From: Bounding the per-protocol effect in randomized trials: an application to colorectal cancer screening
CRC incidence | CRC mortality | All-cause mortality | ||||
---|---|---|---|---|---|---|
Lower bound | Upper bound | Lower bound | Upper bound | Lower bound | Upper bound | |
No Assumptions | ||||||
Risk under no screening | 1.2 | 17.4 | 0.4 | 16.6 | 9.1 | 25.3 |
Risk under screening | 0.2 | 84.0 | 0.03 | 83.9 | 1.1 | 84.9 |
Risk difference | −17.2 | 82.8 | −16.5 | 83.5 | −24.2 | 75.8 |
Risk ratio | 0.01 | 68.95 | 0.00 | 214.54 | 0.04 | 9.32 |
Instrumental conditions | ||||||
Overall | ||||||
Risk under no screeninga | 1.4 | 0.4 | 10.2 | |||
Risk under screening | 0.7 | 35.9 | 0.1 | 35.3 | 4.3 | 39.5 |
Risk difference | −0.7 | 34.5 | −0.3 | 34.9 | −5.9 | 29.3 |
Risk ratio | 0.49 | 24.88 | 0.28 | 80.64 | 0.42 | 3.86 |
Among the “never-takers” (35 %)b | ||||||
Risk under no screeninga | 1.5 | 0.7 | 16.2 | |||
Risk under screening | 0.0 | 100.0 | 0.0 | 100.0 | 0.0 | 100.0 |
Risk difference | −1.5 | 98.5 | −0.7 | 99.3 | −16.2 | 83.8 |
Risk ratio | 0.00 | 64.95 | 0.00 | 141.35 | 0.00 | 6.17 |
Among the “compliers” (65 %)a,b | ||||||
Risk under no screening | 1.4 | 0.3 | 7.0 | |||
Risk under screening | 1.1 | 0.2 | 6.7 | |||
Risk difference | −0.3 | −0.1 | −0.3 | |||
Risk ratio | 0.79 | 0.66 | 0.96 | |||
Instrumental conditions and additive effect homogeneitya | ||||||
Risk under no screening | 1.4 | 0.4 | 10.2 | |||
Risk under screening | 1.1 | 0.3 | 9.9 | |||
Risk difference | −0.3 | −0.1 | −0.3 | |||
Risk ratio | 0.80 | 0.77 | 0.97 | |||
Instrumental conditions and multiplicative effect homogeneitya | ||||||
Risk under no screening | 1.4 | 0.4 | 10.2 | |||
Risk under screening | 1.1 | 0.3 | 9.8 | |||
Risk difference | −0.3 | −0.1 | −0.5 | |||
Risk ratio | 0.79 | 0.66 | 0.96 |