Table 1.

Power calculations of the Weighted Cumulative Geographic Residual Test and Weighted Spatial Scan Statistic for different weights and effect size.

Scenario					CumGeoRes			Spatial Scan*
	Weight		Var ${\sigma }_Z^2$	c	Pow	Sens	Accuracy	Pow	Sens	Accuracy
	η0	ηZ
Change Effect Size	1	1	1	0.5	0.20	0.76	0.45	0.25	0.60	0.50
	1	1	1	1.0	0.68	0.90	0.46	0.88	0.92	0.89
	1	1	1	1.1	0.77	0.91	0.46	0.93	0.82	0.84
	1	1	1	1.2	0.86	0.93	0.45	0.98	0.88	0.89
	1	1	1	1.3	0.90	0.95	0.43	0.99	0.91	0.92
	1	1	1	1.4	0.94	0.97	0.41	0.99	0.93	0.94
	1	1	1	1.5	0.96	0.98	0.40	1.00	1.00	1.00
	1	1	1	2.0	1.00	1.00	0.33	1.00	1.00	1.00
	1	1	1	3.0	1.00	1.00	0.30	1.00	1.00	1.00
Change Z* Weight	1	2	1	1.5	1.00	1.00	0.32	1.00	0.99	0.99
	1	10	1	1.5	1.00	1.00	0.33	1.00	0.97	0.95
	1	100	1	1.5	0.17	0.49	0.56	0.34	0.65	0.56
	1	1000	1	1.5	0.03	0.37	0.67	0.12	0.43	0.40
Change Z*c Weight	2	1	1	1.5	0.57	0.88	0.47	0.99	0.99	0.98
	10	1	1	1.5	0.07	0.57	0.32	0.08	0.56	0.44
	100	1	1	1.5	0.05	0.25	0.13	0.05	0.21	0.14
	1000	1	1	1.5	0.05	0.22	0.13	0.05	0.19	0.40
Change Z* Variance	1	1	2	1.5	0.91	0.97	0.42	0.99	0.95	0.98
	1	1	10	1.5	0.55	0.89	0.48	0.76	0.66	0.90
	1	1	100	1.5	0.15	0.78	0.57	0.44	0.41	0.75
	1	1	1000	1.5	0.08	0.77	0.61	0.34	0.35	0.67
Change All Weights	10	10	1	1.0	0.70	0.89	0.47	0.88	0.75	0.76
	100	100	1	1.0	0.66	0.89	0.46	0.85	0.73	0.74
	5000	5000	1	1.0	0.67	0.91	0.46	0.84	0.72	0.73
	10000	10000	1	1.0	0.65	0.90	0.47	0.88	0.76	0.77

^*Results for Spatial Scan Statistic when available were done and reported by Huang et al. (2009). Otherwise, were performed through simulations as outlined for the Cumulative Geographic Residual Method.

Model Framework: $Y_i\mid Z_i^{\ast }\sim N(c\sqrt{2}{Z}_i^{\ast },{\sigma }_Z^2{Z}_i^{\ast }+Z_i^{\ast c}),w_i\mid Z_i^{\ast }={\eta }_0{Z}_i^{\ast c}+{\eta }_Z{Z}_i^{\ast }$, and $Z_i^{\ast c}=1-Z_i^{\ast }$

$\text{power}=\frac{1}{1000}{\displaystyle \sum _{j=1}^{1000}}I(P_j<0.05)$

$\text{sensitivity}=\frac{1}{1000}{\displaystyle \sum _{j=1}^{1000}}I(P_j<0.05)I(\{{\mathit{CritReg}}_j\cap Z^{\ast }\}\ne \varnothing )$

$\text{accuracy}=\frac{1}{1000}{\displaystyle \sum _{j=1}^{1000}}I(P_j<0.05)\frac{1}{\mid {\mathit{CritReg}}_j\mid }{\sum }_{k=1}^{\mid {\mathit{CritReg}}_j\mid }I(\{{\mathit{CritReg}}_{jk}\in Z^{\ast }\}\ne \varnothing )$