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Table 4 Simulation results based on 1000 data sets with sample size of 50 -- Per cent censoring (40%, 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

(40%, 25%)

0.25

0.238

1. Delete the pair

0.1334

−43.95

0.1858

0.1652

88.1

   

2. Replace by LOD

0.1908

−19.83

0.1525

0.1150

84.3

   

3. Replace by 0.5 × LOD

0.1796

−24.54

0.1467

0.1155

80.2

   

4. Replace by c × LOD

0.1780

−25.22

0.1528

0.1152

81.8

   

5. ML

0.2296

−3.53

0.1395

0.1345

92.4

 

0.50

0.476

1. Delete the pair

0.2735

−42.54

0.1693

0.1516

76.9

   

2. Replace by LOD

0.3673

−22.84

0.2110

0.1004

80.2

   

3. Replace by 0.5 × LOD

0.3366

−29.29

0.2771

0.1011

74.3

   

4. Replace by c × LOD

0.3537

−25.70

0.1788

0.1011

75.9

   

5. ML

0.4617

−3.00

0.1206

0.1135

93.2

 

0.75

0.714

1. Delete the pair

0.4913

−31.19

0.1373

0.1184

62.3

   

2. Replace by LOD

0.6022

−15.66

0.1705

0.0696

78.7

   

3. Replace by 0.5 × LOD

0.5706

−20.08

0.2039

0.0710

74.7

   

4. Replace by c × LOD

0.5689

−20.32

0.2151

0.0713

74.1

   

5. ML

0.7003

−1.92

0.0805

0.0750

93.2

  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 .