Table 2.

Simulation studies for three biomarkers. Results are based on the completed studies from 1000 simulated datasets. The empirical mean (empirical standard error) are given for each estimator of the β, excluding the intercept.

True ROC(0.2)	True β	β̂RB
nD = nD̄ = 400, mD = mD̄ = 200
0.55	$\left[\begin{array}{lll}0.13\hfill & 0.56\hfill & 0.48\hfill \end{array}\right]$	$\left[\begin{array}{lll}0.14(0.11)\hfill & 0.57(0.12)\hfill & 0.49(0.09)\hfill \end{array}\right]$
0.60	$\left[\begin{array}{lll}0.77\hfill & 0.18\hfill & 0.31\hfill \end{array}\right]$	$\left[\begin{array}{lll}0.79(0.13)\hfill & 0.18(0.12)\hfill & 0.31(0.10)\hfill \end{array}\right]$
0.65	$\left[\begin{array}{lll}1.13\hfill & -0.04\hfill & 0.22\hfill \end{array}\right]$	$\left[\begin{array}{lll}1.14(0.14)\hfill & -0.03(0.12)\hfill & 0.22(0.10)\hfill \end{array}\right]$
0.70	$\left[\begin{array}{lll}1.44\hfill & -0.22\hfill & 0.13\hfill \end{array}\right]$	$\left[\begin{array}{lll}1.46(0.14)\hfill & -0.22(0.12)\hfill & 0.14(0.10)\hfill \end{array}\right]$
nD = nD̄ = 200, mD = mD̄ = 100
0.55	$\left[\begin{array}{lll}0.13\hfill & 0.56\hfill & 0.48\hfill \end{array}\right]$	$\left[\begin{array}{lll}0.12(0.17)\hfill & 0.58(0.17)\hfill & 0.49(0.13)\hfill \end{array}\right]$
0.60	$\left[\begin{array}{lll}0.77\hfill & 0.18\hfill & 0.31\hfill \end{array}\right]$	$\left[\begin{array}{lll}0.79(0.18)\hfill & 0.19(0.16)\hfill & 0.32(0.14)\hfill \end{array}\right]$
0.65	$\left[\begin{array}{lll}1.13\hfill & -0.04\hfill & 0.22\hfill \end{array}\right]$	$\left[\begin{array}{lll}1.16(0.20)\hfill & -0.03(0.17)\hfill & 0.22(0.14)\hfill \end{array}\right]$
0.70	$\left[\begin{array}{lll}1.44\hfill & -0.22\hfill & 0.13\hfill \end{array}\right]$	$\left[\begin{array}{lll}1.48(0.21)\hfill & -0.23(0.18)\hfill & 0.14(0.15)\hfill \end{array}\right]$
nD = nD̄ = 100, mD = mD̄ = 50
0.55	$\left[\begin{array}{lll}0.13\hfill & 0.56\hfill & 0.48\hfill \end{array}\right]$	$\left[\begin{array}{lll}0.12(0.26)\hfill & 0.61(0.25)\hfill & 0.50(0.19)\hfill \end{array}\right]$
0.60	$\left[\begin{array}{lll}0.77\hfill & 0.18\hfill & 0.31\hfill \end{array}\right]$	$\left[\begin{array}{lll}0.81(0.27)\hfill & 0.20(0.25)\hfill & 0.32(0.20)\hfill \end{array}\right]$
0.65	$\left[\begin{array}{lll}1.13\hfill & -0.04\hfill & 0.22\hfill \end{array}\right]$	$\left[\begin{array}{lll}1.19(0.29)\hfill & -0.03(0.25)\hfill & 0.23(0.20)\hfill \end{array}\right]$
0.70	$\left[\begin{array}{lll}1.44\hfill & -0.22\hfill & 0.13\hfill \end{array}\right]$	$\left[\begin{array}{lll}1.54(0.32)\hfill & -0.23(0.27)\hfill & 0.14(0.21)\hfill \end{array}\right]$
nD = nD̄ = 50, mD = mD̄ = 25
0.55	$\left[\begin{array}{lll}0.13\hfill & 0.56\hfill & 0.48\hfill \end{array}\right]$	$\left[\begin{array}{lll}0.14(0.38)\hfill & 0.65(0.39)\hfill & 0.54(0.31)\hfill \end{array}\right]$
0.60	$\left[\begin{array}{lll}0.77\hfill & 0.18\hfill & 0.31\hfill \end{array}\right]$	$\left[\begin{array}{lll}0.86(0.42)\hfill & 0.21(0.38)\hfill & 0.35(0.30)\hfill \end{array}\right]$
0.65	$\left[\begin{array}{lll}1.13\hfill & -0.04\hfill & 0.22\hfill \end{array}\right]$	$\left[\begin{array}{lll}1.27(0.45)\hfill & -0.04(0.40)\hfill & 0.24(0.32)\hfill \end{array}\right]$
0.70	$\left[\begin{array}{lll}1.44\hfill & -0.22\hfill & 0.13\hfill \end{array}\right]$	$\left[\begin{array}{lll}1.63(0.75)\hfill & -0.23(0.62)\hfill & 0.13(0.50)\hfill \end{array}\right]$