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Table 2 Comparison of different statistical tests in assessing whether a new biomarker has added value

From: On the assessment of the added value of new predictive biomarkers

Null hypothesis N 0=60 N 0=120 N 0=120 N 0=240 N 0=480
(Type I error) N 1=30 N 1=60 N 1=120 N 1=120 N 1=480
LR test 0.1033 0.0668 0.0585 0.0600 0.0546
Wald Test 0.0781 0.0608 0.0546 0.0571 0.0538
F test of ideal AUC 0.0495 0.0482 0.0481 0.0522 0.0515
Alt. Hypothesis N 0=60 N 0=120 N 0=120 N 0=240 N 0=480
(Power) N 1=30 N 1=60 N 1=120 N 1=120 N 1=480
LR test 0.5956 0.8569 0.9539 0.9896 1.0000
Wald Test 0.5394 0.8453 0.9506 0.9889 1.0000
F test of ideal AUC 0.5196 0.8514 0.9538 0.9915 1.0000
  1. Fraction of significant findings in 20,000 Monte Carlo trials at statistical significance cut-off of 0.05. On the top are the results for the null-hypothesis experiment where the fraction of significant findings is the observed type I error rate. At the bottom are the results for the alternative-hypothesis experiment where the fraction of significant findings is the statistical power.