Simulation study: bias and standard error (SE) based on 200 Monte Carlo replicates analyzed with an unadjusted model and the proposed joint propensity score approach with 100 bootstrap samples.
| Unadjusted . | Joint propensity . | ||||||
|---|---|---|---|---|---|---|---|
| Interventional unit . | Outcome unit . | ||||||
| Bootstrap . | Bootstrap . | ||||||
| Bias . | Bias . | Empirical SE . | Avg. SE . | 95% coverage . | Avg. SE . | 95% coverage . | |
| |$\tau$| | 0.45 | 0.05 | 0.10 | 0.15 | 0.99 | 0.028 | 0.320 |
| |$\Delta(0)$| | −0.60 | −0.01 | 0.61 | 1.16 | 1.00 | 0.168 | 0.385 |
| |$\Delta(1)$| | −0.60 | −0.01 | 0.61 | 1.17 | 1.00 | 0.169 | 0.385 |
| Unadjusted . | Joint propensity . | ||||||
|---|---|---|---|---|---|---|---|
| Interventional unit . | Outcome unit . | ||||||
| Bootstrap . | Bootstrap . | ||||||
| Bias . | Bias . | Empirical SE . | Avg. SE . | 95% coverage . | Avg. SE . | 95% coverage . | |
| |$\tau$| | 0.45 | 0.05 | 0.10 | 0.15 | 0.99 | 0.028 | 0.320 |
| |$\Delta(0)$| | −0.60 | −0.01 | 0.61 | 1.16 | 1.00 | 0.168 | 0.385 |
| |$\Delta(1)$| | −0.60 | −0.01 | 0.61 | 1.17 | 1.00 | 0.169 | 0.385 |
Simulation study: bias and standard error (SE) based on 200 Monte Carlo replicates analyzed with an unadjusted model and the proposed joint propensity score approach with 100 bootstrap samples.
| Unadjusted . | Joint propensity . | ||||||
|---|---|---|---|---|---|---|---|
| Interventional unit . | Outcome unit . | ||||||
| Bootstrap . | Bootstrap . | ||||||
| Bias . | Bias . | Empirical SE . | Avg. SE . | 95% coverage . | Avg. SE . | 95% coverage . | |
| |$\tau$| | 0.45 | 0.05 | 0.10 | 0.15 | 0.99 | 0.028 | 0.320 |
| |$\Delta(0)$| | −0.60 | −0.01 | 0.61 | 1.16 | 1.00 | 0.168 | 0.385 |
| |$\Delta(1)$| | −0.60 | −0.01 | 0.61 | 1.17 | 1.00 | 0.169 | 0.385 |
| Unadjusted . | Joint propensity . | ||||||
|---|---|---|---|---|---|---|---|
| Interventional unit . | Outcome unit . | ||||||
| Bootstrap . | Bootstrap . | ||||||
| Bias . | Bias . | Empirical SE . | Avg. SE . | 95% coverage . | Avg. SE . | 95% coverage . | |
| |$\tau$| | 0.45 | 0.05 | 0.10 | 0.15 | 0.99 | 0.028 | 0.320 |
| |$\Delta(0)$| | −0.60 | −0.01 | 0.61 | 1.16 | 1.00 | 0.168 | 0.385 |
| |$\Delta(1)$| | −0.60 | −0.01 | 0.61 | 1.17 | 1.00 | 0.169 | 0.385 |
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