# Table 3 The power comparisons based on 500 replicates. The underlying parameters are (β0, β1, β2) = (1, 1, 1), and ($σ a 1 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWFdpWCdaqhaaWcbaGaemyyaeMaeGymaedabaGaeGOmaidaaaaa@31D0@$, $σ a 2 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacqWFdpWCdaqhaaWcbaGaemyyaeMaeGOmaidabaGaeGOmaidaaaaa@31D2@$, σ2, α) = (2, 1, 7, 0.5). The assumed s(t) is labeled as "c" for constant, "l" for s0 + s1t, and "q" for s0 + s1t + s2t2.

200 sib pairs 400 sib pairs
T $h g 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGObaAdaqhaaWcbaGaem4zaCgabaGaeGOmaidaaaaa@307B@$ Assumed s(t) Significance level Significance level
0.05 0.01 0.001 0.0001 0.05 0.01 0.001 0.0001
True s(t) = 1 + 0.1t
5 0.392 c 0.77 0.56 0.26 0.09 0.97 0.84 0.62 0.36
l 0.90 0.78 0.45 0.24 0.99 0.95 0.86 0.74
q 0.86 0.64 0.39 0.19 0.99 0.95 0.84 0.67
4 0.353 c 0.68 0.42 0.16 0.04 0.89 0.72 0.44 0.23
l 0.75 0.52 0.23 0.07 0.95 0.87 0.65 0.47
q 0.66 0.42 0.18 0.04 0.93 0.81 0.59 0.38
2 0.272 c 0.43 0.20 0.04 0.01 0.63 0.40 0.19 0.06
l 0.34 0.16 0.04 0.00 0.59 0.37 0.13 0.04
q 0.20 0.06 0.02 0.00 0.42 0.23 0.07 0.02
5 0.2 * 0.77 0.54 0.2 0.06 0.97 0.83 0.60 0.34
1 0.2 ** 0.33 0.13 0.03 0.01 0.60 0.35 0.06 0.00
True s(t) = 1
5 0.276 c 0.49 0.25 0.07 0.01 0.74 0.48 0.20 0.06
l 0.33 0.15 0.02 0.00 0.60 0.33 0.10 0.03
q 0.19 0.07 0.01 0.00 0.51 0.25 0.09 0.02
4 0.258 c 0.45 0.21 0.05 0.01 0.67 0.42 0.15 0.03
l 0.27 0.11 0.02 0.00 0.60 0.33 0.09 0.01
q 0.16 0.05 0.01 0.00 0.51 0.25 0.05 0.01
2 0.220 c 0.35 0.12 0.02 0.00 0.50 0.24 0.03 0.01
l 0.17 0.03 0.01 0.00 0.32 0.14 0.01 0.01
q 0.08 0.01 0.01 0.00 0.18 0.05 0.01 0.01
5 0.2 * 0.46 0.19 0.04 0.01 0.71 0.46 0.19 0.05
1 0.2 ** 0.25 0.07 0.01 0.00 0.46 0.17 0.03 0.01
True s(t) = exp(t)/(1 + exp(t))
5 0.239 c 0.40 0.15 0.02 0.00 0.59 0.36 0.15 0.03
l 0.42 0.22 0.04 0.00 0.62 0.41 0.14 0.06
q 0.35 0.17 0.03 0.00 0.69 0.48 0.18 0.05
4 0.215 c 0.35 0.15 0.02 0.00 0.51 0.25 0.06 0.01
l 0.37 0.16 0.03 0.01 0.61 0.32 0.11 0.03
q 0.24 0.10 0.02 0.00 0.55 0.31 0.11 0.02
2 0.155 c 0.20 0.04 0.01 0.00 0.33 0.14 0.02 0.00
l 0.22 0.07 0.00 0.00 0.35 0.14 0.03 0.01
q 0.09 0.02 0.00 0.00 0.21 0.06 0.02 0.01
5 0.2 * 0.40 0.14 0.03 0.00 0.52 0.31 0.11 0.03
1 0.2 ** 0.15 0.02 0.01 0.00 0.22 0.10 0.00 0.00
1. *based on the average measurement; ** based on one measurement.