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Table 2 Simulation results in the absence of a terminal event

From: Dynamic prediction of repeated events data based on landmarking model: application to colorectal liver metastases data

Scenario DPOs based on AJ estimatora DPOs based on KM estimatorb
u i λ 01 λ 02 λ c no events 1 event 2 events No events 1 event 2 events
Absolute biasc
 1 1 1 0.5 −0.0005 0.0004 0.0001 −0.0005 0.0008 −0.0004
 1 1 2 0.5 −0.0005 0.0005 −0.0001 −0.0005 0.0011 −0.0006
 Γ(0.5, 0.5) 1 1 0.5 −0.0006 0.0004 0.0002 −0.0006 0.0003 0.0003
 Γ(0.5, 0.5) 1 2 0.5 −0.0006 0.0006 −0.00004 −0.0006 0.0007 −0.0001
 1 1 1 2 −0.0034 0.0086 −0.0052 −0.0044 0.0102 −0.0063
 1 1 2 2 −0.0057 0.0105 −0.0048 −0.0067 0.0127 −0.0066
 Γ(0.5, 0.5) 1 1 2 −0.0066 0.0112 −0.0047 −0.0066 0.0088 −0.0022
 Γ(0.5, 0.5) 1 2 2 −0.0113 0.0174 −0.0061 −0.0113 0.0129 −0.0016
Root Mean Squared Error (RMSE)
 1 1 1 0.5 0.0282 0.0340 0.0270 0.0282 0.0347 0.0280
 1 1 2 0.5 0.0282 0.0304 0.0281 0.0282 0.0328 0.0310
 Γ (0.5, 0.5) 1 1 0.5 0.0260 0.0264 0.0220 0.0260 0.0284 0.0243
 Γ (0.5, 0.5) 1 2 0.5 0.0260 0.0241 0.0245 0.0260 0.0268 0.0270
 1 1 1 2 0.0837 0.0969 0.0733 0.0851 0.1004 0.0758
 1 1 2 2 0.0840 0.0935 0.0813 0.0855 0.0997 0.0852
 Γ (0.5, 0.5) 1 1 2 0.0702 0.0762 0.0606 0.0703 0.0797 0.0641
 Γ (0.5, 0.5) 1 2 2 0.0695 0.0693 0.0628 0.0696 0.0753 0.0682
  1. a Proposed in eq.(5)
  2. b Proposed in eq.(6)
  3. c Mean differences between true values and dynamic predicted values; True values are empirical probabilities of event numbers calculated from potential event times. Dynamic predicted values are the expectations of proposed DPOs