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. 2019 Nov 23;22(3):558–574. doi: 10.1093/biostatistics/kxz052

Table 2.

Prediction accuracy at landmark times of the proposed nonparametric kernel Nelson-Aalen estimator (NPNA) compared to the estimator that ignores landmarking (NPNA estimator assuming Inline graphic, denoted as NPNAInline graphic), and the Kaplan–Meier estimator that ignores covariate influence (KM) and modified to adjust for landmarking

  KM NPNA NPNAInline graphic NPNA-KMInline graphic NPNA-NPNAInline graphic
AUC, Setting 1: Inline graphic
Inline graphic 51.2854 64.4163 61.4384 (7.4368, 18.8251) (Inline graphic0.6716, 6.6274)
Inline graphic 55.1505 64.5175 62.8209 (5.0543, 13.6799) (Inline graphic0.3956, 3.7888)
Inline graphic 57.652 65.9349 64.7988 (4.0615, 12.5044) (Inline graphic0.5791, 2.8514)
  BS, Setting 1: Inline graphic
Inline graphic 13.5879 13.084 15.2423 (Inline graphic0.9247, Inline graphic0.0831) (Inline graphic2.8356, Inline graphic1.4809)
Inline graphic 23.3485 22.0813 23.2354 (Inline graphic2.0813, Inline graphic0.4531) (Inline graphic1.7654, Inline graphic0.5428)
Inline graphic 24.369 22.9809 23.6991 (Inline graphic2.3385, Inline graphic0.4377) (Inline graphic1.2936, Inline graphic0.1428)
  AUC, Setting 1: Inline graphic
Inline graphic 56.718 64.7069 61.1501 (3.0307, 12.9472) (0.204, 6.9096)
Inline graphic 58.876 65.9604 63.6971 (2.7056, 11.4633) (Inline graphic0.2317, 4.7584)
  BS, Setting 1: Inline graphic
Inline graphic 19.0458 18.2571 22.9205 (Inline graphic1.5142, Inline graphic0.0632) (Inline graphic5.7315, Inline graphic3.5954)
Inline graphic 23.6235 22.4671 25.2915 (Inline graphic2.1805, Inline graphic0.1323) (Inline graphic3.833, Inline graphic1.816)
  AUC, Setting 2: Inline graphic
Inline graphic 68.672 82.9663 83.0024 (9.9418, 18.6468) (Inline graphic1.3709, 1.2988)
Inline graphic 69.2237 82.9825 83.0218 (10.1455, 17.372) (Inline graphic0.5834, 0.5048)
Inline graphic 70.476 83.3167 83.3574 (8.9964, 16.685) (Inline graphic0.4441, 0.3628)
  BS, Setting 2: Inline graphic
Inline graphic 15.7572 12.7593 12.8608 (Inline graphic4.0232, Inline graphic1.9726) (Inline graphic0.5754, 0.3724)
Inline graphic 21.0976 16.6319 16.5867 (Inline graphic5.8972, Inline graphic3.0343) (Inline graphic0.2675, 0.3579)
Inline graphic 18.859 15.3791 15.3327 (Inline graphic4.7729, Inline graphic2.1868) (Inline graphic0.1358, 0.2287)
  AUC, Setting 2: Inline graphic
Inline graphic 66.1443 78.9501 79.3607 (6.4, 19.2115) (Inline graphic4.5741, 3.7529)
Inline graphic 66.8676 79.7724 79.9264 (9.0036, 16.806) (Inline graphic1.3163, 1.0083)
Inline graphic 68.1474 80.6619 80.7738 (8.7062, 16.3229)  
  BS, Setting 2: Inline graphic
Inline graphic 9.2491 8.3604 10.3928 (Inline graphic1.5438, Inline graphic0.2337) (Inline graphic3.2139, Inline graphic0.8508)
Inline graphic 20.6777 17.2407 17.3808 (Inline graphic4.8153, Inline graphic2.0585) (Inline graphic0.9188, 0.6387)
Inline graphic 20.6045 17.2658 17.1442 (Inline graphic4.6848, Inline graphic1.9927) (Inline graphic0.299, 0.5421)

Inline graphic These columns correspond to the 95% bootstrap confidence intervals for the differences between estimators. We report the AUC and the BS for Inline graphic at specified Inline graphic and landmark times Inline graphic. Results are summarized over 200 simulations with 40% censoring. Note that better prediction accuracy is indicated by higher AUC and lower BS. Sample size is 2000. All results are multiplied by 100.