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Table 1 Simulation results based on 1000 data sets with sample size of 100 -- 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 0.1405 −40.97 0.1119 0.1087 85.2
    2. Replace by LOD 0.2072 −12.94 0.1214 0.0856 91.0
    3. Replace by 0.5 × LOD 0.1863 −21.72 0.1630 0.0848 88.2
    4. Replace by c × LOD 0.1951 −18.03 0.1240 0.0851 89.0
    5. ML 0.2346 −1.43 0.0944 0.0939 94.3
  0.50 0.476 1. Delete the pair 0.2966 −37.69 0.1197 0.0999 61.5
    2. Replace by LOD 0.4169 −12.42 0.1569 0.0735 86.4
    3. Replace by 0.5 × LOD 0.3664 −23.03 0.3516 0.0742 78.0
    4. Replace by c × LOD 0.3821 −19.73 0.1541 0.0744 78.3
    5. ML 0.4701 −1.24 0.0807 0.0780 93.6
  0.75 0.714 1. Delete the pair 0.5307 −25.67 0.0886 0.0762 38.6
    2. Replace by LOD 0.6582 −7.82 0.0996 0.0497 85.1
    3. Replace by 0.5 × LOD 0.6140 −14.01 0.1482 0.0519 71.5
    4. Replace by c × LOD 0.6140 −14.01 0.1662 0.0521 72.1
    5. ML 0.7077 −0.88 0.0525 0.0503 94.8
  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 .