Overview of Recent Developments for Interval-Censored Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 12

1.4 Nonparametric Comparison of Survival Functions

Comparison of different survival functions is always one of the primary ob-

jectives in comparative survival studies such as clinical studies on drug devel-

opment. For the problem, one of the commonly used procedures is to employ

some regression models that include treatment indicators as some covraiates

and then to develop some test procedures such as score tests. On the other

hand or in general, one probably prefers some nonparametric or distribution-
free test procedures.

A number of nonparametric test procedures have been developed for the

comparison of survival functions based on interval-censored data (Sun (2006)).

Most of them are generalizations of the test procedures for right-censored

data. For example, the test procedures for right-censored data that have been

generalized to interval-censored data include the weighted logrank test, the

weighted Kaplain{Meier test, and the weighted Kolmoggorov test. Another

one is the imputation method and in this, one imputes the exact failure time

conditional on the observed interval and generates right-censored data. The

test procedures developed for right-censored data can then be applied to the

imputed right-censored data.

Although there exist many nonparametric test procedures, there does not

seem to exist a comprehensive guideline for the selection of an appropriate

procedure for a given data set or problem. For example, with respect to the

weighted logrank tests, the recommendation for the selection of a weight func-
tion is usually based on the shapes of the underlying hazard functions such

as early, middle, or late differences. In reality, however, it is often the case

that the shape information is unknown and a common procedure is to use the

sensitivity approach by trying different weight functions. It is obvious that

this may or may not give decisive conclusions.

Another issue related to the existing nonparametric test procedures is that