Biomedical Engineering Reference
In-Depth Information
disease. Men are affected somewhat more frequently (100,000 cases/year)
than women (70,000 cases/year). Worldwide, there are 1 million new cases
per year. Over the past 5 decades the number of yearly cases has increased,
and the worldwide incidence may double to 2 million per year in the coming
decade. The average patient is 60 years old, and only 1% of cases are under
40 years old. About 90% of patients have historically died from their disease.
Recently, there has been a great deal of interest in modeling survival
data of cancer patients (see [2], [8], [12] for example).
Survival analysis
is concerned with studying the time between entry to a study and a subse-
quent event, such as death. In practice, after a lung cancer patient is hospi-
talized, a set of medical data regarding the patients' condition is recorded.
This data set may include information such as the patient's survival time,
the tumor's stage, the health grade, the disease free time, etc. With the
data set, we wish to study how the patient's conditions might be associated
with the survival pattern and also a lung cancer patient's survival chance,
or a group of patients' survival distribution over time.
The goal of this study is to develop a survival model for relating the
hospital data profile to censored survival data such as time to cancer death
or recurrence. Censored survival times occur if the event of interest, i.e.,
the death, does not occur for a patient during the study period. Tradition-
ally, there are two approaches to model the unknown survival distribution.
One is to assume a classical parametric model such as normal, lognormal,
gamma, Weibull, Pareto or beta, then use a histogram, kernel or other
nonparametric estimate of the unknown density function. This method is
straightforward but cannot reflect the contribution of patients' hospital con-
ditions to the survival distribution. Another is the
proportional hazards
model
, which was first proposed by D.R. Cox [1] in 1972 to investigate
the effects of covariates on survival patterns, also known as Cox regression
model [7]. The model permits having the patients' hospital conditions as a
vector of covariates in the hazard function and can estimate the unknown
parameters for the covariates by partial likelihood without putting a struc-
ture of baseline hazard. In this study, however, we propose a structure of
the baseline hazard function, and estimate the parameters by the available
censored survival data so that the explicit survival function is determined.
This estimation is achieved by a least square fit for the cum hazard value
computed by SPSS.
In a survey study, the design parameters for the survey are sometimes
related to the hazard function but do not fit in the model. On some other
occasions, the independence assumption of the covariates may be violated.
Search WWH ::
Custom Search