Overview of Recent Developments for Interval-Censored Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 14

cedures is unknown under the alternative hypothesis, they cannot be used for

the sample size calculation. It is well-known that the sample size calculation is
an essential part for the design of many survival studies such as clinical trials.

Thus it would be very useful to develop some nonparametric test procedures

with the established asymptotic distributions in general.

1.5 Regression Analysis

Regression analysis is usually performed if one is interested in quantifying the

effect of some covariates on the survival time of interest or predicting survival

probabilities for new individuals. Of course, the first step in regression analysis

is to specify an appropriate regression model. With respect to the model selec-

tion, there is no major difference between the analysis of right-censored data

and interval-censored data. For example, the proportional hazards model (Cox

(1972)) has been the most commonly used semiparametric regression model

for both cases, and it postulates

(tjz) = 0 (t) e 0 z

for the hazard function of the failure time T of interest given covariates Z = z.

Here 0 (t) denotes an unknown baseline hazard function (the hazard function
for subjects with Z = 0) and is a vector of unknown regression parameters.

In addition to the above proportional hazards model, many other models

have been proposed or investigated. These include some generalizations of

the model above, the proportional odds model, the accelerated failure time

model, the additive hazards model, the partial linear model, and the piecewise

exponential model. A common feature of the models mentioned above is that

they all are specific models in terms of the functional form of the effects of

covariates. Sometimes one may prefer a model that gives more flexibility. One

such model is the linear transformation model (Sun and Sun (2005); Younes