Table 4.
Estimated powers of nominal 0.05-level tests for covariate effects of Si in the model λ(t|Si) = λ0(t) exp{γ(Si)}, i = 1, 2, . . . , n, expressed as percent. λ0(t) = 1; values of Si are equally spaced on the interval [−1.719, 1.719] with step 0.0173; γ(Si) is the true alternative; n = 200. Censoring distribution is uniform on (0, 1.5). Tests and alternatives are as described in the text. Results are based on 1000 simulations for each scenario. The maximum binomial (N = 1000, p = 0.50) standard error for the entries is 1.58%.
| Alternative
|
|||||||
|---|---|---|---|---|---|---|---|
| Null hypothesis | Test | E | L | S1 | Q | C | S2 |
| No effect | Spline-based | 74.0 | 72.4 | 73.8 | 23.1 | 5.8 | 16.2 |
| Linear | 74.4 | 71.5 | 68.9 | 4.5 | 4.3 | 4.2 | |
| Quadratic | 71.5 | 60.4 | 84.1 | 73.6 | 5.9 | 44.7 | |
| Cubic | 67.2 | 55.5 | 84.1 | 67.7 | 6.2 | 38.5 | |
| Optimal | 81.6 | 74.2 | 96.3 | 81.7 | 92.0 | 93.7 | |
| Linear effect | Spline-based | 12.8 | 4.9 | 56.0 | 80.7 | 7.7 | 65.4 |
| Quadratic | 13.7 | 4.9 | 54.0 | 81.7 | 6.9 | 58.5 | |
| Cubic | 12.0 | 7.5 | 54.0 | 73.7 | 6.7 | 46.4 | |
| Optimal | 14.2 | 10.5 | 78.3 | 81.7 | 91.9 | 93.8 | |