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Table 3 Simulation results based on 1000 data sets with sample size of 50 -- Per cent censoring (25%, 25%)

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

Per cent censoring True ρ True ρ c Method Mean ρ ^ c Relative bias (%) Empirical SD Mean SE The percentage of 95% confidence intervals that include true value of CCC
(25%, 25%) 0.25 0.238 1. Delete the pair 0.1402 −41.09 0.1693 0.1486 87.1
    2. Replace by LOD 0.2079 −12.65 0.1509 0.1172 88.2
    3. Replace by 0.5 × LOD 0.1811 −23.91 0.2088 0.1163 83.8
    4. Replace by c × LOD 0.1949 −18.09 0.1813 0.1162 83.9
    5. ML 0.2310 −2.94 0.1351 0.1304 92.7
  0.50 0.476 1. Delete the pair 0.2936 −38.32 0.1481 0.1386 79.4
    2. Replace by LOD 0.4144 −12.94 0.4115 0.1016 87.3
    3. Replace by 0.5 × LOD 0.3661 −23.09 0.1854 0.1024 79.4
    4. Replace by c × LOD 0.3722 −21.81 0.1770 0.1026 81.2
    5. ML 0.4636 −2.61 0.1151 0.1095 93.4
  0.75 0.714 1. Delete the pair 0.5169 −27.61 0.1341 0.1071 66.7
    2. Replace by LOD 0.6429 −9.96 0.1438 0.0694 88.3
    3. Replace by 0.5 × LOD 0.5812 −18.60 0.2127 0.0720 78.5
    4. Replace by c × LOD 0.5909 −17.24 0.1917 0.0727 79.6
    5. ML 0.7025 −1.61 0.0759 0.0716 93.6
  1. Abbreviations: LLD Lower Limit of Detection; ML Maximum Likelihood, C = Random number from uniform distribution (0, 1), CI confidence interval, Relative bias = Mean ρ ^ c True ρ c True ρ c ×100% CCC5= ρ c = 2 COV X , Y VAR X + VAR Y + E X E Y 2 .