Table 1.

Candidate Sampling Designs from Case Study Examples

Case Study 1 (Cross-Sectional): ψ = 1.5 (β3=0.4055) 2-sided test with size (α=0.05) and power (1−β=0.80)
Design	Random Sampling		Covariate Dependent Sampling (Dependent on Z)			Outcome Dependent Sampling
	Cost	Sample Sizes	Cost		Sample Sizes	Cost	Sample Sizes
Classic X	$15,970,150; n = 7210
2-Stage Z_Quest/X ρ=0.288	$8,730,190 (54.7%)	n0 = 96646 n1= 869	$8,710,604 (54.5%)		n0= 92734 n1=990	$7,350,710 (46.0%)	n0= 11751 n1= 1335
2-Stage Z_SF/X ρ=0.892	$5,518,340 (34.6%)	n0= 9505 n1= 90	$8,305,180 (52.0%)		n0=9390 n1=135	$7,082,560 (44.3%)	n0= 7595 n1= 380
Case Study 2 (Cross-Sectional): ψ = 1.5 (β3=0.4055) 2-sided test with size (α =0.05) and power (1−β =0.80)
Design	Random Sampling		Covariate Dependent Sampling (Dependent on E)			Outcome Dependent Sampling
	Cost	Sample Sizes	Cost		Sample Sizes	Cost	Sample Sizes
Classic X	$13,446,000; n = 7210
2-Stage Z_Quest/X ρ=0.288	$8,405,620 (62.5%)	n0= 93266 n1= 991	$5,641,020 (42.0%)		n0= 53382 n1=1029	$2,503,640 (18.6%)	n0 = 16992 n1 = 721
2-Stage Z_SF/X ρ=0.892	$5,015,670 (37.3%)	n0 = 9489 n1= 96	$4,918,830 (36.6%)		n0 = 9218 n1 =128	$4,424,380 (32.9%)	n0= 7595 n1 = 380
Case Study 3 (Longitudinal): β3=−0.01 2-sided test with size (α=0.05) and power (1−β=0.80)
Design	Random Sampling			Covariate Dependent Sampling (Dependent on Z)		Outcome Dependent Sampling
	Cost	Sample Sizes		Cost	Sample Sizes	Cost	Sample Sizes
Classic X	$25,189,225; n = 11,321
2-Stage Z_Quest/X ρ=0.288	$15,477,600 (61.4%)	n0=100,000 n1=3,431		$15,491,200 (61.5%)	n0=99,998 n1 =3,438	$25,443,626 (101.1%)	n0 =12,254 n1 =11,202
2-Stage Z_SF/X ρ=0.892	$8,503,830 (33.8%)	n0 =14,483 n1=107		$12,795,000 (50.8%)	n0=14,385 n1=155	$12,794,824 (50.8%)	n0=14,389 n1=152