Consistent Variance Estimation in Semiparametric Models with Application to Interval-Censored Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 255

increases. As shown in the first simulation study, the proposed method tends

to overestimate the standard error slightly but the overestimation lessens as
sample size increases. As the result of overestimation, the coverage probability

of the 95% confidence interval exceeds the nominal value when sample size is

50 or 100 but gets closer to 95% with sample size increasing to 200.

9.5.2 Applications

This section illustrates the method in two real-life examples: the breast cosme-

sis data reported in Finkelstein and Wolfe (1985) and the data from the blad-
der tumor randomized clinical trial conducted by Byar et al. (1977). We adopt

the cubic B-splines sieve semiparametric MLE method and we estimate the

asymptotic standard error of the estimates of the regression parameters using

the least-squares approach with cubic B-splines as well. The inference is made

based on the asymptotic theorem developed in this chapter.

Example 1: Breast Cosmesis Study. The breast cosmesis study is the

clinical trial for comparing radiotherapy alone with primary radiotherapy with

adjuvant chemotherapy in terms of subsequent cosmetic deterioration of the

breast following tumorectomy. Subjects (46 assigned to radiotherapy alone

and 48 to radiotherapy plus chemotherapy) were followed for up to 60 months,

with prescheduled follow-up visits for every 4 to 6 months. In this chapter, we

propose the Cox proportional hazards model to analyze the difference in time

until appearance of breast retraction,

(tjZ) = 0 (t) exp( 0 Z); (9.17)

where 0 is the baseline hazard (the hazard of the time to appearance of
breast retraction for radiotherapy alone) and Z is the indicator for the treat-

ment of radiotherapy plus chemotherapy. Using the method proposed in this
chapter, the cubic B-splines sieve semiparametric MLE of 0 is b n = 0:8948
with asymptotic standard error given by 0.2926. The Wald test statistic is

Z = 3:0582 with the associated p-value = 0.0011. This indicates that the