Table 3.

Modeling of the Conditions Under which an Unmeasured Factor (U) May Account for Observed Sex-Based Differences in Mortality via Collider-Stratification Bias

		M.U	PAH.U	RR for association of U with PAH in men: 2						RR for association of U with PAH in men: 5
				Prevalence of U in population without PAH						Prevalence of U in population without PAH
RR for association of female sex with mortality	1.0			0.05	0.10	0.20	0.30	0.40	0.50	0.05	0.10	0.20	0.30	0.40	0.50
		2	0.67	0.94	0.90	0.86	0.84	0.83	0.84	0.86	0.79	0.74	0.73	0.74	0.76
		5	0.67	0.82	0.74	0.67	0.66	0.68	0.71	0.62	0.53	0.49	0.51	0.55	0.60
		2	1.00	0.96	0.93	0.90	0.89	0.89	0.90	0.87	0.81	0.77	0.77	0.79	0.82
		5	1.00	0.87	0.81	0.77	0.77	0.79	0.82	0.65	0.58	0.56	0.59	0.64	0.69
		2	1.50	0.98	0.97	0.95	0.95	0.95	0.96	0.89	0.84	0.82	0.83	0.85	0.87
		5	1.50	0.94	0.91	0.90	0.90	0.91	0.93	0.71	0.65	0.65	0.69	0.74	0.78
	0.57	2	0.67	0.54	0.52	0.49	0.48	0.47	0.48	0.49	0.45	0.42	0.41	0.42	0.44
		5	0.67	0.47	0.42	0.38	0.38	0.39	0.40	0.35	0.30	0.28	0.29	0.31	0.34
		2	1.00	0.55	0.53	0.51	0.51	0.51	0.51	0.50	0.46	0.44	0.44	0.45	0.47
		5	1.00	0.50	0.46	0.44	0.44	0.45	0.47	0.37	0.33	0.32	0.34	0.36	0.39
		2	1.50	0.56	0.55	0.54	0.54	0.54	0.55	0.51	0.48	0.47	0.47	0.48	0.50
		5	1.50	0.53	0.52	0.51	0.51	0.52	0.53	0.40	0.37	0.37	0.39	0.42	0.45
Key
RR Model < RR Observed Modeling estimates female sex is more protective than the observed data demonstrate (RR Model < 0.60; below the lower limit of the 95% confidence interval of observed data)					RR Model = RR observed Modeling estimates female sex is as protective as the observed data demonstrate (RR Model 0.60 – 0.92; within the 95% confidence interval of observed data)						RR Model > RR Observed Modeling estimates female sex is less protective than the observed data demonstrate (RR Model > 0.92; above the upper limit of the 95% confidence interval of observed data)

M.U. = risk ratio for association of U with mortality; PAH.U = risk ratio for association of U with PAH among women. Assumptions: (1) prevalence of PAH among men = 5 cases per million⁴⁴; (2) Risk ratio (RR) for effect of female sex on PAH = 3.0 (as seen in PHAR); (3) mortality of men versus women in the general population = RR 1.0 (equivalent) or 0.57 (lower mortality for women, based on U.S.-based longitudinal cohorts)⁴⁵; (4) RR for the association of U with mortality = varied between 2.0 and 5.0; (5) RR for the association of U with PAH among women = varied between 0.67 and 1.50; (6) prevalence of U in the population without PAH = varied between 0.05 and 0.50. Table is color-coded according to whether modeling of collider-stratification bias predicted RR which were below (red), equal to (green), or above (blue) the 95% confidence interval for the observed unadjusted RR for mortality by sex in PHAR (RR 0.74; 95% CI 0.60–0.92).