Bias Assessment in Progression-Free Survival Analysis Using Interval-Censored Methods - Interval-Censored-Time-to-Event Data: Methods and Applications - page 279

a consecutive subset of these nonoverlapping bins. Assuming constant hazard

and survival functions within each bin, the nonparametric maximum likelihood
estimation can be obtained under the constraint that the sum of survival func-

tions of all bins equals to 1 and each component is positive. In other words, this

approach actually simplifies the situation to a finite-dimensional parametric

estimation problem and thus becomes less computationally feasible as sample

size increases. The standard errors of all parameters can be obtained from the

empirical Fisher's information matrix. In practice, numerical stability may be

an issue, as observed by Lindsey and Ryan (1998). One way to overcome the

numerical and computational issue when sample sizes increase is to reduce the

number of parameters by grouping the nonoverlapping bins noninformatively.

The survival functions between treatment arms can be compared by per-

forming the score test for covariate coecients based on Finkelstein's method

for the proportional hazards model. This score statistic can be expressed in

the same form as the weighted logrank statistic for right-censored data with

constant weights. However, it may be hard to justify the assumptions needed
for the regularity conditions of maximum likelihood. Sun et al. (2005) pro-

posed a new class of K-sample test for interval-censored data that includes

Finkelstein's score test statistic as a special case. The null hypothesis of the

homogeneity of the K populations can be tested by comparing the statistic to
a 2

distribution with K 1 degrees of freedom.

An SAS macro for Finkelstein's method has been developed and may be

obtained from Sun and Chen (2010) upon request. A generalized logrank test

proposed by Sun et al. (2005) was developed by So et al. (2010) and can

be downloaded from the SAS website. In this chapter, we mainly use these

SAS macros to conduct the analyses. Some additional implementations for

nonparametric interval-censored methods include the R package intcox (pro-
vides point estimation only), as well as a SAS macro developed by Zhang and

Davidian (2008) (a general framework for semiparametric regression analysis