Biomedical Engineering Reference
In-Depth Information
where
J
is the Jacob matrix. Inserting this to the definition for
F
,weobtain
L
(
θ
):=
1
2
(
h
)
t
(
h
)=
1
2
f
t
f
+
h
t
J
t
f
+
1
2
h
t
J
t
Jh
=
F
(
θ
)+
h
t
J
t
f
+
1
F
(
θ
+
h
)
≈
2
h
t
J
t
Jh.
(3
.
13)
The Gauss-Newton step
h
minimizes
L
(
h
). In practice, the Gauss-Newton
least square fitting the baseline hazard function can be achieved by using
MATLAB software.
3.3.
Neural Network Testing
In the Cox model, the main interest is usually about the parameter vector
β
. However, when one is interested in making predictions about the failure
time for a given set of covariates, or when one assumes a parametric family
for the baseline hazard function, just as what we have performed, then
testing that
h
0
is equal to a specified hazard rate function or evaluating
how stable
h
0
is for varying data source becomes important [12]. In the
field survival analysis, there are two popular methods in order to test a
model. One is to use 1/2 or 2/3 of the time scale in the survival data
to determine the parameters and then use the whole data set to examine
the model. In our study, however, to the short length of data (total of
66 rows, in which approximately two-thirds are censored) and the high
data demand from MLE (refer to section 3.1), this solution is not feasible.
Another way is to use the whole data set to set up the model and then use
a resample method to check the model. This solution also has a problem on
the principle by which we resample the original data. As we have known,
MLE relies heavily on the given data set especially when the length of data
is not exceptionally long. If we randomly resample the original data, the
selected data for testing may be far from the “pattern” of the whole data
set, e.g., having quite different mean and standard deviation.
In this study, we propose an artificial neural network testing model.
First, we let the neural network “learn” the patients' survival pattern from
the given hospital data. We then use the neural network to generate a
long list of “virtual data” and “simulate” the survival pattern to test our
covariate estimation and baseline hazard estimation. By this process, we
also show that the neural network has great potential as a research tool in
survival analysis.
The conception of neural network came up as early as the middle of this
century. A
Neural Network
(NN) is an information processing paradigm
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