Reference-Based Multiple Imputation—What is the Right Variance and How to Estimate It

Figures & data

Table 1 Simulation results from 5000 simulations under the null hypothesis.

Method	Est. log RR	Emp. SE	Est. SE	SE ratio
Low dropout
Rubin J2R	0.000	0.044	0.047	1.058
Bootstrap J2R	0.000	0.044	0.045	1.012
Rubin CR	0.000	0.045	0.047	1.047
Bootstrap CR	0.000	0.045	0.045	1.011
High dropout
Rubin J2R	−0.001	0.036	0.052	1.454
Bootstrap J2R	0.000	0.035	0.035	1.005
Rubin CR	−0.001	0.039	0.052	1.331
Bootstrap CR	−0.001	0.039	0.039	1.005

NOTE: Mean estimated log rate ratio (Est. log RR), empirical standard error (Emp. SE), mean estimated standard error (Est. SE) and ratio of mean estimated SE to empirical SE (SE ratio).

Table 2 Simulation results from 5000 simulations under the alternative hypothesis.

Method	Est. log RR	Emp. SE	Est. SE	SE ratio
Low dropout
Rubin J2R	–0.650	0.049	0.053	1.089
Bootstrap J2R	– 0.650	0.049	0.049	0.998
Rubin CR	–0.659	0.050	0.053	1.068
Bootstrap CR	– 0.659	0.050	0.050	0.997
High dropout
Rubin J2R	–0.398	0.034	0.060	1.754
Bootstrap J2R	–0.398	0.033	0.032	0.982
Rubin CR	–0.447	0.039	0.060	1.516
Bootstrap CR	–0.446	0.038	0.038	0.982

NOTE: Mean estimated log rate ratio (Est. log RR), empirical standard error (Emp. SE), mean estimated standard error (Est. SE) and ratio of mean estimated SE to empirical SE (SE) ratio).