Regression Analysis for Current Status Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 105

tumor onset is usually of interest but not directly observable. Instead, only

the death or sacrifice time of an animal is observed along with the presence or
absence of a tumor at the time. If the tumor can be considered to be rapidly

lethal, meaning that its occurrence kills the animal right away, it is reasonable

to treat the time as an exact or right-censored observation of the tumor onset

time. On the other hand, if the tumor is nonlethal, then it is reasonable to

assume that the tumor onset time and death time are independent of given

treatments.

The data considered here arose from 144 male RFM mice and consist of the

death time of each animal measured in days and an indicator of lung tumor

presence (z i = 1) or absence (z i = 0) at the time of death. The experiment
involves two treatments: conventional environment (96 mice) and germ-free

environment (48 mice). One of the objectives of the study was to compare the

lung tumor incidence rates of the two treatment groups and lung tumors in

RFM mice are predominantly nonlethal. The authors who have discussed this

set of data include Hoel and Walburg (1972) and Huang (1996).
To analyze the data, define zi i = 1 if the i-th animal was in the conven-
tional environment, and 0 otherwise. As mentioned in Section 4.4, the PH

model and proportional odds model are special cases of the linear transforma-

tion model. For the survival time T, suppose the baseline hazard function of

the error term in the model Equation (4.3) takes the form

exp(t)
1 + r exp(t) ;

(t) =

where r is a constant. This model corresponds to the proportional hazards

model if r = 0 and gives the proportional odds model if letting r = 1.
We obtained ^ n = 0:5576 with the estimated standard error of 0.3201 for
r = 0. By taking r = 0:5 and 1, we have ^ n = 1:0679 and 1:2226 with
the corresponding standard errors being 0.5533 and 0.6315, respectively. These

yielded p-values 0.082, 0.054, and 0.053 for testing 0 = 0 or no treatment
dierence with r = 0; r = 0:5, and r = 1, respectively, which indicates that