12.8 - Example

( 13.5_ph regression.sas ): A safety and efficacy study was conducted in 83 patients with malignant mesothelioma, an uncommon lung cancer that is strongly associated with asbestos exposure. Patients underwent one of three types of surgery, namely, biopsy, limited resection, and extrapleural pneumonectomy (EPP). Treatment assignment was nonrandomized and based on the extent of disease at the time of diagnosis. Thus, there can be a strong procedure selection bias.

***********************************************************************
* This is a program that illustrates the use of PROC PHREG in SAS     *
* to perform proportional hazards regression.                         *
*                                                                     *
* The sample data set is based on the results from an SE trial on 83  *
* patients with malignant mesothelioma, an uncommon lung cancer that  *
* is strongly associated with asbestos exposure.  Patients underwent  *
* one of three types of surgery, namely, biopsy, limited resection,   *
* and extrapleural pneumonectomy (EPP).  Treatment assignment was     *
* based on the extent of disease at the time of diagnosis.            *
***********************************************************************;

proc format;
value sexfmt 0='female' 1='male';
value psfmt 0='low' 1='high';
value wtchgfmt 1='no' 2='yes';
value surgfmt 1='biopsy' 2='limited resection' 3='EPP';
value eventfmt 0='no' 1='yes';
run;

data mesoth;
input age sex ps hist wtchg surg pftime prog stime dead;
label age='Age'
      sex='Sex'
      ps='Performance Status'
      hist='Histologic Subtype'
      wtchg='Weight Change at DX'
      surg='Surgery Type'
      pftime='PFT Event'
      prog='PFtime Censoring'
      stime='Survival Time'
      dead='Death Event';
format sex sexfmt.
       ps psfmt.
       wtchg wtchgfmt.
       surg surgfmt.
       prog eventfmt.
       dead eventfmt.;
cards;
60 1 1 136 1 3 394   1 823  1
59 1 0 136 2 3 1338  0 1338 0
51 0 0 130 1 1 184   1 270  1
73 1 1 136 1 3 320   0 320  1
74 1 0 136 2 1 168   0 168  1
39 0 0 136 1 1 36    1 247  1
46 1 1 131 1 3 552   1 694  0
71 1 0 136 1 1 133   1 316  1
69 1 0 136 1 1 175   1 725  0
49 1 0 131 1 1 327   0 327  1
69 1 0 131 1 2 0     0 0    1
72 1 0 131 1 1 676   1 963  0
44 0 0 130 2 2 223   1 265  1
45 1 0 136 2 2 184   1 237  1
57 1 0 132 1 2 145   1 176  1
60 0 1 131 1 1 316   0 316  1
22 1 1 131 1 2 87    1 310  1
46 0 1 131 1 1 135   1 166  1
60 1 0 131 1 3 1     1 28   1
72 1 0 131 1 2 199   1 730  1
65 1 0 131 1 3 39    0 39   1
65 1 1 131 1 2 61    1 116  1
60 1 0 131 1 3 17    0 17   1
64 1 0 131 2 3 799   1 1229 1
61 1 0 131 2 1 61    1 294  1
38 1 0 131 1 1 176   1 322  1
65 1 1 136 1 3 6     0 6    1
73 0 1 131 1 2 292   1 422  1
74 1 0 136 2 2 22    1 22   1
76 1 0 136 1 1 106   1 375  1
57 1 1 131 1 3 248   1 302  1
60 0 0 .   1 1 63    1 365  1
56 1 0 136 1 1 145   1 387  1
62 0 0 136 1 1 104   1 327  1
60 1 0 131 1 1 20    1 247  1
67 0 0 131 1 1 181   1 669  1
64 1 0 131 1 2 89    1 948  1
67 1 1 136 1 1 0     1 400  1
56 0 1 131 1 2 724   1 1074 0
52 1 0 160 2 1 62    1 137  1
56 1 0 131 1 3 93    1 210  1
44 1 0 136 1 3 402   1 648  1
50 0 0 136 2 2 141   1 520  1
63 1 0 .   2 1 156   1 304  1
68 1 1 131 1 2 265   1 349  1
50 1 0 .   2 3 305   1 317  1
41 0 1 131 1 1 181   1 395  1
60 1 0 131 1 1 274   1 503  1
65 1 0 136 2 2 20    1 20   1
47 1 1 131 1 3 411   1 679  0
46 1 1 131 1 2 624   0 624  0
70 1 1 131 1 2 278   1 617  0
58 1 0 136 1 1 20    1 85   1
57 1 1 132 1 3 112   1 139  1
75 1 0 132 2 2 47    1 47   1
66 1 1 136 1 3 294   1 523  1
77 1 0  .  1 1 126   1 157  1
65 0 0  .  2 1 117   1 545  0
46 0 0 131 1 1 63    1 218  1
71 0 1 132 2 1 139   0 139  1
61 1 0 136 1 1 538   1 1170 0
58 1 0 131 1 3 390   1 722  1
49 1 1 136 1 3 1102  0 1102 0
50 1 0 136 1 3 166   1 182  1
73 1 0 136 1 2 58    1 136  1
44 1 0 136 1 1 406   0 406  1
47 0 1 131 1 3 1123  0 1123 0
68 1 0 136 1 1 1009  1 1029 0
66 1 0 132 1 2 37    1 112  1
46 1 1 131 1 1 104   1 764  1
56 1 1 136 1 2 33    1 225  1
68 1 1 136 1 1 20    1 122  1
59 1 0 136 1 2 73    1 165  1
58 0 0 131 1 1 4     0 4    1
66 1 1 132 2 2 205   1 361  1
82 1 0 160 1 1 78    0 78   1
73 1 0 131 1 1 1265  0 1265 1
57 0 0 130 1 2 273   1 318  1
72 1 1 136 2 1 2     1 362  1
69 1 1   . 1 2 1093  0 1093 0
64 0 1 130 1 1 475   0 475  1
65 1 1 130 1 2 292   0 292  1
72 1 1 130 1 2 324   1 499  0
run;

proc print data=mesoth;
title 'Mesothelioma Example';
run;

data mesoth2;
set mesoth;
biop_EPP=0;
lr_EPP=0;
if surg=1 then biop_EPP=1;
if surg=2 then lr_EPP=1;
wtchg=wtchg-1;
run;

proc phreg data=mesoth2;
model stime*dead(0)=biop_EPP lr_EPP age sex ps hist wtchg/selection=stepwise
      include=2 slentry=0.10 slstay=0.10 risklimits;
title2 "Proportional Hazards Regression of Survival Time";
run;

A proportional hazards regression analysis was applied that included a stepwise selection process to build a model with prognostic factors in addition to surgery type. Examine the program:

Run the program. Do you agree that histologic subtype is the only statistically significant covariate (p = 0.025) ?

If there is a large amount of correlation among a set of regressors, then a problem known as collinearity can exist. Collinearity can cause difficulties in interpretation because it is not obvious which regressor in a set of highly correlated regressors should be used in the model.

In addition, collinearity, if not diagnosed, can lead to numerical instabilities in the software and yield strange results. It is recommended that the correlations among the set of regressors be examined prior to the model-building process, e.g., using PROC CORR of SAS.

If two or more regressors are observed to be highly correlated (say with correlations above 0.8 or below -0.8), then most of the variables in a correlated set should not be included in the model-building process.