Table 2.

Type I Error, Statistical Power, and Coverage Probability in a Simulation Study of Quintile-Stratification based on a Misspecified Propensity Score: Correlation among propensity covariates, ${\rho }_{x_T}=0.20$

Time Invariant Confounds				Time-Varying Confounds				Type I Error	Statistical Power		Coverage
x1	x2	x3	x4	x5	x6	x7	x8	α1 = 0	α2 = .22	α3 = .56	α1 = 0	α2 = .22	α3 = .56
1.25	1.00	1.25	1.00	1.25	1.00	1.25	1.00	0.06	0.88	1.00	0.94	0.95	0.95
	1.25		1.00		1.00		1.00	0.06	0.86	1.00	0.94	0.95	0.95
	1.00		1.25		1.00		1.00	0.06	0.87	1.00	0.94	0.95	0.95
	1.00		1.00		1.25		1.00	0.07	0.90	1.00	0.93	0.95	0.93
	1.00		1.00		1.00		1.25	0.05	0.88	1.00	0.95	0.94	0.95
	1.25		1.25		1.00		1.00	0.05	0.86	1.00	0.95	0.95	0.95
	1.00		1.00		1.25		1.25	0.07	0.91	1.00	0.93	0.94	0.92
	1.25		1.00		1.25		1.00	0.06	0.90	1.00	0.94	0.95	0.95
	1.00		1.25		1.00		1.25	0.05	0.87	1.00	0.95	0.94	0.94
	1.25		1.00		1.00		1.25	0.06	0.88	1.00	0.94	0.94	0.94
	1.00		1.25		1.25		1.00	0.05	0.91	1.00	0.95	0.95	0.93
1.75	1.00	1.75	1.00	1.75	1.00	1.75	1.00	0.07	0.84	1.00	0.93	0.95	0.96
	1.75		1.00		1.00		1.00	0.07	0.82	1.00	0.93	0.94	0.93
	1.00		1.75		1.00		1.00	0.06	0.83	1.00	0.94	0.94	0.94
	1.00		1.00		1.75		1.00	0.13	0.94	1.00	0.87	0.86	0.72
	1.00		1.00		1.00		1.75	0.09	0.87	1.00	0.91	0.92	0.91
	1.75		1.75		1.00		1.00	0.07	0.83	1.00	0.93	0.94	0.94
	1.00		1.00		1.75		1.75	0.18	0.96	1.00	0.82	0.77	0.53
	1.75		1.00		1.75		1.00	0.14	0.95	1.00	0.86	0.85	0.67
	1.00		1.75		1.00		1.75	0.08	0.85	1.00	0.92	0.91	0.89
	1.75		1.00		1.00		1.75	0.09	0.88	1.00	0.91	0.91	0.89
	1.00		1.75		1.75		1.00	0.16	0.92	1.00	0.84	0.83	0.69

Notes:

1) x₁, x₂, x₅, and x₆ are continuous variables

2) x₃, x₄, x₇, and x₈ are binary variables

3) x₂, x₄, x₆, and x₈ have been ignored in stratification

4) Treatment effects (α_k) for dose k, are expressed in standard deviation units (i.e., effect size).