Research Article
A Two-Stage Joint Model for Nonlinear Longitudinal Response and a Time-to-Event with Application in Transplantation Studies
Table 3
Bias and residual mean squared error (RMSE) for the method with true (GS), Empirical Bayes estimates (Plug-in), sampled , and fully Bayesian approach.
| | 7 time points | | censoring | 20 | 40 |
| | 0.5 |
| | | | | | | | | GS | 0.00 (0.04) | −0.02 (0.03) | 0.01 (0.03) | −0.01 (0.04) | 0.02 (0.04) | −0.02 (0.04) | | plug-in | −0.05 (0.06) | −0.04 (0.05) | 0.06 (0.07) | −0.08 (0.09) | −0.04 (0.05) | 0.12 (0.12) | | sampling | −0.04 (0.05) | 0.03 (0.08) | 0.02 (0.07) | −0.05 (0.11) | −0.02 (0.06) | 0.03 (0.10) | | Bayesian | −0.03 (0.04) | −0.02 (0.04) | 0.01 (0.02) | −0.01 (0.04) | −0.02 (0.04) | 0.02 (0.07) |
| | 1 |
| | GS | 0.04 (0.05) | 0.04 (0.07) | −0.03 (0.07) | −0.05 (0.09) | −0.04 (0.06) | −0.03 (0.05) | | plug-in | −0.07 (0.08) | −0.08 (0.09) | 0.07 (0.09) | −0.10 (0.12) | −0.08 (0.09) | 0.08 (0.11) | | sampling | −0.07 (0.09) | −0.06 (0.10) | −0.02 (0.11) | −0.05 (0.12) | 0.05 (0.11) | −0.03 (0.12) | | Bayesian | 0.01 (0.03) | 0.05 (0.06) | −0.03 (0.07) | 0.05 (0.06) | 0.04 (0.06) | −0.04 (0.07) |
| | 5 |
| | GS | 0.04 (0.06) | 0.05 (0.06) | 0.04 (0.08) | 0.05 (0.10) | 0.01 (0.05) | −0.02 (0.06) | | plug-in | −0.09 (0.10) | −0.10 (0.11) | 0.08 (0.11) | −0.20 (0.22) | −0.21 (0.22) | 0.14 (0.18) | | sampling | 0.08 (0.13) | 0.06 (0.12) | −0.05 (0.12) | 0.07 (0.14) | −0.05 (0.13) | −0.11 (0.18) | | Bayesian | 0.09 (0.10) | 0.05 (0.09) | −0.09 (0.10) | −0.09 (0.10) | 0.08 (0.12) | −0.12 (0.18) |
| | 14 time points | | censoring | 20 | 40 |
| | 0.5 |
| | | | | | | | | GS | −0.03 (0.03) | 0.00 (0.02) | −0.02 (0.03) | 0.02 (0.03) | −0.03 (0.04) | 0.02 (0.04) | | plug-in | −0.02 (0.03) | −0.03 (0.04) | 0.05 (0.07) | −0.02 (0.04) | −0.03 (0.04) | 0.05 (0.06) | | sampling | 0.03 (0.04) | 0.02 (0.06) | 0.02 (0.07) | 0.02 (0.04) | 0.04 (0.05) | 0.02 (0.08) | | Bayesian | −0.03 (0.04) | −0.02 (0.04) | −0.02 (0.04) | 0.02 (0.04) | 0.03 (0.04) | −0.05 (0.06) |
| | 1 |
| | GS | −0.03 (0.04) | −0.03 (0.04) | −0.01 (0.03) | 0.00 (0.03) | −0.02 (0.04) | 0.05 (0.06) | | plug-in | −0.09 (0.06) | −0.05 (0.06) | 0.06 (0.07) | −0.02 (0.04) | −0.04 (0.05) | 0.11 (0.11) | | sampling | 0.04 (0.08) | 0.02 (0.08) | −0.02 (0.07) | −0.02 (0.04) | −0.02 (0.08) | 0.04 (0.09) | | Bayesian | −0.03 (0.04) | 0.04 (0.05) | −0.03 (0.05) | 0.02 (0.04) | 0.03 (0.05) | 0.06 (0.07) |
| | 5 |
| | GS | −0.03 (0.04) | −0.03 (0.04) | 0.01 (0.04) | −0.01 (0.04) | −0.02 (0.04) | 0.05 (0.06) | | plug-in | −0.05 (0.06) | −0.10 (0.11) | 0.07 (0.09) | −0.10 (0.11) | −0.09 (0.10) | 0.11 (0.12) | | sampling | 0.04 (0.09) | 0.04 (0.11) | −0.05 (0.11) | 0.07 (0.12) | 0.05 (0.11) | −0.06 (0.16) | | Bayesian | 0.03 (0.05) | 0.03 (0.08) | −0.05 (0.10) | 0.02 (0.04) | 0.06 (0.10) | −0.09 (0.14) |
|
|
