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 $\widehat{\mathit{OR}}$ 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

Figures in italics in cells are unobserved; OR odds ratio; n_ij number of participants in that cell, S_ij cell selection probability; N_ij total participants in each cell if all eligible patients had been recruited