SURVIVAL MODEL AND ESTIMATION FOR LUNG CANCER PATIENTS - Quantitative Medical Data Analysis Using Mathematical Tools and Statistical Techniques - page 214

Following the Gauss-Newton least square estimation discussed by sec-
tion 3.2, we find estimations for a and b . The MATLAB computation results
are summarized below.
FITTEDMODEL =
General model:
FITTEDMODEL(x) = a/b*(x-1/b*(1-exp(-b*x)))
Coefficients (with 95% confidence bounds):
a = 0.002185 (0.001524, 0.002845)
b = 0.01727 (-0.01574, 0.05029)
GOODNESS =
sse: 0.0129
rsquare: 0.9854
dfe: 11
adjrsquare: 0.9840
rmse: 0.0342
OUTPUT =
numobs: 13
numparam: 2
residuals: [13x1 double]
Jacobian: [13x2 double]
exitflag: 1
iterations: 7
funcCount: 22
firstorderopt: 1.4601e-004
algorithm: 'Gauss-Newton'

The estimated baseline hazard function is

h 0 ( t )=0 . 1265(1 − exp( − 0 . 01727 t )) . (4 . 1)

Figure 2 shows the fit for the cumulative baseline hazard. Figure 3 plots
the baseline hazard as a function of time.

4.4. Survival Model Testing

With the help of MATLAB command newff , a feed-forward backpropaga-
tion network is constructed to simulate the survival model. This network
has a total of three layers: an input layer of dimension 6, a hidden layer of
dimension 3, and an output layer of dimension 1. The unit of output layer
may assume a value of “0” or “1”, representing “alive” and “dead” respec-
tively. More hidden levels are proven not to improve NN performance. Since