Consistent Variance Estimation in Semiparametric Models with Application to Interval-Censored Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 253

TABLE 9.1: Monte Carlo Simulation Results for B-Splines Sieve MLE of 0
with 1,000 Repetitions for Semiparametric Analysis of Interval-Censored Data

n = 50 n = 100 n = 200

Bias 0.1194 0.0572 0.0196

M-C sd 0.7850 0.4966 0.3422

ASE 0.8649 0.5212 0.3506

95%-CP 97.4% 96.4% 95.6%

and the knots are evenly placed in (0; 5) in the rst example and (0; 1) in the

second example.

Simulation 1: Interval-Censored Data. We generate the data in a way
similar to what was used in Huang and Rossini (1997). For each subject, we

independently generate Xi i = (U i ;V i ; i;1 i;2 ;Z i ), for i = 1; 2; ;n, where
Z i Bernoulli(0:5); we simulate a series of examination times by the partial
sum of inter-arrival times that are independently and identically distributed

according to exp(1); then Ui i is the last examination time within 5 at which
the event has not occurred yet and V i is the first observation time within 5 at
which the event has occurred; the event time is generated according to the Cox

proportional hazards model (tjz) = t exp(z) for which the true parameters

are 0 = 1 and 0 (t) = t. Similarly, a Monte Carlo study with 1,000 repetitions
is performed and the corresponding results are displayed in Table 9.1.

The results show that both bias and Monte Carlo standard deviation de-

crease as sample size increases. The proposed least-squares estimate of the

standard error may overestimate the true value but the overestimation lessens