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Table 1 Simulation results for registration system with two occasions. p11 is the probability for capture at occasion 1 and occasion 2, p10 is the probability for capture at occasion 1 but not at occasion 2, and so forth. The marginal probabilities for capture at occasion 1 and 2 are p1=p11+p10 and p2=p11+p01, respectively. In settings 1 to 6 inclusion on occasion 1 is independent of inclusion on occasion 2. In settings 7 and 8, occasions become dependent (odds ratio larger than 1) but the conditional probability for capture at occasion 2 given no capture at occasion 1 is identical to the unconditional probability for capture at occasion 1, the capture-removal estimator works fine. In settings 9 and 10, those conditional and unconditional probabilities are different and the capture-removal estimator breaks down

From: Correspondence: Some general points regarding Ledberg and Wennberg, BMC Medical Research Methodology 2014 April 27;14:58

        LP Chapman Removal
Setting p 1 p 2 p 11 p 10 p 01 p 00 \(\bar N_{\textit {LP}}\) SD \(\bar N_{\textit {Ch}}\) SD \(\bar N_{R}\) SD
1 0.5 0.5 0.25 0.25 0.25 0.25 1001 31 1000 31 1007 59
2 0.3 0.3 0.09 0.21 0.21 0.49 1006 77 1000 76 1064 262
3 0.5 0.6 0.30 0.20 0.30 0.20 1002 27 1001 27 1271 113
4 0.3 0.35 0.105 0.195 0.245 0.455 1004 66 1000 65 1825 6475
5 0.5 0.3 0.15 0.35 0.15 0.35 1000 48 998 47 714 21
6 0.3 0.1 0.03 0.27 0.07 0.63 1021 155 999 146 392 17
7 0.5 0.55 0.30 0.20 0.25 0.25 955 28 955 28 1003 57
8 0.5 0.625 0.375 0.125 0.25 0.25 834 18 834 18 1009 56
9 0.3 0.1 0.065 0.235 0.035 0.665 464 34 462 34 340 15
10 0.5 0.5 0.4 0.1 0.1 0.4 625 17 626 17 625 17
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