Stat Computing > SAS > Textbook Examples > Survival Analysis, by Klein and Moeschberger

SAS Textbook Examples
Survival Analysis by John P. Klein and Melvin L. Moeschberger
Chapter 10: Additive Hazards Regression Model

The material in this chapter is based on the M215 (Fall 2001) Final Project Report by Dong Ding, Weihua Huang, Luohua Jiang, Liyuan Xiong and Kefei Zhou. We thank them for permission to adapt and distribute this page via our web site. This chapter is all done using the SAS macro program for the additive hazard model provided from the author's website. The page is revised on May  4, 2009.

Section 12.2: Least-Squares Estimation for the Nonparametric, Additive Hazard Model

Example 10.1 on page 309 using the breast cancer data set described in Section 1.5. We have created a data step for it and you can download it from here.

%include 'c:\sasmacros\additive.sas';

proc sort data = sec1_5;
 by time; 
run;
data bcnew; 
  set sec1_5; 
  positive = (group=2);
  drop group; 
run;
proc iml;
  option={y, n, y, n, n};
  contr={1 -1}; 
  effects={'positive'};
  timeunit={'month'};
%additive (bcnew,0.05, timeunit, effects,  option, contr, betab, testb);
quit;

proc print data = betab (obs=10) noobs;
run;

COL1      COL2       COL3        COL4        COL5        COL6        COL7        COL8       COL9

 19     0.02778    -0.02778    0.027778    0.02778    -0.026666    -0.08222    0.08222    0.02667
 22     0.02778     0.08333    0.027778    0.11453    -0.026666    -0.14114    0.08222    0.30781
 23     0.02778     0.20833    0.027778    0.16954    -0.026666    -0.12395    0.08222    0.54062
 25     0.05635     0.17976    0.039849    0.17193    -0.021753    -0.15721    0.13445    0.51673
 30     0.08576     0.15035    0.049528    0.17442    -0.011311    -0.19151    0.18283    0.49221
 34     0.11606     0.12005    0.058063    0.17704     0.002264    -0.22694    0.22986    0.46703
 37     0.14731     0.08880    0.065938    0.17977     0.018078    -0.26355    0.27655    0.44115
 38     0.14731     0.23165    0.065938    0.22962     0.018078    -0.21840    0.27655    0.68171
 42     0.14731     0.39832    0.065938    0.28373     0.018078    -0.15779    0.27655    0.95443
 46     0.17957     0.36606    0.073406    0.28556     0.035699    -0.19363    0.32344    0.92575

Notice:
Col1: time
Col2: beta_0
col3: beta_1
col4: standard error for beta_0
col5: standard error for beta_1
col6: lower confidence limit for beta_0
col7: lower confidence limit for beta_1
col8: upper confidence limit for beta_0
col9: upper confidence limit for beta_1

title "Figure 10.1";
axis1 label=(j=c 'Months') order=(0 to 100 by 20) minor = none;
axis2 label=(a=90 j=c 'Estimated Baseline Cumulative Hazard Rate for Immunoperoxidase Negative Patients')
      order=(0.0 to 1.0 by 0.2) minor = none;
symbol1 interpol=stepjr c=black l=1 value=none;
symbol2 interpol=stepjr c=blue l=3 value=none;
symbol3 interpol=stepjr c=red l=3 value=none;

proc gplot data=betab;
  plot col2*col1 col6*col1 col8*col1/overlay haxis=axis1 vaxis=axis2;
run;
quit;

title "Figure 10.2";
axis1 label=(j=c 'Months') order=(0 to 100 by 20) minor=none;
axis2 label=(a=90 j=c 'Estimated Cumulative Excess Risk for Immunoperosidase Positive Patients')
      order=(-0.5 to 2.0 by 0.5) minor=none;
 
proc gplot data=betab;
  plot col3*col1 col7*col1 col9*col1/overlay haxis=axis1 vaxis=axis2;
run;
quit;

Example 10.2 on page 311 using data set larynx described in section 1.8.

data larynx1;
  length time death z1-z3 age 8.;
  set larynx; 
  z1=(stage=2); 
  z2=(stage=3); 
  z3=(stage=4); 
  age=age-64.11;
  keep time death z1 z2 z3 age; 
run;
proc sort data = larynx1; 
   by time; 
run;

proc iml;
  option={y, n, y, n, n};
  contrast={0 1 -1 0 0, 0 0 1 -1 0};
  effects={'z1', 'z2' ,'z3', 'age'};
  timeunit={'Years'};
  %additive (larynx1, 0.05, timeunit, effects,  option, contrast, beta, test);
quit;

Col1: time
Col2-7:  beta_0-beta_4
col7-11: standard errors for beta_0-beta_4
col2-16: lower confidence limit for beta_0-beta_4
col7-21: upper confidence limit for beta_0-beta_4

title "Figure 10.3";
axis1 label=(j=c 'Years') minor=none;
axis2 label=(a=90 j=c 'Estimated Baseline Cumulative Hazard Rate for Stage I Patients')
      minor = none;

proc gplot data=beta;
plot col2*col1 col12*col1 col17*col1/overlay haxis=axis1 vaxis=axis2;
run;
quit;

title "Figure 10.4";
axis1 label=(j=c 'Years') minor=none;
axis2 label=(a=90 j=c 'Estimated Cumulative Excess Risk of Stage II Patients')
      order=(-0.4 to 0.6 by 0.2) minor = none;

proc gplot data=beta;
plot col3*col1 col13*col1 col18*col1/overlay haxis=axis1 vaxis=axis2;
run;
quit;

title "Figure 10.5";
axis1 label=(j=c 'Years') minor=none;
axis2 label=(a=90 j=c 'Estimated Cumulative Excess Risk of Stage III Patients')
      order=(-0.2 to 0.8 by 0.2) minor=none;

proc gplot data=beta;
plot col4*col1 col14*col1 col19*col1/overlay haxis=axis1 vaxis=axis2;
run;
quit;

title "Figure 10.6";
axis1 label=(j=c 'Years') minor = none;
axis2 label=(a=90 j=c 'Estimated Cumulative Excess Risk of Stage IV Patients')
      order=(-0.5 to 3.5 by 0.5) minor = none;

proc gplot data=beta;
  plot col5*col1 col15*col1 col20*col1/overlay haxis=axis1 vaxis=axis2;
run;
quit;

title "Figure 10.7";
axis1 label=(j=c 'Years') minor = none;
axis2 label=(a=90 j=c 'Estimated Cumulative Excess Risk Due to Age')
      order=(-0.02 to 0.04 by 0.02) minor = none;

proc gplot data=beta;
plot col6*col1 col16*col1 col21*col1/overlay haxis=axis1 vaxis=axis2;
run;
quit;

Section 10.3: Testing in the Nonparametric Additive Hazard Model

Table in the middle of page 323 of Example 10.2 (continued).

options nocenter;
proc iml;
  option={ n, y, n, n, y}; 
  contrast={0 1 -1 0 0, 0 0 1 -1 0};
  effects={'z1', 'z2' ,'z3', 'age'};
  timeunit={'Years'};
%additive (larynx1, 0.05, timeunit, effects,  option, contrast, beta, test);
quit;

    Additive Hazards Model

No missing data: all observations were used in analysis.

       90 observations used.

Estimates are restricted to the time interval 0 to 4.30

               Global Test

Chi-Square d.f p-value

   10.9613   4  0.0270

           Analysis of Variance

Effect Chi-Square d.f p-value

z1         0.1456   1  0.7027
z2         3.0062   1  0.0829
z3         8.4655   1  0.0036
age        0.2333   1  0.6291

        Test of Linear Combinations

Contrast Matrix         0         1        -1         0         0
                        0         0         1        -1         0

Chi-Square d.f p-value

    6.8131   2  0.0332

title "beta_1=beta_2";
proc iml;
  option={ n, y, n, n, y}; 
  contrast={0 1 -1 0 0};
  effects={'z1', 'z2' ,'z3', 'age'};
  timeunit={'Years'};
%additive (larynx1, 0.05, timeunit, effects,  option, contrast, beta, test);
quit;

Contrast Matrix         0         1        -1         0         0

Chi-Square d.f p-value

    1.5884   1  0.2076

title "beta_1=beta_3";
proc iml;
  option={ n, y, n, n, y}; 
  contrast={0 1 0 -1  0};
  effects={'z1', 'z2' ,'z3', 'age'};
  timeunit={'Years'};
%additive (larynx1, 0.05, timeunit, effects,  option, contrast, beta, test);
quit;

Contrast Matrix         0         1         0        -1         0

Chi-Square d.f p-value

    6.9390   1  0.0084

title "beta_2=beta_3";
proc iml;
  option={ n, y, n, n, y}; 
  contrast={0 0 1 -1  0};
  effects={'z1', 'z2' ,'z3', 'age'};
  timeunit={'Years'};
%additive (larynx1, 0.05, timeunit, effects,  option, contrast, beta, test);
quit;

Contrast Matrix         0         0         1        -1         0

Chi-Square d.f p-value

    3.4238   1  0.0643

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