Table 1.
Empirical sizes of the proposed spline-based nominal 0.05-level tests for proportional hazards of Si in the model λ(t|Si) = λ0(t) exp{Siδ0}, i = 1, 2, . . . , n, expressed as percent. λ0(t) = 1; values of Si are equally spaced on the interval (0, 1) with an equal number of subjects having each distinct Si value. Results are based on 2000 simulations for each scenario. The binomial (N = 2000, p = 0.05) standard error for the entries is 0.49%.
| True value of δ0 |
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|---|---|---|---|---|---|---|---|
|
n = 100
|
n = 200
|
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| Censoring distribution | Number of distinct covariate Si values | 0 | 1 | 2 | 0 | 1 | 2 |
| Unit exponential | 2 | 5.10 | 5.70 | 6.10 | 6.20 | 5.40 | 4.95 |
| 4 | 5.70 | 6.05 | 5.10 | 5.60 | 4.65 | 4.85 | |
| 10 | 5.70 | 6.30 | 5.95 | 6.40 | 5.00 | 5.30 | |
| 20 | 5.60 | 6.35 | 5.85 | 6.40 | 4.75 | 4.85 | |
| 50 | 5.90 | 6.20 | 6.00 | 6.45 | 4.65 | 4.60 | |
| 100 | 5.70 | 6.60 | 5.95 | 6.35 | 4.65 | 4.60 | |
| 200 | 6.40 | 4.90 | 4.70 | ||||
| Uniform (0,2) | 2 | 5.20 | 4.45 | 5.20 | 5.60 | 4.60 | 4.35 |
| 4 | 5.55 | 4.55 | 4.55 | 4.85 | 4.75 | 4.25 | |
| 10 | 5.35 | 4.10 | 5.20 | 5.00 | 4.45 | 4.75 | |
| 20 | 5.30 | 4.30 | 4.50 | 4.95 | 4.95 | 4.75 | |
| 50 | 5.35 | 4.15 | 4.90 | 4.85 | 4.70 | 4.60 | |
| 100 | 5.40 | 4.30 | 4.90 | 4.80 | 4.65 | 4.45 | |
| 200 | 4.80 | 4.85 | 4.55 | ||||