Table 1.
Average estimated standard error [−] (×10−1) and the empirical standard error or the standard deviation of the parameter estimates (×10−1) across 1000 replications (−) of the simulation. All parameter estimates were unbiased (i.e., less than 4 percent bias for all estimators) and so they are not shown. Data for the original cohorts were generated from a marginalized transition model with parameter values shown in the first column of the table. From the original cohort, the random sampling design, and the ODS designs, sampled a total of 250 subjects from the original cohort of 1000. Estimation used maximum likelihood (ML) for the random sampling design and both ACML and WEE for the ODS designs. The value ni corresponds to the distribution of cluster sizes, (N0, N(0,ni), Nni) is the average number subjects allocated to each of the three response strata (Σjyij = 0, 0 < Σj yij < ni, Σjyij = ni), and denotes the design with the average number of subjects sampled within the three strata.
| (β0, β1, β2, β3, α1) | ni | (N0, N(0,ni), Nni) | ( ) | Estimation Procedure | β0 | β1 | β2 | β3 | β1 |
|---|---|---|---|---|---|---|---|---|---|
| (−1.5, −0.15, 3, 0.15, 2) | 4 | (475, 375, 150) | Random Sampling | ML | [1.81] (1.77) | [0.94] (0.93) | [3.65] (3.80) | [1.80] (1.85) | [2.29] (2.35) |
| D[0, 250, 0] | ACML | [2.69] (2.76) | [0.58] (0.59) | [5.17] (5.27) | [1.10] (1.06) | [2.93] (2.82) | |||
| D[15, 220, 15] | ACML | [1.93] (1.85) | [0.62] (0.60) | [3.36] (3.31) | [1.17] (1.18) | [2.15] (2.02) | |||
| D[15, 220, 15] | WEE | [2.35] (2.32) | [0.63] (0.62) | [4.00] (4.27) | [1.22] (1.23) | [2.69] (2.74) | |||
| D[30, 190, 30] | ACML | [1.75] (1.72) | [0.66] (0.63) | [3.10] (2.95) | [1.26] (1.20) | [2.02] (1.95) | |||
| D[30, 190, 30] | WEE | [1.87] (1.85) | [0.67] (0.63) | [3.40] (3.35) | [1.29] (1.24) | [2.22] (2.22) | |||
| U(3,7) | (440, 425, 135) | Random Sampling | ML | [1.72] (1.79) | [0.66] (0.65) | [3.40] (3.39) | [1.20] (1.19) | [2.05] (2.00) | |
| D[0, 250, 0] | ACML | [2.21] (2.20) | [0.44] (0.44) | [4.12] (4.16) | [0.81] (0.81) | [2.26] (2.29) | |||
| D[15, 220, 15] | ACML | [1.79] (1.78) | [0.47] (0.45) | [3.13] (3.04) | [0.85] (0.82) | [1.85] (1.84) | |||
| D[15, 220, 15] | WEE | [2.25] (2.30) | [0.53] (0.52) | [3.74] (4.05) | [0.93] (0.93) | [2.24] (2.32) | |||
| D[30, 190, 30] | ACML | [1.67] (1.77) | [0.50] (0.50) | [2.96] (3.12) | [0.91] (0.93) | [1.79] (1.81) | |||
| D[30, 190, 30] | WEE | [1.81] (1.87) | [0.52] (0.53) | [3.25] (3.48) | [0.94] (0.97) | [1.93] (1.95) | |||
| (−1.85, −0.15, 1, 0.15, 1.5) | 10 | (400, 600, 0) | Random Sampling | ML | [1.61] (1.64) | [0.35] (0.35) | [2.62] (2.61) | [0.51] (0.53) | [1.51] (1.51) |
| D[0, 250, 0] | ACML | [1.49] (1.49) | [0.23] (0.24) | [2.04] (2.01) | [0.34] (0.34) | [1.18] (1.17) | |||
| D[15, 235, 0] | ACML | [1.59] (1.58) | [0.28] (0.29) | [2.33] (2.30) | [0.41] (0.43) | [1.35] (1.32) | |||
| D[15, 235, 0] | WEE | [1.93] (1.91) | [0.28] (0.29) | [2.82] (2.91) | [0.41] (0.43) | [1.59] (1.59) | |||
| D[45, 205, 0] | ACML | [1.52] (1.53) | [0.30] (0.30) | [2.37] (2.36) | [0.44] (0.44) | [1.37] (1.37) | |||
| D[45, 205, 0] | WEE | [1.55] (1.56) | [0.30] (0.30) | [2.44] (2.42) | [0.44] (0.44) | [1.40] (1.40) | |||
| U(5,15) | (400, 600, 0) | Random Sampling | ML | [1.54] (1.48) | [0.32] (0.31) | [2.48] (2.45) | [0.44] (0.45) | [1.53] (1.49) | |
| D[0, 250, 0] | ACML | [1.50] (1.47) | [0.22] (0.21) | [2.04] (1.96) | [0.30] (0.29) | [1.19] (1.19) | |||
| D[15, 235, 0] | ACML | [1.58] (1.54) | [0.26] (0.26) | [2.30] (2.32) | [0.36] (0.37) | [1.36] (1.36) | |||
| D[15, 235, 0] | WEE | [1.94] (1.90) | [0.28] (0.28) | [2.90] (3.04) | [0.39] (0.40) | [1.57] (1.64) | |||
| D[45, 205, 0] | ACML | [1.48] (1.47) | [0.27] (0.28) | [2.31] (2.26) | [0.39] (0.38) | [1.39] (1.39) | |||
| D[45, 205, 0] | WEE | [1.52] (1.51) | [0.28] (0.28) | [2.39] (2.30) | [0.39] (0.38) | [1.41] (1.42) | |||
| (−2.85, −0.15, 1, 0.15, 1.5) | 10 | (650, 350, 0) | Random Sampling | ML | [2.33] (2.36) | [0.53] (0.53) | [3.49] (3.34) | [0.71] (0.69) | [2.46] (2.45) |
| D[0, 250, 0] | ACML | [2.79] (2.73) | [0.35] (0.34) | [3.30] (3.27) | [0.47] (0.45) | [2.02] (1.95) | |||
| D[15, 235, 0] | ACML | [2.05] (2.01) | [0.32] (0.31) | [2.68] (2.64) | [0.43] (0.43) | [1.74] (1.71) | |||
| D[15, 235, 0] | WEE | [2.59] (2.62) | [0.32] (0.31) | [3.88] (4.15) | [0.43] (0.43) | [2.50] (2.68) | |||
| D[45, 205, 0] | ACML | [1.84] (1.82) | [0.34] (0.33) | [2.61] (2.60) | [0.46] (0.44) | [1.76] (1.72) | |||
| D[45, 205, 0] | WEE | [1.92] (1.93) | [0.34] (0.33) | [2.93] (2.95) | [0.46] (0.44) | [1.98] (2.01) | |||
| U(5,15) | (650, 350, 0) | Random Sampling | ML | [2.23] (2.14) | [0.48] (0.47) | [3.30] (3.16) | [0.62] (0.60) | [2.47] (2.65) | |
| D[0, 250, 0] | ACML | [2.82] (2.85) | [0.33] (0.31) | [3.32] (3.30) | [0.42] (0.42) | [2.01] (2.00) | |||
| D[15, 235, 0] | ACML | [2.04] (2.06) | [0.30] (0.29) | [2.66] (2.63) | [0.39] (0.39) | [1.73] (1.73) | |||
| D[15, 235, 0] | WEE | [2.61] (2.63) | [0.34] (0.34) | [4.08] (4.09) | [0.47] (0.49) | [2.43] (2.65) | |||
| D[45, 205, 0] | ACML | [1.80] (1.78) | [0.32] (0.32) | [2.55] (2.58) | [0.41] (0.42) | [1.76] (1.76) | |||
| D[45, 205, 0] | WEE | [1.89] (1.88) | [0.33] (0.33) | [2.94] (2.98) | [0.44] (0.46) | [1.97] (2.02) |