Table 2.

Measures of improvement in prediction ×100 when risk models are fit to a training dataset of 50 observations and assessed on a test dataset of 5000 observations where P(D = 1) = 0.5. The linear logistic regression models fit to the training data are (i) baseline logitP(D = 1|X) = α₀ + α₁X; (ii) model(X, Y₁) : logitP(D = 1|X, Y₁) = β₀ + β₁X + β₂Y₁; (iii) model(X, Y₁, Y₂) : logitP(D = 1|X, Y₁, Y₂) = γ₀ + γ₁X + γ₂Y₁ + γ₃Y₂. Data generation is described in Supplementary Materials. Shown are averages over 1000 simulations. Neither Y₁ nor Y₂ are informative — the true values of β₂, γ₂, and γ₃ are zero.

Two Uninformative Markers
Average PerformanceIncrement ×100
	NRI		ΔROC(0.2)		ΔAUC		Δ Brier		ΔSNB(ρ)
Model	(X, Y1)	(X, Y1, Y2)	(X, Y1)	(X, Y1, Y2)	(X, Y1)	(X, Y1, Y2)	(X, Y1)	(X, Y1, Y2)	(X, Y1)	(X, Y1, Y2)
AUCX
0.60	0.61	0.78	−1.81	−2.91	−1.30	−2.18	−0.55	−1.12	−1.84	−3.06
0.70	2.08	3.63	−2.63	−4.55	−1.66	−2.95	−0.52	−1.08	−2.44	−4.36
0.80	6.18	10.60	−1.75	−3.50	−0.95	−1.89	−0.47	−0.96	−1.61	−3.14
0.90	17.83	28.00	−1.33	−2.57	−0.65	−1.27	−0.51	−1.03	−1.36	−2.63