NONPARAMETRIC REGRESSION TECHNIQUES IN SURVIVAL ANALYSIS - Quantitative Medical Data Analysis Using Mathematical Tools and Statistical Techniques - page 223

CHAPTER 11
NONPARAMETRIC REGRESSION TECHNIQUES IN
SURVIVAL ANALYSIS
Chin-Shang Li
Department of Biostatistics, St. Jude Children's Research Hospital,
332 N. Lauderdale St., Memphis, TN, USA
E-mail: [e-mail]
Some nonparametric regression techniques for estimating hazard or log-
hazard functions and functional forms of covariate eects in Cox's pro-
portional hazard model are introduced. Some nonparametric and semi-
parametric regression models for a conditional hazard function are dis-
cussed as alternatives to the proportional hazard model.
1. Introduction
In biomedical follow-up or industrial life-testing studies, the time to oc-
currence of a certain event of interest (generically called a failure) is the
primary endpoint, e.g., time to hypothyroidism after treatment for pediatric
Hodgkin lymphoma. The interval of interest, called failure time, survival
time, or event time, is often subject to right censoring, that is, the value of
the event time is not known but only that it is greater than or equal to the
censoring time. Other censoring forms include left censoring and interval
censoring . In left censoring, some observed times are greater than or equal
to the actual failure times. Interval censoring means that some failures have
occurred only within some time interval. We will conne this discussion to
right-censored data.
Of particular interest are the survival and hazard functions in summariz-
ing failure time data. Let T be a nonnegative, continuous random variable
representing the failure time of an individual in a homogeneous population
(i.e., no explanatory variables). The survival function is the probability
that the individual survives until time t, i.e., S(t) = Pr(Tt). The hazard
function is the risk or hazard of failure at time t given that failure has not