* Weibull Fitting to Cox Regression.sps.
* Written by PSKL on 21/05/03.

GET DATA /TYPE=XLS
   /FILE='H:\documents\PhD\Full Longitudinal\Cox Regression Survival.xls'
   /SHEET=name 'Sheet1'
   /CELLRANGE=full
   /READNAMES=on .

save outfile= 'd:\temp1.sav'
 /keep time survival.

get file=  'd:\temp1.sav'.

* Check log-cumulative hazard plot for linearity.

Compute LLS=ln(-ln( survival)).
compute Ltime=ln(time).


GRAPH
  /SCATTERPLOT(BIVAR)=Ltime WITH LLS
  /MISSING=LISTWISE
  /TITLE= 'Log Cumulative Hazard Plot '.

Graph

Notes
Output Created 21-MAY-2003 18:25:35
Comments
Input Data d:\temp1.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 3764
Syntax GRAPH
/SCATTERPLOT(BIVAR)=Ltime WITH LLS
/MISSING=LISTWISE
/TITLE= 'Log Cumulative Hazard Plot '.
Resources Elapsed Time 0:00:00.18

Scatter of log cumulative hazard plot 

* Weibull fitting, with starting values derived from overall plot.

* NonLinear Regression.
MODEL PROGRAM LAMBDA=0.0000454 GAMMA=1 .
COMPUTE Weipred = exp(-lambda*time**gamma).
NLR survival
  /PRED WEIPRED
  /SAVE PRED RESID
  /CRITERIA SSCONVERGENCE 1E-9 PCON 1E-9 .

Non-linear Regression

Notes
Output Created 21-MAY-2003 18:25:36
Comments
Input Data d:\temp1.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 3764
Syntax MODEL PROGRAM LAMBDA=0.0000454 GAMMA=1 .
COMPUTE Weipred = exp(-lambda*time**gamma).
NLR survival
/PRED WEIPRED
/SAVE PRED RESID
/CRITERIA SSCONVERGENCE 1E-9 PCON 1E-9 .
Resources Elapsed Time 0:00:01.92 

All the derivatives will be calculated numerically.

The following new variables are being created:

Name          Label

WEIPRED       Predicted Values
RESID         Residuals




 Iteration  Residual SS      LAMBDA       GAMMA

     1      412.1269358  .000045400  1.00000000
     1.1    672.9363194  .000795523  -.61988490
     1.2    604.8898884  .000380342  .538556458
     1.3    3.171811649  .000198129  1.04546895
     2      3.171811649  .000198129  1.04546895
     2.1    49.99267769  .000442051  .885199603
     2.2    2.737176386  .000221700  1.02851242
     3      2.737176386  .000221700  1.02851242
     3.1    2.252128005  .000273055  .999452263
     4      2.252128005  .000273055  .999452263
     4.1    1.702245112  .000328373  .976324586
     5      1.702245112  .000328373  .976324586
     5.1    1.666413371  .000441317  .934344826
     6      1.666413371  .000441317  .934344826
     6.1    .7418645929  .000501598  .922967769
     7      .7418645929  .000501598  .922967769
     7.1    .6012124609  .000620164  .893578802
     8      .6012124609  .000620164  .893578802
     8.1    .3317988728  .000740928  .871564909
     9      .3317988728  .000740928  .871564909
     9.1    .2000497401  .000862360  .852558894
    10      .2000497401  .000862360  .852558894
    10.1    .1493013321  .000984233  .835850907
    11      .1493013321  .000984233  .835850907
    11.1    .1220508864  .001008520  .833833721
    12      .1220508864  .001008520  .833833721
    12.1    .1220219191  .001007569  .833993599
    13      .1220219191  .001007569  .833993599
    13.1    .1220219185  .001007585  .833991713
    14      .1220219185  .001007585  .833991713
    14.1    .1220219185  .001007584  .833991774

Run stopped after 31 model evaluations and 14 derivative evaluations.
Iterations have been stopped because the relative reduction between successive
residual sums of squares is at most SSCON = 1.000E-09


Nonlinear Regression Summary Statistics     Dependent Variable SURVIVAL

  Source                 DF  Sum of Squares  Mean Square

  Regression              2     1520.60774      760.30387
  Residual             3762         .12202   3.243539E-05
  Uncorrected Total    3764     1520.72976

  (Corrected Total)    3763      108.10777

  R squared = 1 - Residual SS / Corrected SS =     .99887

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  LAMBDA      .001007584  5.07795E-06   .000997628   .001017540
  GAMMA       .833991774   .000653264   .832710987   .835272560

  Asymptotic Correlation Matrix of the Parameter Estimates

              LAMBDA     GAMMA

  LAMBDA      1.0000    -.9980
  GAMMA       -.9980    1.0000


GRAPH
  /SCATTERPLOT(OVERLAY)=time time  WITH survival weipred (PAIR)
  /MISSING=LISTWISE .

Graph

Notes
Output Created 21-MAY-2003 18:25:37
Comments
Input Data d:\temp1.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 3764
Syntax GRAPH
/SCATTERPLOT(OVERLAY)=time time WITH survival weipred (PAIR)
/MISSING=LISTWISE .
Resources Elapsed Time 0:00:00.09

Scatter of survival weipred time time 

SAVE TRANSLATE OUTFILE='I:\Research Projects\Longevity\Weibull Fitting to Cox Regression.xls'
  /TYPE=XLS /MAP /REPLACE /FIELDNAMES.

Data written to I:\Research Projects\Longevity\Weibull Fitting to Cox Regression.xls.
6 variables and 3764 cases written to range: SPSS.
Variable: TIME       Type: Number   Width: 11   Dec: 0
Variable: SURVIVAL   Type: Number   Width: 11   Dec: 5



Variable: LLS        Type: Number   Width:  8   Dec: 2
Variable: LTIME      Type: Number   Width:  8   Dec: 2
Variable: WEIPRED    Type: Number   Width:  8   Dec: 2
Variable: RESID      Type: Number   Width:  8   Dec: 2