Biomedical Engineering Reference
In-Depth Information
in this research were SPSS, EXCEL and MATLAB.
2. MLE is a powerful statistical tool but it has its own limitation. When
the data length is short, MLE might be heavily biased. In this study, there
were data for 66 patients, but two thirds were censored and only one third
is used in MLE. The shortage of data resulted in a unideal significance level
of the estimation.
3. Neural network simulation is a new idea for testing the model, es-
pecially when the original data set is short. Neural network application in
survival analysis has promising prospects.
4. Although we assume a linear combination format in the score func-
tion, the five covariates are believed to be correlated with each other. A
randomly generated covariate matrix may not result in a convergent Cox
regression.
5. When the NN generated data assume the same mean and SD with
the original data, they tend to have similar baseline hazard functions by
LSE. This supports our assumption on the format of baseline function.
6. The score function provides a good indication for the risk of death.
This supports the Cox regression for
β
estimation.
7. In future work, we may do regression for longer hospital data for a
more stable
β
estimation and attempt to find out the correlation among
the parameters, assuming a more accurate model for
f
(
x
β
) in the hazard
function and re-formulate the MLE in proportional hazards regression. This
is quite complex work but truly worth to do. We may also explore more
NN applications in survival analysis.
8. In survival analysis with long-term survivors, handling situations con-
sisting of a proportion of subjects under study that may never experience
the event of interest, one proposes to formulate the model as a mixture of
long-term survivors (subjects that will never “fail”) and susceptibles (sub-
jects that will “fail” eventually). In [18], comparing (4.3), the hazard rate
function is modeled as
h
(
t
|
pf
0
(
t
)
1
−
pF
0
(
t
)
|
x
i
)=
h
0
(
t
)exp(
s
)with
h
0
(
t
)=
and
0
<p
1, here,
f
(
t
)and
F
(
t
) are defined in (2.1). Partial likelihood and
full likelihood are then used to obtain the estimators of the coecients of
covariates and the proportion of long-term survivors.
≤
Acknowledgments
The authors would like to thank William Wu, Department of Biostatistics,
Vanderbilt University for providing data sets for this study. This research
was supported in part by Lung Cancer SPORE (P50 CA90949), Breast
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