Table 2.

Simulation results for the improvement in predictive accuracy associated with a biomarker X for the sub-optimal linear combination of X and Z and for the optimal combination of X and Z in settings (1) and (2). Summaries presented as the average estimate across 1000 iterations (`Mean') and the average standard error obtained as the average standard deviation of estimates from 200 bootstrap samples (`SE'); p value obtained from a hypothetical two-sided, one-sample z test based on average estimate and average standard error.

	Mean (SE)	p
Setting (1): M = 1.0X + 1.5X2 + 1.0Z
Difference in AUC
{X, Z} versus {Z}	0.038 (0.028)	0.18
{X,X2,Z} versus {Z}	0.168 (0.030)	< 0.01
NRI
{X, Z} versus {Z}	7.3% (13.5%)	0.59
{X,X2,Z} versus {Z}	37.7% (8.3%)	< 0.01
Setting (2): M = 0.5X + 0.5Z + 1.5X × Z
Difference in AUC
{X, Z} versus {Z}	0.043 (0.030)	0.16
{X,Z,X × Z} versus {Z}	0.183 (0.043)	< 0.01
NRI
{X, Z} versus {Z}	19.3% (28.9%)	0.50
{X,Z,X × Z} versus {Z}	41.3% (10.7%)	< 0.01