Table 1.

Results from the simulation studies of Section 3.1. The true value of γ_x, the slope coefficient on x_i for predicting the clearance rates, is 0. From left the right, the columns represent the average value and standard deviation of the two-stage estimator across simulations; the average value and standard deviation of the Bayesian estimator across simulations; the percentage reduction in average loss (under squared error loss) attained by using the Bayesian estimator; the proportion of 95% intervals from the two-stage method that capture the true difference in means and length of those intervals; and the proportion of 95% intervals from the Bayesian method that capture the true difference in means and the length of those intervals

$\widehat{\mathbb{E}}[{\widehat{\gamma }}_x^{TS}]$(SD)	$\widehat{\mathbb{E}}[{\widehat{\gamma }}_x^B]$ (SD)	% Red. in Avg. Loss	$\widehat{\mathbb{P}}[{\gamma }_x\in C{I}_{95\%}^{TS}]$ (Length)	$\widehat{\mathbb{P}}[{\gamma }_x\in C{I}_{95\%}^B]$ (Length)
0.755 (0.261)	−0.05 (0.40)	74.5%	24.6% (1.04)	94.6% (1.57)