Bias and Its Remedy in Interval-Censored Time-to-Event Applications - Interval-Censored-Time-to-Event Data: Methods and Applications - page 325

test.surv=ictest(Surv(left,right,type="interval2")~group,

data=dat)
#printtheresulttest.surv

The p-value associated with the test is small (p value < 0:00001), indicating a
statistically significantly difference between the two groups in probability of survival.

Fitting the \IntCox" approach, the estimated parameter for group dierence is 1.867.
Because the \IntCox" approach at present has not been implemented to produce

standard errors, the standard error for this treatment parameter is then estimated
using a standard bootstrap approach. We obtain random samples of the observed
data with replacement 1,000 times and t the \IntCox" to the resulting bootstrap

samples. The bootstrap distribution can then be constructed for statistical inference.
From the bootstrap distribution, the 95% bootstrap confidence interval for the group

eect is (1:494; 2:359) with 50% quantile 1.872, which again conrms the statistical
significance of group difference.

11.5 Discussions and Conclusions

In this chapter, we investigated the bias inherent in the common practice of analyzing

interval-censored time-to-event data as though it were right-censored. We have found
that there are biases by approximating the interval-censored data using the interval

midpoint or the first observed and using methodology developed for analyzing right-
censored time-to-event data. Depending on the probability of censoring, the bias
could have a magnitude of up to 50%. Consequently, underlying significant treatment

effects may fail to be detected and the power of the statistical procedure may be
reduced. To mitigate the bias, the \IntCox" method was used and results compared to

those from the common practice of approximating the data by either the midpoint or
right endpoint of the intervals and using methodology developed for analyzing right-

censored time-to-event data. We found that the \IntCox" method yielded almost
unbiased estimation results with appropriate coverage probability.

Further simulations from Henschel et al. (2007) also showed that there is a slight