1                                                          The SAS System                         22:20 Wednesday, February 14, 1996

NOTE: Copyright (c) 1989-1992 by SAS Institute Inc., Cary, NC, USA. 
NOTE: SAS (r) Proprietary Software Release 6.09  TS042
      Licensed to UNIVERSITY OF NORTH CAROLINA, Site 0005540009.




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NOTE: AUTOEXEC processing beginning; file is /home/users/qaqish/autoexec.sas.

NOTE: SAS initialization used:
      real time           0.48 seconds
      cpu time            0.26 seconds


NOTE: AUTOEXEC processing completed.

1          * TIES.SAS
2          * xref:
3          * input:
4          * output:
5          * does: - Simulate grouped survival data
6                  - Evaluate methods of tie handling
7                  - exponential distribution
8                  - no censoring
9          ***************************************************;
10         %let n=20;      * sample size;
11         %let nsim=1000; * # simulations;
12         %let width=0.1; * width of rounding interval;
13         %let beta=0.69; * slope for z;
14         ***************************************************;
15         data A (keep=sim t delta z);
16           retain
17             h      &width
18             n      &n
19             beta   &beta
20             nsim   &nsim
21             beta   &beta
22             delta  1
23             seed   21496
24           ;
25         
26           array zz (*) zz1 - zz&n;
27         
28           x = -1; d = 2/(n-1);   * equally spaced on [-1,1];
29           do i=1 to n; zz(i)=x; x+d;  end;
30         
31           do sim = 1 to nsim;
32             do i = 1 to n;
33               z = zz(i);
34               psi = exp(z * beta);
35               t = -log(ranuni(seed)) / psi;
36               t = round(t, h);
37               output;
38             end;
39           end;
40         
2 The SAS System                                             22:20 Wednesday, February 14, 1996

41           run;

NOTE: The data set WORK.A has 20000 observations and 4 variables.
NOTE: DATA statement used:
      real time           1.82 seconds
      cpu time            0.70 seconds


42         ***************************************************;
43         proc freq data=A;
44           table t;  * ties?;
45           run;

NOTE: The PROCEDURE FREQ printed pages 1-2.
NOTE: PROCEDURE FREQ used:
      real time           0.58 seconds
      cpu time            0.24 seconds


46         ***************************************************;
47         proc phreg data=A outest=EX noprint;
NOTE: PROCEDURE PHREG used:
      real time           28.41 seconds
      cpu time            27.30 seconds

NOTE: The data set WORK.EX has 1000 observations and 6 variables.

48           model t    * delta(0) = z  / ties = Exact;
49           by sim;
50           run;
51         ***************************************************;
52         proc phreg data=A outest=EF noprint;
NOTE: PROCEDURE PHREG used:
      real time           7.09 seconds
      cpu time            6.44 seconds

NOTE: The data set WORK.EF has 1000 observations and 6 variables.

53           model t    * delta(0) = z  / ties = Efron;
54           by sim;
55           run;
56         ***************************************************;
57         proc phreg data=A outest=BR noprint;
NOTE: PROCEDURE PHREG used:
      real time           5.74 seconds
      cpu time            5.15 seconds

NOTE: The data set WORK.BR has 1000 observations and 6 variables.

58           model t    * delta(0) = z  / ties = breslow;
59           by sim;
60           run;
61         ***************************************************;
62         proc phreg data=A outest=DI noprint;
NOTE: PROCEDURE PHREG used:
      real time           8.05 seconds
      cpu time            7.44 seconds

NOTE: The data set WORK.DI has 1000 observations and 6 variables.

63           model t    * delta(0) = z  / ties = discrete;
64           by sim;
65           run;
3 The SAS System                                             22:20 Wednesday, February 14, 1996

66         ***************************************************;
67         
68         data B (keep = ex ef br di ef_e br_e di_e);
69           merge
70             EX (rename=(z=ex))
71             EF (rename=(z=ef))
72             BR (rename=(z=br))
73             DI (rename=(z=di))
74           ;
75           if (_type_ = "PARMS");
76           ef_e = ef-ex;
77           br_e = br-ex;
78           di_e = di-ex;
79           label
80             ex   = "Exact"
81             ef   = "Efron approximation"
82             br   = "Breslow approximation"
83             di   = "Discrete approximation"
84             ef_e = "Efron approximation error"
85             br_e = "Breslow approximation error"
86             di_e = "Discrete approximation error"
87           ;
88         
89           run;

NOTE: The data set WORK.B has 1000 observations and 7 variables.
NOTE: DATA statement used:
      real time           0.37 seconds
      cpu time            0.13 seconds


90         
91         ***************************************************;
92         
93         proc univariate data=B;
94           var ex ef_e br_e di_e;
95           run;

NOTE: The PROCEDURE UNIVARIATE printed pages 3-6.
NOTE: PROCEDURE UNIVARIATE used:
      real time           0.15 seconds
      cpu time            0.12 seconds


NOTE: The SAS System used:
      real time           53.41 seconds
      cpu time            47.88 seconds

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