Table 4:

Risk prediction and accuracy measurement of simulation. The reported values are absolute error to the target truth and ratio of standard deviation. “Interval”: absolute risk intervals defined in (4); “Risk”: averaged risk within each interval; “Cases”: predicted number of cases. “True” represents risks and number of cases from the well calibrated external model; “Proposed” stands for the proposed method; “Ad Hoc” stands for the Ad Hoc method; “ratio of $\widehat{\text{sd}}$” stands for the ratio of standard deviation of the proposed method to that of the Ad Hoc method.

Intervals	Risk				Cases
	True	Proposed	Ad Hoc	ratio of $\widehat{\mathbf{\text{sd}}}$	True	Proposed	Ad Hoc	ratio of $\widehat{\mathbf{\text{sd}}}$
$\phi (S=1,\mathbf{\text{x}})\in [2.28\%,23.34\%)$	0.054	0.004	0.007	0.99	2194	37	52	0.65
$\phi (S=2,\mathbf{\text{x}})\in [6.18\%,45.51\%)$	0.134	0.005	0.003	0.99	8011	247	711	0.61
$\phi (S=1,\mathbf{\text{x}})\in [2.28\%,5.20\%)$	0.035	0.003	0.005	0.44	930	46	54	0.89
$\phi (S=1,\mathbf{\text{x}})\in [5.20\%,7.92\%)$	0.063	0.004	0.008	0.50	581	25	24	0.85
$\phi (S=1,\mathbf{\text{x}})\in [7.92\%,11.91\%)$	0.097	0.008	0.014	0.46	423	1	3	0.81
$\phi (S=1,\mathbf{\text{x}})\in [11.91\%,23.34\%)$	0.162	0.013	0.019	0.22	260	32	28	0.56
$\phi (S=2,\mathbf{\text{x}})\in [6.18\%,13.09\%)$	0.093	0.004	0.003	0.48	3378	37	414	0.83
$\phi (S=2,\mathbf{\text{x}})\in [13.09\%,19.11\%)$	0.158	0.005	0.003	0.49	2074	64	203	0.73
$\phi (S=2,\mathbf{\text{x}})\in [19.11\%,27.06\%)$	0.229	0.011	0.007	0.42	1623	122	38	0.73
$\phi (S=2,\mathbf{\text{x}})\in [27.06\%,45.51\%)$	0.349	0.014	0.007	0.21	936	25	54	0.47