Comparison of standard error/coverage of bias-corrected |$ \hat{\delta}_{RD} $| and |$ \hat{\delta}_{RR} $| estimated with the matrix method estimator when outcomes are correlated, with empirical standard errors (ESE) compared to analytical ones unadjusted for clustering (ASE), the ASE inflated by the design effect (DE), network bootstrap standard errors (NB), and likelihood-based standard errors (MLE), for select scenarios, with |$ K=1000 $| and |$ n_{k}=3 $|.
Effect . | Scenario . | ICC . | ESE . | ASE . | DE . | NB . | MLE . |
---|---|---|---|---|---|---|---|
|$ \hat{\delta}_{RD} $| | |$ P_{M}=0.50 $|, |$ P_{Y0}=0.10 $|, |$ \delta_{RR}=0.75 $|, |$ P_{R}=0.20 $| | 0.10 | 0.03/0.94 | 0.03/0.94 | 0.04/0.95 | 0.04/0.94 | 0.03/0.96 |
0.25 | 0.04/0.93 | 0.04/0.93 | 0.04/0.96 | 0.04/0.94 | 0.03/0.96 | ||
|$ P_{M}=0.90 $|, |$ P_{Y0}=0.10 $|, |$ \delta_{RR}=1.25 $|, |$ P_{R}=0.50 $| | 0.10 | 0.02/0.94 | 0.02/0.94 | 0.02/0.95 | 0.02/0.94 | 0.02/0.95 | |
0.25 | 0.02/0.95 | 0.02/0.94 | 0.02/0.96 | 0.02/0.95 | 0.02/0.95 | ||
|$ \hat{\delta}_{RR} $| | |$ P_{M}=0.50 $|, |$ P_{Y0}=0.10 $|, |$ \delta_{RR}=0.75 $|, |$ P_{R}=0.20 $| | 0.10 | 0.30/0.96 | 0.28/0.94 | 0.29/0.95 | 0.31/0.95 | 0.27/0.95 |
0.25 | 0.24/0.95 | 0.23/0.95 | 0.26/0.96 | 0.26/0.96 | 0.26/0.95 | ||
|$ P_{M}=0.90 $|, |$ P_{Y0}=0.10 $|, |$ \delta_{RR}=1.25 $|, |$ P_{R}=0.50 $| | 0.10 | 0.16/0.95 | 0.16/0.94 | 0.17/0.95 | 0.17/0.95 | 0.17/0.96 | |
0.25 | 0.15/0.95 | 0.13/0.93 | 0.15/0.96 | 0.15/0.95 | 0.16/0.96 |
Effect . | Scenario . | ICC . | ESE . | ASE . | DE . | NB . | MLE . |
---|---|---|---|---|---|---|---|
|$ \hat{\delta}_{RD} $| | |$ P_{M}=0.50 $|, |$ P_{Y0}=0.10 $|, |$ \delta_{RR}=0.75 $|, |$ P_{R}=0.20 $| | 0.10 | 0.03/0.94 | 0.03/0.94 | 0.04/0.95 | 0.04/0.94 | 0.03/0.96 |
0.25 | 0.04/0.93 | 0.04/0.93 | 0.04/0.96 | 0.04/0.94 | 0.03/0.96 | ||
|$ P_{M}=0.90 $|, |$ P_{Y0}=0.10 $|, |$ \delta_{RR}=1.25 $|, |$ P_{R}=0.50 $| | 0.10 | 0.02/0.94 | 0.02/0.94 | 0.02/0.95 | 0.02/0.94 | 0.02/0.95 | |
0.25 | 0.02/0.95 | 0.02/0.94 | 0.02/0.96 | 0.02/0.95 | 0.02/0.95 | ||
|$ \hat{\delta}_{RR} $| | |$ P_{M}=0.50 $|, |$ P_{Y0}=0.10 $|, |$ \delta_{RR}=0.75 $|, |$ P_{R}=0.20 $| | 0.10 | 0.30/0.96 | 0.28/0.94 | 0.29/0.95 | 0.31/0.95 | 0.27/0.95 |
0.25 | 0.24/0.95 | 0.23/0.95 | 0.26/0.96 | 0.26/0.96 | 0.26/0.95 | ||
|$ P_{M}=0.90 $|, |$ P_{Y0}=0.10 $|, |$ \delta_{RR}=1.25 $|, |$ P_{R}=0.50 $| | 0.10 | 0.16/0.95 | 0.16/0.94 | 0.17/0.95 | 0.17/0.95 | 0.17/0.96 | |
0.25 | 0.15/0.95 | 0.13/0.93 | 0.15/0.96 | 0.15/0.95 | 0.16/0.96 |
Comparison of standard error/coverage of bias-corrected |$ \hat{\delta}_{RD} $| and |$ \hat{\delta}_{RR} $| estimated with the matrix method estimator when outcomes are correlated, with empirical standard errors (ESE) compared to analytical ones unadjusted for clustering (ASE), the ASE inflated by the design effect (DE), network bootstrap standard errors (NB), and likelihood-based standard errors (MLE), for select scenarios, with |$ K=1000 $| and |$ n_{k}=3 $|.
Effect . | Scenario . | ICC . | ESE . | ASE . | DE . | NB . | MLE . |
---|---|---|---|---|---|---|---|
|$ \hat{\delta}_{RD} $| | |$ P_{M}=0.50 $|, |$ P_{Y0}=0.10 $|, |$ \delta_{RR}=0.75 $|, |$ P_{R}=0.20 $| | 0.10 | 0.03/0.94 | 0.03/0.94 | 0.04/0.95 | 0.04/0.94 | 0.03/0.96 |
0.25 | 0.04/0.93 | 0.04/0.93 | 0.04/0.96 | 0.04/0.94 | 0.03/0.96 | ||
|$ P_{M}=0.90 $|, |$ P_{Y0}=0.10 $|, |$ \delta_{RR}=1.25 $|, |$ P_{R}=0.50 $| | 0.10 | 0.02/0.94 | 0.02/0.94 | 0.02/0.95 | 0.02/0.94 | 0.02/0.95 | |
0.25 | 0.02/0.95 | 0.02/0.94 | 0.02/0.96 | 0.02/0.95 | 0.02/0.95 | ||
|$ \hat{\delta}_{RR} $| | |$ P_{M}=0.50 $|, |$ P_{Y0}=0.10 $|, |$ \delta_{RR}=0.75 $|, |$ P_{R}=0.20 $| | 0.10 | 0.30/0.96 | 0.28/0.94 | 0.29/0.95 | 0.31/0.95 | 0.27/0.95 |
0.25 | 0.24/0.95 | 0.23/0.95 | 0.26/0.96 | 0.26/0.96 | 0.26/0.95 | ||
|$ P_{M}=0.90 $|, |$ P_{Y0}=0.10 $|, |$ \delta_{RR}=1.25 $|, |$ P_{R}=0.50 $| | 0.10 | 0.16/0.95 | 0.16/0.94 | 0.17/0.95 | 0.17/0.95 | 0.17/0.96 | |
0.25 | 0.15/0.95 | 0.13/0.93 | 0.15/0.96 | 0.15/0.95 | 0.16/0.96 |
Effect . | Scenario . | ICC . | ESE . | ASE . | DE . | NB . | MLE . |
---|---|---|---|---|---|---|---|
|$ \hat{\delta}_{RD} $| | |$ P_{M}=0.50 $|, |$ P_{Y0}=0.10 $|, |$ \delta_{RR}=0.75 $|, |$ P_{R}=0.20 $| | 0.10 | 0.03/0.94 | 0.03/0.94 | 0.04/0.95 | 0.04/0.94 | 0.03/0.96 |
0.25 | 0.04/0.93 | 0.04/0.93 | 0.04/0.96 | 0.04/0.94 | 0.03/0.96 | ||
|$ P_{M}=0.90 $|, |$ P_{Y0}=0.10 $|, |$ \delta_{RR}=1.25 $|, |$ P_{R}=0.50 $| | 0.10 | 0.02/0.94 | 0.02/0.94 | 0.02/0.95 | 0.02/0.94 | 0.02/0.95 | |
0.25 | 0.02/0.95 | 0.02/0.94 | 0.02/0.96 | 0.02/0.95 | 0.02/0.95 | ||
|$ \hat{\delta}_{RR} $| | |$ P_{M}=0.50 $|, |$ P_{Y0}=0.10 $|, |$ \delta_{RR}=0.75 $|, |$ P_{R}=0.20 $| | 0.10 | 0.30/0.96 | 0.28/0.94 | 0.29/0.95 | 0.31/0.95 | 0.27/0.95 |
0.25 | 0.24/0.95 | 0.23/0.95 | 0.26/0.96 | 0.26/0.96 | 0.26/0.95 | ||
|$ P_{M}=0.90 $|, |$ P_{Y0}=0.10 $|, |$ \delta_{RR}=1.25 $|, |$ P_{R}=0.50 $| | 0.10 | 0.16/0.95 | 0.16/0.94 | 0.17/0.95 | 0.17/0.95 | 0.17/0.96 | |
0.25 | 0.15/0.95 | 0.13/0.93 | 0.15/0.96 | 0.15/0.95 | 0.16/0.96 |
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