Table 1.
Percent relative bias (PRB) comparing complete-case analysis (CCA), single missing indicator (SMI), modeled missing indicator (MMI), and multiple imputation (MI) for 1:1 design, number of case–control sets = 400, exp(βX ) = 2, exp(βZ) = 1.42, pr(X = 1) = 0.5. PRB is computed as the ratio of the bias in the rate ratio estimate from SMI, MMI, or CCA to the true rate ratio. Based on 1000 trials.
| PRB in exp(β̂X) | PRB in exp(β̂Z) | ||||||
|---|---|---|---|---|---|---|---|
| Missing | |||||||
| pr(M = 1)-Confounding | type | CCA | SMI | MMI | CCA | SMI | MMI |
| 50%-no | MCAR | 1.6 | 0.9 | 1.1 | 1.9 | 0.8 | 0.7 |
| MAR(Z) | 1.8 | 0.7 | 0.9 | 2.1 | 0.8 | 0.5 | |
| MAR(D) | 3.0 | 2.3 | 2.6 | 2.4 | 0.6 | 0.5 | |
| NI(X) | 4.4 | 1.4 | 1.7 | 2.7 | 0.9 | 0.9 | |
| NI(X,Z) | 2.7 | 1.8 | 2.1 | 1.9 | 2.1 | 0.6 | |
| 50%-strong | MCAR | 2.6 | −9.6 | 0.2 | 1.5 | −11 | 0.7 |
| MAR(Z) | 2.0 | −7.9 | 1.1 | 1.0 | −12 | 0.9 | |
| MAR(D) | 4.7 | −8.2 | 1.9 | 2.8 | −11 | 1.0 | |
| NI(X) | 3.7 | −5.4 | 1.0 | 1.0 | −7.5 | 0.0 | |
| NI(X,Z) | 3.9 | −3.6 | 1.0 | 1.3 | −7.4 | −0.1 | |
| 20%-no | MCAR | 0.6 | 0.4 | 0.5 | 1.5 | 0.8 | 1.1 |
| MAR(Z) | 0.5 | 0.5 | 0.6 | 1.2 | 0.9 | 1.1 | |
| MAR(D) | 0.2 | 0.2 | 0.2 | 0.9 | 0.6 | 0.7 | |
| NI(X) | 0.6 | 0.4 | 0.5 | 1.3 | 0.8 | 1.1 | |
| NI(X,Z) | 0.3 | 0.5 | 0.6 | 1.2 | 1.1 | 0.9 | |
| 20%-strong | MCAR | 1.7 | −3.3 | 1.2 | 1.0 | −4.5 | 0.9 |
| MAR(Z) | 2.4 | −3.4 | 1.4 | 0.9 | −5.3 | 0.7 | |
| MAR(D) | 1.7 | −1.3 | 1.5 | 0.7 | −2.7 | 0.6 | |
| NI(X) | 0.4 | −1.7 | 0.5 | 0.2 | −2.1 | 0.4 | |
| NI(X,Z) | 1.2 | 0.9 | 1.0 | 0.5 | −1.8 | 0.7 | |
MCAR, missing at random unconditionally; MAR(D), missing at random conditional on D; MAR(Z), missing at random conditional on Z; NI(X), missing not at random conditional on X; NI(X,Z), missing not at random conditional on X,Z.