Bias and Its Remedy in Interval-Censored Time-to-Event Applications - Interval-Censored-Time-to-Event Data: Methods and Applications - page 316

regression: one that uses the right endpoint (i.e., t 2 ) corresponding to the
first observed time and the other that uses the mid-point. For these two
data sets, we proceed as though the data are right-censored and use Cox

regression described in Section 11.2.2 to estimate the regression parameter
vector = ( 1 ; 2 ; 3 ; 4 ). Hereafter, we denote the parameter estimates from
the rst data set as \Cox.Right" and the second data set by \Cox.Mid." At the
same time, we use the semiparametric method described in Section 11.2.2 to

estimate the regression parameter , which is denoted by \IntCox".

Steps 1 to 5 are run 1,000 times to generate 1,000 samples of the parameter
vector . A sampling distribution is then generated. The mean, bias, standard de-

viations, and mean squared error (MSE) are calculated for plotting. In addition, a
95% sampling confidence interval (CI) is constructed to see whether it covers zero

for significance testing for that parameter.
To investigate the effect of the probability of censoring on the parameter esti-

mates, we consider nine values for the probability of censored observations: p = 0.1,
0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9. High probability p = 0.9 indicates that most
observations in the simulated data set are censored, while low probability p = 0.1

implies that most observations in the data set are noncensored points. Note that
when p = 0.9, the Cox regression and \IntCox" algorithm crashed for the case of less

frequent visits of every 3 months due to higher proportion of censoring.

11.3.2 Simulation Results

The bias associated with the comparison of treatment groups is summarized in Table
11.1. In this table, p denotes the probability of censoring and \Month" denotes the
monthly interval visit. It can be seen that the bias is generally lower when visit fre-

quency is every month (i.e., Month=1) than for less frequent visits (i.e., Month=3).
This is intuitively what one expects because the survival time would be closer to

the true survival time. Comparing \IntCox" with \Cox.Right" and \Cox.Mid," \Int-
Cox" always gave the smallest bias, and \Cox.Right" the worst. For the case of the

most frequent visit schedule, \IntCox" is biased only a few percentage points and
\Cox.Right" is biased by 10% to 20%. The midpoint approximation \Cox.Mid" is

not bad because the visit interval is small and the midpoint would be close to the