Assessing the agreement of biomarker data in the presence of left-censoring

Table 6 Simulation results based on 1000 data sets with sample size of 25 -- Per cent censoring (40%, 25%)

Per cent censoring	True ρ	True ρ _c	Method	Mean ${\hat{ρ}}_{c}$	Relative bias (%)	Empirical SD	Mean SE	The percentage of 95% confidence intervals that include true value of CCC
(40%, 25%)	0.25	0.238	1. Delete the pair	0.1357	−42.98	0.2485	0.2130	85.5
			2. Replace by LOD	0.1703	−28.45	0.4223	0.1530	80.1
			3. Replace by 0.5 × LOD	0.1822	−23.45	0.2936	0.1535	74.3
			4. Replace by c × LOD	0.1751	−26.45	0.2033	0.1533	75.4
			5. ML	0.2193	−7.86	0.1948	0.1824	93.0
	0.50	0.476	1. Delete the pair	0.2667	−43.97	0.2296	0.1982	82.3
			2. Replace by LOD	0.3628	−23.78	0.2088	0.1334	78.6
			3. Replace by 0.5 × LOD	0.3307	−30.53	0.2283	0.1350	71.7
			4. Replace by c × LOD	0.3304	−30.59	0.2416	0.1352	72.8
			5. ML	0.4449	−6.53	0.1693	0.1570	93.3
	0.75	0.714	1. Delete the pair	0.4600	−35.57	0.2050	0.1608	75.9
			2. Replace by LOD	0.5599	−21.58	0.2482	0.0947	78.4
			3. Replace by 0.5 × LOD	0.5246	−26.53	0.2619	0.0961	72.8
			4. Replace by c × LOD	0.5266	−26.25	0.2678	0.0964	74.0
			5. ML	0.6847	−4.10	0.1180	0.1074	92.2

Abbreviations: LLD Lower Limit of Detection, ML Maximum Likelihood, C = Random number from uniform distribution (0, 1), CI confidence interval, Relative bias = $\frac{(Mean {\hat{ρ}}_{c} - True ρ_{c})}{True ρ_{c}} \times 100 %$ , CCC⁵= $ρ_{c} = \frac{2 COV (X, Y)}{VAR (X) + VAR (Y) + {(E (X) - E (Y))}^{2}}$ .