. 2019 Aug 16;34(9):823–835. doi: 10.1007/s10654-019-00551-0

Table 4.

Simulation results as in Table 1 but with the correlation between X₁ and X₂ increased to 0.9

Model	Imputation	Interaction
Average $\hat{Δ α}$	3.001	3.001
Average ${\hat{Δ β}}_{1}$	1.003	1.003
Average ${\hat{Δ β}}_{2}$	0.493	0.493
Average ${\hat{Δ β}}_{3}$	− 0.000	− 0.000
Average standard error of $\hat{Δ α}$	0.182	0.182
Average standard error of ${\hat{Δ β}}_{1}$	0.232	0.232
Average standard error of ${\hat{Δ β}}_{2}$	0.232	0.232
Average standard error of ${\hat{Δ β}}_{3}$	0.122	0.122
95% CI coverage $\hat{Δ α}$	0.945	0.949
95% CI coverage ${\hat{Δ β}}_{1}$	0.939	0.947
95% CI coverage ${\hat{Δ β}}_{2}$	0.952	0.954
95% CI coverage ${\hat{Δ β}}_{3}$	0.944	0.948

Result in the first column were obtained from the imputation/prediction model outlined in steps 1–4 using bootstrap for statistical inference, whereas results in the second column were obtained from a standard regression model with interactions