Table II.
Percentage of tree models that identified the correct splitting covariate: assessed separately at each node and also for all four possible splits combined. Simulation results from models A and B, based on 1000 datasets of N = 300 observations each.
| Statistic* (per cent Missing) | Model A |
Model B |
|||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Method† | h1 | h2‡ | h3‡ | h4§ | Total (95 per cent CI) | h1 | h2‡ | h3‡ | h4§ | Total (95 per cent CI) | |
| FLD (0 per cent) | COMP | 100 | 97.60 | 99.90 | 91.69 | 89.3 (85.80, 92.80) | 100 | 83.80 | 97.60 | 98.16 | 80.3 (75.80, 84.80) |
| FLD (10 per cent) | COBS | 100 | 95.40 | 99.30 | 91.64 | 86.5 (82.42, 90.58) | 100 | 79.10 | 93.70 | 97.44 | 72.1 (66.75, 77.45) |
| SS | 100 | 94.90 | 99.70 | 92.08 | 87.1 (83.31, 90.89) | 100 | 57.00 | 93.90 | 97.44 | 51.5 (45.84, 57.16) | |
| CS | 99.80 | 94.29 | 99.80 | 92.07 | 86.5 (82.63, 90.37) | 100 | 74.80 | 98.00 | 97.35 | 71.3 (66.18, 76.42) | |
| MI-1 | 99.70 | 95.89 | 100 | 92.08 | 87.9 (84.21, 91.59) | 99.90 | 73.37 | 97.60 | 97.74 | 69.6 (64.39, 74.81) | |
| MI-10 | 99.90 | 95.90 | 99.90 | 92.18 | 87.9 (84.21, 91.59) | 100 | 76.20 | 97.80 | 97.96 | 72.7 (67.66, 77.74) | |
| FLD (25 per cent) | COBS | 100 | 90.70 | 93.70 | 90.72 | 77.4 (71.94, 82.86) | 100 | 66.70 | 80.10 | 96.63 | 51.7 (44.97, 58.03) |
| SS | 99.80 | 84.57 | 97.29 | 91.56 | 74.8 (69.89, 79.71) | 99.70 | 27.88 | 82.65 | 96.84 | 22.1 (17.40, 26.80) | |
| CS | 97.30 | 79.96 | 99.08 | 89.42 | 69.9 (64.71, 75.09) | 98.10 | 50.25 | 96.63 | 94.20 | 45.8 (40.16, 51.43) | |
| MI-1 | 95.70 | 86.65 | 99.90 | 91.54 | 75.6 (70.73, 80.46) | 97.60 | 55.33 | 98.67 | 96.16 | 51.6 (45.94, 57.26) | |
| MI-10 | 97.30 | 85.30 | 99.90 | 92.29 | 76.2 (71.38, 81.02) | 98.70 | 56.74 | 98.28 | 96.62 | 53.9 (48.26, 59.54) | |
| FLD (40 per cent) | COBS | 100 | 79.50 | 60.40 | 88.08 | 41.7 (34.50, 48.90) | 100 | 51.40 | 37.30 | 91.15 | 17.7 (12.12, 23.28) |
| SS | 99.00 | 69.90 | 72.83 | 89.04 | 43.9 (38.28, 49.52) | 97.80 | 11.96 | 39.47 | 91.71 | 5.1 (2.61, 7.59) | |
| CS | 90.90 | 53.14 | 82.51 | 84.53 | 38.3 (32.80, 43.80) | 92.50 | 26.92 | 88.54 | 90.96 | 22.5 (17.7, 27.23) | |
| MI-1 | 82.30 | 73.03 | 99.88 | 90.88 | 54.6 (48.97, 60.23) | 83.30 | 29.65 | 99.28 | 95.16 | 23.7 (18.89, 28.51) | |
| MI-10 | 87.10 | 67.16 | 99.77 | 92.06 | 53.7 (48.06, 59.34) | 87.60 | 29.79 | 98.63 | 95.14 | 24.9 (20.00, 29.79) | |
| LR (0 per cent) | COMP | 99.90 | 95.70 | 99.90 | 90.68 | 86.4 (81.40, 89.40) | 100 | 86.40 | 96.80 | 97.31 | 81.5 (77.11, 85.89) |
| LR (10 per cent) | COBS | 99.90 | 93.29 | 99.00 | 90.39 | 83.3 (78.85, 87.75) | 100 | 82.60 | 91.80 | 96.41 | 73 (67.70, 78.30) |
| SS | 99.80 | 93.89 | 99.40 | 90.73 | 84.7 (80.63, 88.77) | 100 | 64.90 | 92.00 | 96.85 | 57.8 (52.21, 63.39) | |
| CS | 99.20 | 88.41 | 99.40 | 89.45 | 79.4 (74.82, 83.98) | 100 | 71.60 | 97.10 | 95.57 | 66.4 (61.05, 71.75) | |
| MI-1 | 99.50 | 93.27 | 99.80 | 90.94 | 84.1 (79.96, 88.24) | 99.90 | 78.18 | 96.80 | 97.00 | 72.7 (67.34, 77.46) | |
| MI-10 | 99.50 | 94.17 | 99.90 | 90.74 | 84.9 (80.85, 88.95) | 100 | 78.40 | 97.50 | 96.62 | 73.6 (68.61, 78.59) | |
| LR (25 per cent) | COBS | 100 | 90.00 | 92.80 | 89.22 | 74.6 (68.91, 80.29) | 100 | 68.9 | 76.20 | 95.80 | 50.5 (43.97, 57.03) |
| SS | 99.60 | 84.94 | 96.69 | 90.34 | 73.7 (68.72, 78.68) | 99.30 | 35.55 | 78.55 | 95.51 | 25.8 (20.85, 30.75) | |
| CS | 94.80 | 68.57 | 96.20 | 87.17 | 58.2 (52.62, 63.78) | 96.40 | 41.49 | 93.88 | 93.48 | 38.3 (32.80, 43.80) | |
| MI-1 | 93.80 | 85.29 | 99.89 | 90.18 | 72.3 (67.24, 77.36) | 94.20 | 57.64 | 97.66 | 95.43 | 51.6 (45.94, 58.55) | |
| MI-10 | 94.80 | 82.17 | 99.89 | 91.13 | 70.6 (65.49, 75.76) | 96.00 | 58.75 | 98.02 | 95.54 | 52.9 (47.25, 58.55) | |
| LR (40 per cent) | COBS | 99.90 | 79.38 | 53.45 | 83.15 | 35.0 (28.03, 41.97) | 100 | 38.0 | 28.60 | 83.92 | 8.7 (4.58, 12.82) |
| SS | 97.70 | 72.26 | 67.35 | 86.62 | 41.4 (35.83, 46.97) | 96.00 | 19.90 | 31.25 | 86.33 | 5.8 (3.16, 8.45) | |
| CS | 90.70 | 43.66 | 68.47 | 81.00 | 28.3 (23.20. 33.40) | 89.30 | 18.14 | 72.79 | 87.23 | 13.3 (9.46, 17.14) | |
| MI-1 | 75.10 | 66.31 | 98.27 | 88.89 | 44.7 (39.07, 50.33) | 74.20 | 34.50 | 91.71 | 94.16 | 23.8 (18.98, 28.62) | |
| MI-10 | 80.00 | 62.63 | 97.75 | 91.56 | 45.4 (39.77, 51.03) | 78.60 | 34.35 | 96.69 | 93.55 | 24.8 (19.91, 29.69) | |
*
FLD, reduction in full exponential likelihood deviance; LR, two-sample log rank.
†
COMP, full simulated data; COBS, completely observed cases only; SS, surrogate splitting; CS, Conversano and Siciliano's single imputation; MI-1, multiple imputation with one draw of normal error; and MI-10, multiple imputation with 10 draws of normal error.
‡
Correct variable selection at nodes h2 and h3 is conditional on correct variable selection at node h1.
§
Correct variable selection at node h4 is conditional on correct variable selection at both nodes h1 and h3.