Table 5.

Mean Rate Ratios, Empirical Variance, and Percent Coverage of 95% Confidence Intervals From 1,000 Simulated Data Sets in the Presence of Unmeasured Confounding Due to “Last Resort Treatment” and “Treatment Withheld” Without or With Asymmetric Trimming of the Propensity Score According to Analytic Strategy (True RR = 2.0)

PS Implementation and Trimming Range	Treatment Prevalence = 0.2				Treatment Prevalence = 0.05
	RR	Variancea	MSEb	Coveragec	RR	Variancea	MSEb	Coveragec
Crude	2.86	0.006	0.131	0.0	2.98	0.015	0.169	3.6
True outcome model	2.00	0.003	0.003	95.5	1.99	0.007	0.007	93.7
Outcome model (X1–X6)d	1.39	0.006	0.142	0.0	1.45	0.014	0.124	5.0
PS analysesd
PS continuous
Unrestricted	1.38	0.007	0.149	0.0	1.46	0.022	0.128	10.6
Restricted
0–100	1.38	0.007	0.149	0.0	1.49	0.018	0.109	12.0
1–99	1.63	0.006	0.049	9.6	1.62	0.015	0.061	33.4
2.5–97.5	1.85	0.006	0.012	69.3	1.77	0.015	0.032	66.2
5–95	2.01	0.005	0.005	93.6	1.90	0.015	0.018	85.9
PS quintiles (Mantel-Haenszel)
Unrestricted	1.60	0.007	0.057	6.3	1.72	0.016	0.041	44.7
Restricted
0–100	1.59	0.007	0.062	4.8	1.69	0.015	0.046	40.8
1–99	1.75	0.006	0.024	35.2	1.77	0.014	0.031	61.6
2.5–97.5	1.92	0.005	0.007	83.3	1.86	0.014	0.021	78.8
5–95	2.04	0.005	0.005	92.3	1.95	0.015	0.016	88.1
PS quintiles (standardized mortality ratio)
Unrestricted	1.53	0.008	0.084	3.1	1.69	0.016	0.047	39.4
Restricted
0–100	1.51	0.008	0.089	2.1	1.67	0.015	0.052	34.5
1–99	1.67	0.006	0.039	17.3	1.74	0.014	0.035	57.2
2.5–97.5	1.87	0.006	0.011	73.2	1.83	0.014	0.023	76.0
5–95	2.02	0.005	0.005	93.4	1.93	0.015	0.016	88.0
PS matching
Unrestricted	1.28	0.009	0.215	0.0	1.35	0.036	0.202	15.0
Restricted
0–100	1.28	0.009	0.214	0.0	1.35	0.035	0.201	15.0
1–99	1.53	0.008	0.084	5.1	1.59	0.035	0.096	48.3
2.5–97.5	1.78	0.008	0.023	59.3	1.76	0.037	0.059	60.7
5–95	1.99	0.008	0.008	93.2	1.90	0.040	0.045	81.7
Inverse probability of treatment weighting
Unrestricted	1.49	0.008	0.096	8.9	1.90	0.019	0.023	92.5
Restricted
0–100	1.48	0.008	0.101	6.7	1.86	0.019	0.026	89.9
1–99	1.83	0.006	0.014	79.5	2.05	0.019	0.019	94.0
2.5–97.5	2.02	0.005	0.005	96.4	2.13	0.019	0.022	92.9
5–95	2.11	0.005	0.008	90.2	2.18	0.020	0.026	90.7

Abbreviations: MSE, mean squared error; PS, propensity score; RR, rate ratio.

^aVariance of treatment effect estimates [log(RR)] over 1,000 simulated data sets.

^bMean of [log(RR) – log(2.0)]² over 1,000 simulated data sets.

^cPercentage of simulated studies in which the 95% confidence interval includes the true value (RR = 2.0).

^dOutcome and PS models including all measured covariates X₁–X₆ but not including unmeasured covariate X₇.