Table 3.
Power and Type I error for different 2-year parallel design.
| 6 clusters |
10 clusters |
14 clusters |
18 clusters |
|||||
|---|---|---|---|---|---|---|---|---|
| Power | Type 1 error | Power | Type 1 error | Power | Type 1 error | Power | Type 1 error | |
| Models—Random effect of 0.05 | ||||||||
| MM 1: PL (IL9) | 80.8 | 12.2 | 94.7 | 7.7 | 99.1 | 7.9 | 99.7 | 6.5 |
| MM 1: PLKR(ILII) | 58.0 | 4.5 | 89.3 | 4.4 | 98.6 | 4.9 | 99.4 | 5.2 |
| MM 1: Laplace (ILI0) | 88.0 | 18.4 | 96.6 | 11.2 | 99.4 | 10.1 | 99.9 | 8.3 |
| MM 1: AGQ-10 (ILI2) | 88.0 | 18.4 | 96.6 | II.1 | 99.4 | 10.1 | 99.9 | 8.3 |
| GEE: Model-based SE (ILI3) | 59.2 | 5.1 | 89.0 | 4.6 | 98.4 | 5.3 | 99.3 | 5.2 |
| GEE: Empirical SE (ILI4) | 73.3 | 8.2 | 92.4 | 7.0 | 98.6 | 7.8 | 99.6 | 6.5 |
| GEE: MBN correction (ILI5) | 48.5 | 2.9 | 80.7 | 2.5 | 94.9 | 2.5 | 98.8 | 3.8 |
| GEE: FG correction (ILI6) | 56.1 | 3.6 | 87.8 | 3.6 | 97.3 | 4.7 | 99.3 | 4.8 |
| Cluster level: Treatment + Time (CL7) | 85.8 | 16.8 | 97.3 | 13.9 | 99.7 | 16.4 | 100.0 | 16.0 |
| Cluster level: Weighted treatment + Time (CL8) | 88.2 | 17.8 | 97.6 | 16.5 | 99.5 | 17.1 | 100.0 | 17.4 |
| Cluster level: Unweighted t-test (CL5) | 57.7 | 4.8 | 88.5 | 4.6 | 97.5 | 4.7 | 99.3 | 5.4 |
| Cluster level: Adjusted residual (CL6) | 57.8 | 4.8 | 88.2 | 4.6 | 98.2 | 5.2 | 99.3 | 5.2 |
| Models—Random effect of 0.10 | ||||||||
| MM 1: PL (IL9) | 60.0 | 10.1 | 77.4 | 8.7 | 90.6 | 6.8 | 93.8 | 6.8 |
| MM 1: PLKR(ILII) | 35.6 | 3.8 | 66.2 | 5.3 | 86.4 | 4.4 | 90.9 | 5.0 |
| MM 1: Laplace (ILI0) | 71.2 | 15.5 | 83.1 | 12.8 | 92.8 | 8.1 | 95.9 | 8.6 |
| MM 1: AGQ-10 (ILI2) | 71.2 | 15.5 | 83.1 | 12.8 | 92.8 | 8.1 | 95.9 | 8.6 |
| GEE: Model-based SE (ILI3) | 34.7 | 4.1 | 67.1 | 5.3 | 86.8 | 5.1 | 91.4 | 5.8 |
| GEE: Empirical SE (ILI4) | 51.0 | 7.9 | 74.0 | 8.6 | 89.2 | 6.6 | 92.1 | 6.9 |
| GEE: MBN correction (ILI5) | 28.8 | 2.8 | 54.6 | 2.4 | 75.6 | 2.3 | 86.6 | 3.5 |
| GEE: FG correction (ILI6) | 35.4 | 3.2 | 64.6 | 3.9 | 83.6 | 4.4 | 89.7 | 4.5 |
| Cluster level: Treatment + Time (CL7) | 65.8 | 14.2 | 86.8 | 16.9 | 96.1 | 15.7 | 98.1 | 15.4 |
| Cluster level: Weighted treatment + Time (CL8) | 71.7 | 16.9 | 88.4 | 18.9 | 96.5 | 17.0 | 97.9 | 19.4 |
| Cluster level: Unweighted t-test (CL5) | 32.9 | 4.0 | 61.9 | 5.2 | 83.1 | 4.2 | 90.2 | 4.6 |
| Cluster level: Adjusted residual (CL6) | 33.0 | 4.2 | 62.3 | 5.0 | 83.0 | 4.3 | 90.1 | 4.7 |
PL: pseudo-likelihood; PLKR: pseudo-likelihood Kenward-Roger correction; AGQ-IO: Adaptive Gaussian Quadrature with 10 quadrature points; GEE: generalized estimating equation; SE: standard error; MBN: Morel, Bokossa, and Neerchal; FG: Fay and Graubard; RIMDAMAL II: 2-year parallel follow-up of repeated ivermectin mass drug administrations for control of malaria.
Power and Type I error rates for 2-year parallel designs with a range of total cluster numbers (6, 10, 14, and 18) and two different village random effect variances for (0.05 and 0.10). The simulated intervention effect is the expected effect for RIMDAMAL II, as in Table 2. Labels in the parentheses (e.g. (IL9)) are meant to direct the reader to model descriptions in the text and code in the supplementary material.