Biomedical Engineering Reference
In-Depth Information
PN
: occurrence of lymph notes, a symptom of cancer invasion, ranges
from
N
0to
N
2
STAGE
: pathological diagnosis of cancer and it is ordinal, ranges from
1
A
to
IV
DF
−
INT
: disease free time, in months
GRADE
: the fitness condition when patient in hospital, ranges from
well to poor
STATUS
: indicating if the patient is still alive (A) or deceased (D). If
the
of a patient is “A” (alive), this row of data is censored.
In our study, we take
PT,PN,STAGE,DF
−
INT
,and
GRADE
six
variables as covariates to be estimated. The original hospital data set
records information for 66 patients and is listed in Appendix 1.
STATUS
4.2.
Estimation for Covariates
The proportional hazard regression to estimate
β
is performed by SPSS.
The results are shown in Appendix 2:
The Cox regression gives the mean and standard deviation for each
covariate in given data. The
β
is estimated at a certain significance level.
For “patient term” and “grade,”
β
is positive, which means a higher value
for these two variables will result in higher hazard or risk of death. For
“disease free time,”
β
assumes a negative value. This means that the longer
the patient is disease free, the less likely that he or she will die shortly,
which is reasonable. The
β
values for
PN
and
STAGE
are both near zero,
which indicates that these two variables do not associated much with the
hazard rate.
The Cox regression gives baseline cumulative hazard and overall cumu-
lative hazard vs. survival time, at mean value of covariates. To estimate the
hazard function, we fix the covariates at their mean values, then use least
square regression to estimate the parameters
a
and
b
in (2.20), by fitting
two columns of data in the survival table in Appendix 2.
4.3.
Estimation for Baseline Hazard Function
Starting from the results of the Cox regression, let
X
τ
=SurvivalTime=[123456891116171833]
,
H
τ
= CumBaselineHazard
=[
.
006
.
010
.
022
.
029
.
037
.
054
.
065
.
089
.
129
.
163
.
303
.
377
.
991]
.
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