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Table 4 Alternative Model Simulation

From: Design considerations in a sib-pair study of linkage for susceptibility loci in cancer

Model A – no heterogeneity:
  Affected Sibs Unaffected Sibs       
Parents Total Sampled Total Sampled Zc Zp ARE(Zc) ARE(Zp) Nc(80%) Np(80%)
0 2 2 2 0 3.19   100   304  
0 2 2 2 1 2.70 2.42 72 38 424 528
0 2 2 2 2 3.03 3.17 90 49 337 308
0 3 2 2 0 6.09   364   83  
0 3 2 2 1 6.46 6.00 410 236 74 86
0 3 2 2 2 6.12 6.47 368 206 83 74
2 2 2 2   2.88   41   373  
2 2 2 2 1 3.17 2.69 49 28 308 427
2 2 2 2 2 3.17 3.33 49 36 308 279
Model B – less common, equally penetrant locus:
0 2 2 2 0 2.37   100   550  
0 2 2 2 1 3.04 2.88 165 98 334 373
0 2 2 2 2 2.73 2.81 133 70 415 391
0 3 2 2 0 4.66   387   142  
0 3 2 2 1 5.29 5.11 498 310 110 118
0 3 2 2 2 4.86 5.18 421 239 131 115
2 2 2 2 0 2.73   66   415  
2 2 2 2 1 2.46 2.22 54 35 511 627
2 2 2 2 2 2.92 2.95 76 52 363 355
Model C – equally common, equally penetrant locus:
0 2 2 2 0 2.38   100   546  
0 2 2 2 1 1.93 1.95 66 45 830 813
0 2 2 2 2 2.33 2.36 96 49 569 555
0 3 2 2 0 3.45   210   260  
0 3 2 2 1 3.47 3.33 213 131 257 279
0 3 2 2 2 3.48 3.84 214 130 255 210
2 2 2 2 0 2.26   45   605  
2 2 2 2 1 2.56 2.44 58 42 472 519
2 2 2 2 2 2.22 2.14 44 27 627 675
  1. Mean Z score, asymptotic relative efficiency per genotype (ARE–see text), and sample size required to attain 80% power for two-point linkage (θ = 0.05) for predisposition to colorectal cancer with a baseline risk of 0.018, a relative risk to carriers of 20, allele frequency of 0.003, with a lifetime penetrance of 0.27, under 3 different heterogeneity models: A) no heterogeneity; B) an equally penetrant, less common (allele frequency 0.001) unlinked predisposing locus; C) an equally penetrant, equally common unlinked predisposing locus. All results based on 500 simulated families and 20 replicate simulations per parameter set.
  2. Zc mean concordant test; Zp mean paired test; ARE(Zc) asymptotic relative efficiency concordant test; ARE(Zp) asymptotic relative efficiency paired test; Nc(80%) number of families required for 80% power using concordant test; Np(80%) number of families required for 80% power using paired test.