Table 3.

Comparison of % bias and confidence interval coverage (%CI) of parameter estimates from the joint model with correction for left truncation (JM-C) to estimates from the joint model without correction for left truncation (JM-UN). Data generated from lognormal model.

Left Truncation Age	Parameter	True value	Probability of left truncation
			0.2				0.5				0.8
			JM-C		JM-UN		JM-C		JM-UN		JM-C		JM-UN
			%Bias	%CI	%Bias	%CI	%Bias	%CI	%Bias	%CI	%Bias	%CI	%Bias	%CI
10	${\alpha }_{b_0}$	108.0	0.0	92.2	0	92.6	0.1	91.8	0.0	94.2	0.0	92.0	−0.2*	95.6
	${\alpha }_{b_1}$	−1.65	0.1	94.2	−0.6*	94.4	0.4	95.2	−0.9*	92.8	0.0	94.0	−2.0*	93.8
	${\alpha }_T$	3.6	0.0	94.8	0.0	94.6	0.0	96.8	0.1*	91.8	0.0	94.8	0.2*	94.4
	${\alpha }_{b_0|w}$	10.8	−0.2	94.4	0.6	94.4	−0.2	95.6	1.4*	95.6	0.4	95.4	1.2*	94.2
	${\alpha }_{b_1|w}$	0.165	2.5	94.0	−7.3*	94.8	2.0	95.6	−19.6*	92.2	−1.0	94.6	−22.2*	93.2
	${\alpha }_{T|w}$	0.36	0.7	94.4	−2.4*	93.0	0.3	94.8	−5.4*	89.2	0.4	95.2	−7.2*	86.8
20	${\alpha }_{b_0}$	108.0	−0.1	94.4	−0.2*	93.4	−0.2*	93.8	−0.8*	90.0	0.0	94.6	−0.9*	91.4
	${\alpha }_{b_1}$	−1.65	−0.2	96.4	−2.7*	91.0	−0.3	95.8	−8.2*	66.6	0.0	94.6	−12.8*	41.0
	${\alpha }_T$	3.6	0.0	96.2	0.5*	92.2	0.0	94.0	1.4*	65.0	0.0	95.4	2.3*	21.2
	${\alpha }_{b_0|w}$	10.8	0.7	94.2	1.6*	92.6	−0.8	95.0	3.4*	93.2	0.1	95.6	7.4*	92.2
	${\alpha }_{b_1|w}$	0.165	−0.2	95.4	−22.1*	94.0	3.8	94.8	−47.5*	87.0	3.8	94.6	−90.3*	65.2
	${\alpha }_{T|w}$	0.36	0.1	94.4	−5.6*	89.0	0.3	95.0	−−13.8*	65.2	1.4*	96.4	−26.7*	15.2
30	${\alpha }_{b_0}$	108.0	0.1	93.2	0.5*	94.6	0.0	94.2	−1.2*	88.0	0.0	94.4	−2.3*	79.2
	${\alpha }_{b_1}$	−1.65	−0.2	96.0	−5.2*	83.2	−0.3	95.8	−14.1*	31.2	−0.5	94.8	−27.0*	2.0
	${\alpha }_T$	3.6	0.1	96.2	1.1*	80.6	0.1	93.2	3.2*	11.4	0.2*	94.2	5.6*	0.0
	${\alpha }_{b_0|w}$	10.8	−0.7	94.0	0.9	95.6	−0.4	94.0	3.8*	93.8	−1.0	95.4	8.8*	92.2
	${\alpha }_{b_1|w}$	0.165	−0.9	94.4	−15.4*	93.8	−1.4	95.2	−50.2*	87.6	−2.4	94.8	−117.9*	56.0
	${\alpha }_{T|w}$	0.36	0.1	96.2	−2.7*	94.0	−0.2	95.4	−8.6*	82.4	−2.1	93.4	−29.0*	25.2

^*significant bias (p<0.05)