Table 2 Simple bias analysis applied to 6-month pain outcome; (A) selection probabilities within treatment arm are assumed to be nondifferential with respect to outcome at 6 months (i.e. no selection bias); (B) selection probabilities within treatment arm are differential with respect to outcome at 6 months, such that the selection probability of patients with high pain is the same in intervention and control arms (i.e. selection bias producing worse outcomes in intervention arm)
(A) | Intervention (=1) | Control (= 0) |
Outcome at 6 months = high pain (= A) | nA1 = 159 | NA0 = 236 |
S A1 = 0.123 | S A0 = 0.160 | |
N A1 = 1293 | N A0 = 1471 | |
Outcome at 6 months = low pain (= B) | NB1 = 215 | nB0 = 444 |
S B1 = 0.123 | S B0 = 0.160 | |
N B1 = 1748 | N B0 = 2767 | |
Total potentially eligible | N1 = 3041 | N0 = 4238 |
Total actually recruited and retained to 6 months | n1 = 374 | n0 = 680 |
Overall selection probability within treatment arm | S1 = 374/3041 = 0.123 | S0 = 680/4238 = 0.160 |
Selection odds ratio (OR) | S A1 S B0 /S A0 S B1 = (0.123 × 0.160)/(0.160 × 0.123) = 1 | |
Crude \( \widehat{OR} \) for treatment effect | nA1nB0/nA0nB1 = (159 × 444)/(236 × 215) = 1.39 | |
(B) | Intervention (= 1) | Control (= 0) |
Outcome at 6 months = high pain (= A) | nA1 = 159 | NA0 = 236 |
S A1 = 0.160 | S A0 = 0.160 | |
N A1 = 991 | N A0 = 1471 | |
Outcome at 6 months = low pain (= B) | NB1 = 215 | nB0 = 444 |
S B1 = 0.105 | S B0 = 0.160 | |
N B1 = 2050 | N B0 = 2767 | |
Total potentially eligible | N1 = 3041 | N0 = 4238 |
Total actually recruited and retained to 6 months | n1 = 374 | n0 = 680 |
Overall selection probability within treatment arm | S1 = 374/3041 = 0.123 | S0 = 680/4238 = 0.160 |
Selection OR | S A1 S B0 /S A0 S B1 = (0.160 × 0.160)/(0.160 × 0.105) = 1.52 | |
Crude OR for treatment effect | nA1nB0/nA0nB1 = (159 × 444)/(236 × 215) = 1.39 | |
Bias-corrected OR for treatment effect | Crude OR/Selection OR = 1.39/1.52 = 0.91 | |