Table 3.
Averaged estimates of β over 1,000 Monte Carlo replications along with asymptotic standard errors (s.e.) and type I error rates α for sample size 50, 100, 2000, with about 25% missing data at post-treatment based on ML for linear mixed-effects model, and GEE, WGEE and AWGEE for distribution-free linear model, with true β0 = 1 and β1 = 1 and within-subject correlation ρ = 0.1.
| Methods | Weight Function | Prediction Model | Normal Distribution | Chi-square Distribution | ||||
|---|---|---|---|---|---|---|---|---|
| β0 (s.e.) | β1 (s.e.) | α | β0 (s.e.) | β1 (s.e.) | α | |||
| Sample size = 50 | ||||||||
| ML | 1.00(0.21) | 0.98(0.30) | 0.06 | 1.00(0.22) | 1.10(0.23) | 0.07 | ||
| GEE | 1.01(0.21) | 1.05(0.31) | 0.05 | 1.00(0.20) | 1.05(0.30) | 0.05 | ||
| WGEE | Right | 0.99(0.21) | 1.00(0.33) | 0.08 | 1.01(0.21) | 1.00(0.31) | 0.06 | |
| Wrong | 1.01(0.21) | 1.04(0.31) | 0.06 | 1.00(0.20) | 1.04(0.30) | 0.06 | ||
| AWGEE | Right | Right | 1.00(0.21) | 1.00(0.39) | 0.07 | 1.00(0.21) | 1.01(0.38) | 0.07 |
| Wrong | Right | 1.01(0.21) | 0.99(0.32) | 0.08 | 1.01(0.20) | 0.99(0.32) | 0.09 | |
| Right | Wrong | 0.99(0.21) | 1.00(0.40) | 0.06 | 0.99(0.21) | 1.00(0.39) | 0.06 | |
| Wrong | Wrong | 1.01(0.21) | 1.05(0.33) | 0.07 | 1.01(0.21) | 1.05(0.34) | 0.07 | |
| Sample size = 100 | ||||||||
| ML | 1.00(0.15) | 1.00(0.21) | 0.06 | 1.00(0.15) | 1.09(0.17) | 0.06 | ||
| GEE | 1.00(0.15) | 1.04(0.22) | 0.06 | 1.00(0.15) | 1.05(0.22) | 0.05 | ||
| WGEE | Right | 1.00(0.15) | 1.00(0.23) | 0.05 | 1.00(0.15) | 1.00(0.22) | 0.06 | |
| Wrong | 1.00(0.15) | 1.04(0.22) | 0.07 | 1.00(0.15) | 1.05(0.22) | 0.05 | ||
| AWGEE | Right | Right | 1.00(0.15) | 1.00(0.29) | 0.04 | 1.00(0.15) | 1.00(0.30) | 0.04 |
| Wrong | Right | 1.00(0.15) | 1.00(0.23) | 0.05 | 1.00(0.15) | 1.00(0.22) | 0.06 | |
| Right | Wrong | 1.00(0.15) | 1.01(0.30) | 0.04 | 1.00(0.15) | 1.00(0.30) | 0.04 | |
| Wrong | Wrong | 1.00(0.15) | 1.04(0.24) | 0.07 | 1.00(0.15) | 1.06(0.23) | 0.07 | |
| Sample size = 2000 | ||||||||
| ML | 1.00(0.033) | 1.00(0.049) | 0.06 | 1.00(0.035) | 1.10(0.038) | 0.59 | ||
| GEE | 1.00(0.033) | 1.04(0.049) | 0.14 | 1.00(0.033) | 1.05(0.049) | 0.21 | ||
| WGEE | Right | 1.00(0.033) | 1.00(0.054) | 0.05 | 1.00(0.033) | 1.00(0.050) | 0.05 | |
| Wrong | 1.00(0.033) | 1.04(0.049) | 0.12 | 1.00(0.033) | 1.05(0.049) | 0.17 | ||
| AWGEE | Right | Right | 1.00(0.033) | 1.00(0.052) | 0.05 | 1.00(0.033) | 1.00(0.051) | 0.05 |
| Wrong | Right | 1.00(0.033) | 1.00(0.048) | 0.06 | 1.00(0.033) | 1.00(0.047) | 0.06 | |
| Right | wrong | 1.00(0.033) | 1.00(0.053) | 0.05 | 1.00(0.033) | 1.00(0.052) | 0.05 | |
| Wrong | Wrong | 1.00(0.033) | 1.04(0.049) | 0.12 | 1.00(0.033) | 1.05(0.048) | 0.15 | |