0.25 | 0.15 | |
Critical hypotensiona (MAP< 70 mmHg) (π = 80%; πM = 75%) | Blinded | 0.49 | 0.50 | 0.51 |
Unblinded | 0.66 | 0.51 | 0.29 | |
Overall Rate | 0.32 | 0.26 | 0.15 | |
Seizures during HBO treatmenta (π = 1%; πM = 1%) | Blinded | 0.21 | 0.22 | 0.22 |
Unblinded | 0.74 | 0.56 | 0.28 | |
Overall Rate | 0.16 | 0.12 | 0.06 | |
Hypercarbia during transportationa (PaCO2 > 45 mmHg) (π = 13%; πM = 10%) | Blinded | 0.39 | 0.39 | 0.38 |
Unblinded | 0.67 | 0.50 | 0.28 | |
Overall Rate | 0.26 | 0.19 | 0.11 |
Example AEs (True Proportion; Expected Event Rate) | Blinded: Proportion with signal for early termination Unblinded: Termination Proportion with confirmed by unblinded data | (Pcrit1, Pcrit2) | ||
---|---|---|---|---|
(0.9, 0.7) | (0.9, 0.8) | (0.9, 0.9) | ||
Pneumothorax Induced by HBO therapya (π = 3%; πM = 2%) | Blinded | 0.32 | 0.33 | 0.33 |
Unblinded | 0.45 | 0.24 | 0.09 | |
Overall Rate | 0.15 | 0.08 | 0.03 | |
Signs of Pulmonary Dysfunctiona (π = 32%; πM = 25%) | Blinded | 0.60 | 0.60 | 0.59 |
Unblinded | 0.40 | 0.25 | 0.12 | |
Overall Rate | 0.24 | 0.15 | 0.07 | |
Pneumoniaa (π = 49%; πM = 40%) | Blinded | 0.65 | 0.66 | 0.64 |
Unblinded | 0.40 | 0.27 | 0.13 | |
Overall Rate | 0.26 | 0.18 | 0.08 | |
Critical decreased CPPa (< 60 mmHg) (π = 81%; πM = 75%) | Blinded | 0.62 | 0.63 | 0.62 |
Unblinded | 0.42 | 0.28 | 0.13 | |
Overall Rate | 0.26 | 0.18 | 0.08 | |
Critical hypotensiona (MAP< 70 mmHg) (π = 81%; πM = 75%) | Blinded | 0.61 | 0.62 | 0.61 |
Unblinded | 0.42 | 0.28 | 0.12 | |
Overall Rate | 0.26 | 0.17 | 0.07 | |
Seizures during HBO treatmenta (π = 1%; πM = 1%) | Blinded | 0.28 | 0.28 | 0.28 |
Unblinded | 0.44 | 0.26 | 0.09 | |
Overall Rate | 0.12 | 0.07 | 0.02 | |
Hypercarbia during transportationa (PaCO2 > 45 mmHg) (π = 14%; πM = 10%) | Blinded | 0.49 | 0.49 | 0.49 |
Unblinded | 0.41 | 0.27 | 0.11 | |
Overall Rate | 0.20 | 0.13 | 0.05 |
Scenarios | AE #1 | AE #2 | AE #3 | AE #4 | AE #5 | AE #6 | AE #7 |
---|---|---|---|---|---|---|---|
Scenario I (Safe: #1234567) | Safe | Safe | Safe | Safe | Safe | Safe | Safe |
Baseline proportions | |||||||
Scenario II (Unsafe: #1234567 same effect) | Unsafe | Unsafe | Unsafe | Unsafe | Unsafe | Unsafe | Unsafe |
Compare to Baseline proportions scenario I | |||||||
Proportions increase a lot (All effect scenario) | |||||||
Scenario III (Safe: #4,5,6,7; Unsafe: #1,2,3 same effect) | Unsafe | Unsafe | Unsafe | Safe | Safe | Safe | Safe |
Compare to Baseline proportions scenario I | |||||||
Higher proportions | Smaller proportions | ||||||
Scenario IV (Unsafe: #4,5,7 flat effect; Unsafe: #1,2,3,6 same effect) | Unsafe | Unsafe | Unsafe | Unsafe | Unsafe | Unsafe | Unsafe |
Comparing to scenario II | |||||||
Similar proportions | Proportion decreases | Proportion decreases | Similar proportion | Proportion decreases | |||
Scenario V (Unsafe: #1234567 flat effect; unsafe for control arms) | Unsafe | Unsafe | Unsafe | Unsafe | Unsafe | Unsafe | Unsafe |
The model flags potential signals at the blinded stage but not at the unblinded stage with fewer proportions comparing to other scenarios. |