Table 1.

The posterior mean estimates and average standard deviations (in parentheses) of the joint model based on 200 simulations at each three levels of risk.

P	E	${\mathit{\alpha }}_{\mathit{z}},{\mathit{\alpha }}_{\mathit{o}}$	$1/\sqrt{{\widehat{\mathit{\tau }}}_{\mathit{\gamma }}}$	$\widehat{\mathit{\phi }}$	$\mathit{\beta }$
Constant risk $\left(\mathbf{1}/\sqrt{{\mathit{\tau }}_{\mathit{\gamma }}}=\mathbf{0} \& \mathit{\phi }=\mathbf{0}\right)$
0.50	1	−0.02(0.10), −0.06(0.12)	0.17(0.14)	0.39(0.27)	1.12(0.29)
	5	0.16(0.10), −0.03(0.03)	0.07(0.04)	0.36(0.29)	0.98(0.30)
	15	0.16(0.10), 0.01(0.02)	0.02(0.008)	0.25(0.23)	0.93(0.32)
	60	0.12(0.10), −0.01(0.01)	0.01(0.004)	0.26(0.24)	0.91(0.33)
	200	−0.07(0.10), 0.004(0.006)	0.02(0.02)	0.36(0.23)	0.85(0.36)
0.70	1	−0.91(0.11), −0.21(0.17)	0.05(0.02)	0.28(0.23)	0.99(0.31)
	5	−0.53(0.11), 0.001(0.04)	0.03(0.01)	0.26(0.24)	0.95(0.32)
	15	−0.82(0.11), −0.002(0.03)	0.07(0.05)	0.21(0.22)	0.96(0.32)
	60	−0.85(0.11), −0.02(0.01)	0.02(0.01)	0.27(0.26)	0.95(0.32)
	200	−1.03(0.12), −0.01(0.008)	0.01(0.01)	0.31(0.28)	0.92(0.32)
Spatially unstructured risk $\left(\mathbf{1}/\sqrt{{\mathit{\tau }}_{\mathit{\gamma }}}=\mathbf{0.5} \& \mathit{\phi }=\mathbf{0}\right)$
0.50	1	0.12(0.11), 0.08(0.11)	0.39(0.04)	0.32(0.25)	1.01(0.30)
	5	−0.11(0.11), −0.20(0.07)	0.40(0.03)	0.07(0.08)	1.11(0.26)
	15	0.16(0.11), −0.18(0.05)	0.49(0.0.4)	0.06(0.07)	1.12(0.21)
	60	−0.04(0.11), −0.12(0.05)	0.45(0.04)	0.05(0.05)	1.13(0.14)
	200	0.07(0.11), −0.13(0.04)	0.43(0.05)	0.03(0.03)	1.32(0.08)
0.70	1	−1.01(0.12), −0.43(0.26)	0.50(0.03)	0.14(0.13)	1.28(0.26)
	5	−0.82(0.12), −0.20(0.10)	0.51(0.04)	0.06(0.08)	1.20(0.25)
	15	−0.83(0.12), −0.15(0.07)	0.48(0.03)	0.08(0.14)	1.06(0.22)
	60	−0.70(0.11), 0.02(0.05)	0.48(0.02)	0.08(0.02)	1.18(0.10)
	200	−0.98(0.12), −0.16(0.06)	0.42(0.04)	0.06(0.07)	1.17(0.18)
Spatially structured risk $\left(\mathbf{1}/\sqrt{{\tau }_{\gamma }}=0.5 \& \mathit{\phi }=\mathbf{1}\right)$
0.50	1	0.08(0.11), −0.08(0.14)	0.34(0.04)	0.18(0.17)	1.11(0.27)
	5	0.19(0.11), −0.06(0.05)	0.52(0.03)	0.89(0.08)	1.60(0.21)
	15	0.02(0.11), −0.10(0.03)	0.55(0.03)	0.84(0.11)	1.46(0.22)
	60	−0.02(0.11), −0.06(0.02)	0.53(0.03)	0.89(0.08)	1.37(0.21)
	200	−0.01(0.11), −0.07(0.02)	0.48(0.04)	0.95(0.05)	1.48(0.21)
0.70	1	−0.92(0.12), −0.28(0.20)	0.36(0.02)	0.26(0.25)	1.04(0.31)
	5	−0.78(0.11), −0.08(0.07)	0.57(0.04)	0.66(0.22)	1.16(0.26)
	15	−0.85(0.11), −0.04(0.05)	0.53(0.04)	0.62(0.20)	1.44(0.23)
	60	−0.95(0.12), −0.09(0.04)	0.51(0.04)	0.87(0.09)	1.43(0.22)
	200	−0.82(0.11), −0.06(0.04)	0.56(0.03)	0.87(0.10)	1.37(0.21)