Practical Issues on Using Weighted Logrank Tests with Interval-Censored Events in Clinical Trials - Interval-Censored-Time-to-Event Data: Methods and Applications - page 369

13.6 Recommendations

We have presented many logrank-type tests for interval-censored data. We

can group the tests into roughly three categories: the single imputation meth-

ods on the observed intervals (e.g., right endpoint imputation or midpoint

imputation); the method of Freidlin et al. (2007), which forces the assess-

ment distributions to be equal in the treatment groups; and the tests based

on the NPMLE found in the interval package, which are more complicated
and use the NPMLE of the joint distribution to create rank-like scores. Our

simulations and those of others (Law and Brookmeyer, 1992; Sun and Chen,

2010; Fay and Shih, 2012) have shown that the single imputation methods

can severely inflate the type I error, and they are not recommended. For small

sample sizes, Fay and Shih (2012) showed that the multiple imputation test

with Monte Carlo inferences were alpha-level tests in all simulations studied,

and we have confirmed that with new simulations, which include informative

censoring. Further, Fay and Shih (2012) showed that the PCLT method was

approximately valid with noninformative assessments, even with assessment

treatment dependence. The Freidlin et al. (2007) method is the only method

that theoretically accounts for informative censoring, although the simulated

size was not too bad (always less than 8%) for all the interval-based methods

and was less than the nominal level using multiple imputation with Monte

Carlo inferences. The limitation of the Freidlin et al. (2007) method is that

there must be regularly scheduled assessments for which all patients are ob-
served. When there are regularly scheduled assessments, the price of using the

test of Freidlin et al. (2007) is a loss in power. When regular assessment is

not possible, the NPMLE-based methods are recommended. There does not

appear to be much difference between the tests based on the NPMLE for mod-

erate sample sizes; however, if maintaining the proper size is important, then

the multiple imputation test using Monte Carlo inferences is recommended.