Table 1.

Simulation results for estimating $\mathit{\beta }$ with incident cohort data only $(m_1=300)$ or with the combined cohort ($m_1=300$ and $m_2=300$) under different censoring rates for the prevalent cohort. The coefficient vector for k-l transition is denoted by ${\mathit{\beta }}_{\mathit{kl}}={({\beta }_{\mathit{kl}}^{(1)},{\beta }_{\mathit{kl}}^{(2)})}^{\prime }$, where ${\beta }_{\mathit{kl}}^{(1)}$ for $Z_1$ and ${\beta }_{\mathit{kl}}^{(1)}$ for $Z_2$

	${\beta }_{01}^{(1)}$	${\beta }_{01}^{(2)}$	${\beta }_{03}^{(1)}$	${\beta }_{03}^{(2)}$	${\beta }_{10}^{(1)}$	${\beta }_{10}^{(2)}$	${\beta }_{12}^{(1)}$	${\beta }_{12}^{(2)}$	${\beta }_{13}^{(1)}$	${\beta }_{13}^{(2)}$	${\beta }_{23}^{(1)}$	${\beta }_{23}^{(2)}$
Truth	0.20	$-$0.20	0.10	$-$0.20	$-$0.20	0.20	0.20	$-$0.30	0.20	0.20	0.30	$-$0.20
Incident cohort only
${\text{Bias}}^a$	$-$0.01	$-$0.01	0.02	$-$0.02	$-$0.01	0.06	0.01	0.04	$-$0.01	$-$0.08	$-$0.01	$-$0.01
${\text{ESE}}^b$	0.15	0.67	0.27	1.04	0.33	1.32	0.28	1.22	0.27	1.09	0.36	1.62
${\text{SE}}^c$	0.15	0.65	0.25	1.05	0.32	1.31	0.27	1.17	0.26	1.10	0.36	1.57
${\text{CP}}^d$	0.95	0.95	0.96	0.96	0.95	0.95	0.96	0.94	0.95	0.96	0.95	0.95
Combined cohorts with no censored prevalent samples
Bias	$-$0.01	$-$0.02	0.01	$-$0.02	$-$0.02	0.05	0.01	0.04	$-$0.01	$-$0.05	0.00	0.01
ESE	0.15	0.63	0.26	1.02	0.32	1.30	0.26	1.16	0.25	1.03	0.11	0.48
SE	0.15	0.62	0.25	1.02	0.32	1.29	0.26	1.11	0.24	1.03	0.11	0.46
CP	0.95	0.95	0.95	0.96	0.96	0.95	0.95	0.94	0.94	0.96	0.95	0.94
${\text{RE}}^e$	1.10	1.13	1.05	1.04	1.07	1.03	1.08	1.10	1.16	1.11	11.28	11.63
Combined cohorts with 15% censored prevalent samples
Bias	0.01	$-$0.01	0.00	0.03	0.03	0.07	$-$0.01	$-$0.03	0.00	$-$0.05	$-$0.01	0.01
ESE	0.15	0.60	0.25	1.05	0.32	1.32	0.27	1.16	0.25	1.08	0.12	0.50
SE	0.15	0.62	0.25	1.03	0.32	1.30	0.26	1.11	0.24	1.03	0.12	0.49
CP	0.95	0.95	0.96	0.94	0.95	0.95	0.94	0.94	0.94	0.94	0.95	0.96
RE	1.07	1.24	1.14	0.99	1.05	1.00	1.04	1.10	1.16	1.02	9.25	10.50
Combined cohorts with 30% censored prevalent samples
Bias	$-$0.01	0.02	0.01	0.03	0.01	0.08	$-$0.01	0.01	0.00	0.00	0.00	0.01
ESE	0.15	0.63	0.25	1.02	0.32	1.31	0.27	1.16	0.24	1.05	0.13	0.52
SE	0.15	0.62	0.25	1.03	0.32	1.29	0.26	1.11	0.24	1.03	0.12	0.53
CP	0.95	0.94	0.95	0.95	0.95	0.95	0.95	0.95	0.95	0.94	0.95	0.96
RE	1.11	1.12	1.13	1.03	1.06	1.01	1.08	1.11	1.29	1.08	8.12	9.86

${}^a$ the empirical bias

${}^b$ the empirical standard error of the parameter estimator

${}^c$ the average of the standard error estimator

${}^d$ the coverage of the 95% confidence interval with the Normal approximation

${}^e$ the relative efficiency obtained by the ratio of the mean-squared error from the combined cohort to that from the incident cohort