. 2021 Jul 7;30(9):2165–2183. doi: 10.1177/09622802211008945

Table 2.

Empirical penetrance estimates by age 70 for the competing risks model with a time varying covariate (TVC) under low ( $k_{1} = 7$ ), medium ( $k_{1} = 3.5$ ), and high ( $k_{1} = 1$ ) familial dependence; permanent exposure (PE), exponential decay (ED) or Cox and Oakes (CO) models are considered for TVC; $F_{1} (70; TVC, G)$ and $F_{2} (70; TVC, G)$ are cause-specific penetrance estimators (%) by age 70 for event 1 and event 2, respectively, given TVC and mutation status (G), and TVC occurred at age 35 if $TVC = 1$ .

TVC		True	$k_{1} = 7, τ = 0.07$				True	$k_{1} = 3.5, τ = 0.13$				True	$k_{1} = 1, τ = 0.33$
model		value	Bias	ESE	ASE	ECP	value	Bias	ESE	ASE	ECP	value	Bias	ESE	ASE	ECP
PE	$F_{1} (70; TVC = 0, G = 0)$	12.56	−0.10	1.38	1.36	0.95	12.45	0.01	1.33	1.40	0.94	11.93	0.07	1.48	1.45	0.94
	$F_{1} (70; TVC = 1, G = 0)$	21.92	−0.01	2.45	2.45	0.94	21.58	0.02	2.37	2.48	0.95	20.09	0.13	2.49	2.50	0.96
	$F_{1} (70; TVC = 0, G = 1)$	56.52	−0.33	3.20	3.18	0.94	54.51	0.12	3.39	3.42	0.94	46.80	−0.02	3.84	3.92	0.95
	$F_{1} (70; TVC = 1, G = 1)$	75.63	−0.23	3.75	3.74	0.94	72.59	0.03	4.08	4.06	0.94	61.08	−0.04	4.61	4.79	0.94

	$F_{2} (70; TVC = 0, G = 0)$	4.73	−0.08	0.82	0.85	0.94	4.73	−0.08	0.87	0.85	0.93	4.74	−0.05	0.79	0.88	0.95
	$F_{2} (70; TVC = 1, G = 0)$	4.45	−0.08	0.77	0.80	0.94	4.45	−0.08	0.82	0.80	0.93	4.49	−0.05	0.75	0.83	0.95
	$F_{2} (70; TVC = 0, G = 1)$	9.68	0.04	1.16	1.15	0.94	9.85	−0.04	1.16	1.18	0.95	10.52	0.02	1.29	1.28	0.95
	$F_{2} (70; TVC = 1, G = 1)$	7.12	0.01	0.91	0.89	0.94	7.42	−0.04	0.91	0.92	0.95	8.56	0.00	1.04	1.04	0.95

ED	$F_{1} (70; TVC = 0, G = 0)$	13.55	−0.05	1.39	1.42	0.94	13.42	−0.02	1.41	1.44	0.94	12.82	−0.04	1.47	1.47	0.94
	$F_{1} (70; TVC = 1, G = 0)$	15.49	0.03	1.64	1.64	0.94	15.32	0.05	1.62	1.66	0.94	14.54	0.00	1.61	1.68	0.97
	$F_{1} (70; TVC = 0, G = 1)$	55.65	−0.28	2.70	3.07	0.97	53.68	−0.05	3.03	3.27	0.96	46.14	0.12	3.56	3.68	0.96
	$F_{1} (70; TVC = 1, G = 1)$	60.49	−0.10	2.99	3.33	0.97	58.24	0.10	3.26	3.54	0.97	49.69	0.21	3.67	3.94	0.96

	$F_{2} (70; TVC = 0, G = 0)$	5.39	0.01	0.90	0.91	0.95	5.39	−0.07	0.86	0.92	0.95	5.41	−0.05	0.85	0.93	0.96
	$F_{2} (70; TVC = 1, G = 0)$	5.26	0.01	0.87	0.89	0.95	5.26	−0.07	0.83	0.89	0.95	5.28	−0.06	0.83	0.91	0.95
	$F_{2} (70; TVC = 0, G = 1)$	11.38	0.05	1.18	1.22	0.96	11.57	0.04	1.29	1.24	0.95	12.34	−0.05	1.34	1.35	0.95
	$F_{2} (70; TVC = 1, G = 1)$	9.97	0.01	1.05	1.09	0.96	10.22	0.01	1.12	1.12	0.95	11.20	−0.07	1.20	1.22	0.95

CO	$F_{1} (70; TVC = 0, G = 0)$	13.54	0.02	1.36	1.42	0.95	13.41	0.02	1.44	1.43	0.95	12.81	0.08	1.34	1.43	0.96
	$F_{1} (70; TVC = 1, G = 0)$	16.60	−0.04	2.00	2.03	0.95	16.41	−0.04	2.02	2.03	0.94	15.52	−0.02	1.89	1.99	0.95
	$F_{1} (70; TVC = 0, G = 1)$	61.12	0.07	2.90	2.93	0.96	58.82	0.25	3.15	3.10	0.94	50.11	0.32	3.32	3.49	0.97
	$F_{1} (70; TVC = 1, G = 1)$	67.55	−0.15	3.94	3.73	0.93	64.90	0.06	3.80	3.86	0.95	54.88	0.09	3.94	4.09	0.95

	$F_{2} (70; TVC = 0, G = 0)$	5.53	0.04	0.87	0.93	0.95	5.53	0.05	0.88	0.93	0.95	5.55	−0.02	0.89	0.95	0.95
	$F_{2} (70; TVC = 1, G = 0)$	5.39	0.03	0.85	0.90	0.95	5.39	0.04	0.85	0.91	0.95	5.42	−0.02	0.87	0.93	0.95
	$F_{2} (70; TVC = 0, G = 1)$	14.27	−0.06	1.24	1.37	0.98	14.61	−0.02	1.38	1.41	0.94	15.91	−0.08	1.51	1.55	0.95
	$F_{2} (70; TVC = 1, G = 1)$	12.35	−0.06	1.22	1.28	0.96	12.77	−0.02	1.31	1.32	0.95	14.36	−0.07	1.41	1.45	0.95

For each scenario, the mean bias, empirical standard error (ESE), average standard error (ASE), and estimated 95% coverage probability (ECP) are obtained from 500 replicates each with n = 500 families.