Example


Example 73.1. Analysis of the VA Lung Cancer Data

This example uses the Veteran's Administration lung cancer data presented in Appendix 1 of Kalbfleisch and Prentice (1980). In this trial, males with advanced inoperable lung cancer were randomized to a standard therapy and a test chemotherapy. The primary end point for the therapy comparison was time to death in days, represented by the variable Time . Negative values of Time are censored values. The data include information on a number of explanatory variables : Therapy (type of therapy: standard or test), Cell (type of tumor cell: adeno, large, small, or squamous), Prior (prior therapy: 0=no, 10=yes), Age (age in years ), Duration (months from diagnosis to randomization), and Kps (Karnofsky performance scale). A censoring indicator variable Censor is created from the data, with value 1 indicating a censored time and value 0 an event time.

  proc format;   value yesno 0='no' 10='yes';   run;   data VALung;   drop check m;   retain Therapy Cell;   infile cards column=column;   length Check $ 1;   label Time='time to death in days'   Kps='Karnofsky performance scale'   Duration='months from diagnosis to randomization'   Age='age in years'   Prior='prior therapy'   Cell='cell type'   Therapy='type of treatment';   format Prior yesno.;   M=Column;   input Check $ @@;   if M>Column then M=1;   if Check='s'Check='t' then do;   input @M Therapy $ Cell $;   delete;   end;   else do;   input @M Time Kps Duration Age Prior @@;   censor=(Time<0);   Time=abs(Time);   end;   datalines;   standard squamous   72 60  7 69  0   411 70  5 64 10   228 60  3 38  0   126 60  9 63 10   118 70 11 65 10    10 20  5 49  0    82 40 10 69 10   110 80 29 68  0   314 50 18 43  0   100 70  6 70  0    42 60  4 81  0     8 40 58 63 10   144 30  4 63  0   25 80  9 52 10    11 70 11 48 10   standard small   30 60  3 61  0   384 60  9 42  0     4 40  2 35  0    54 80  4 63 10   13 60  4 56  0   123 40  3 55  0   97 60  5 67  0   153 60 14 63 10   59 30  2 65  0   117 80  3 46  0    16 30  4 53 10   151 50 12 69  0   22 60  4 68  0    56 80 12 43 10    21 40  2 55 10    18 20 15 42  0   139 80  2 64  0    20 30  5 65  0    31 75  3 65  0    52 70  2 55  0   287 60 25 66 10    18 30  4 60  0    51 60  1 67  0   122 80 28 53  0   27 60  8 62  0    54 70  1 67  0     7 50  7 72  0    63 50 11 48  0   392 40  4 68  0    10 40 23 67 10   standard adeno   8 20 19 61 10    92 70 10 60  0    35 40  6 62  0   117 80  2 38  0   132 80  5 50  0    12 50  4 63 10   162 80  5 64  0     3 30  3 43  0   95 80  4 34  0   standard large   177 50 16 66 10   162 80  5 62  0   216 50 15 52  0   553 70  2 47  0   278 60 12 63  0    12 40 12 68 10   260 80  5 45  0   200 80 12 41 10   156 70  2 66  0   182 90  2 62  0   143 90  8 60  0   105 80 11 66  0   103 80  5 38  0   250 70  8 53 10   100 60 13 37 10   test squamous   999 90 12 54 10   112 80  6 60  0   87 80  3 48  0   231 50  8 52 10   242 50  1 70  0   991 70  7 50 10   111 70  3 62  0     1 20 21 65 10   587 60  3 58  0   389 90  2 62  0    33 30  6 64  0    25 20 36 63  0   357 70 13 58  0   467 90  2 64  0   201 80 28 52 10     1 50  7 35  0   30 70 11 63  0    44 60 13 70 10   283 90  2 51  0    15 50 13 40 10   test small   25 30  2 69  0   103 70 22 36 10    21 20  4 71  0    13 30  2 62  0   87 60  2 60  0     2 40 36 44 10    20 30  9 54 10     7 20 11 66  0   24 60  8 49  0    99 70  3 72  0     8 80  2 68  0    99 85  4 62  0   61 70  2 71  0    25 70  2 70  0    95 70  1 61  0    80 50 17 71  0   51 30 87 59 10    29 40  8 67  0   test adeno   24 40  2 60  0    18 40  5 69 10   83 99  3 57  0    31 80  3 39  0   51 60  5 62  0    90 60 22 50 10    52 60  3 43  0    73 60  3 70  0   8 50  5 66  0    36 70  8 61  0    48 10  4 81  0     7 40  4 58  0   140 70  3 63  0   186 90  3 60  0    84 80  4 62 10    19 50 10 42  0   45 40  3 69  0    80 40  4 63  0   test large   52 60  4 45  0   164 70 15 68 10    19 30  4 39 10    53 60 12 66  0   15 30  5 63  0    43 60 11 49 10   340 80 10 64 10   133 75  1 65  0   111 60  5 64  0   231 70 18 67 10   378 80  4 65  0    49 30  3 37  0   ;  

PROC TPHREG is invoked to fit the Cox proportional hazards model to these data. Variables Prior , Cell ,and Therapy , which are categorical variables, are declared in the CLASS statement. By default, PROC TPHREG parameterizes the CLASS variables using the reference coding with the last category as the reference category. However, you can explicitly specify the reference category of your choice. Here, Prior =no is chosen as the reference category for prior therapy, Cell =large is chosen as the reference category for type of tumor cell, and Therapy =standard is chosen as the reference category for the type of therapy. Both the continuous explanatory variables ( Kps , Duration ,and Age ) and the CLASS explanatory variables ( Prior , Cell , and Therapy ) are specified in the MODEL statement. Knowing how the Cell variable is parameterized, the hazards ratios of all pairs of cell-type groups can be estimated using the ESTIMATE=EXP option in a CONTRAST statement.

  proc tphreg data=VALung;   class Prior(ref='no') Cell(ref='large') Therapy(ref='standard');   model Time*censor(1) = Kps Duration Age Prior Cell Therapy;   contrast 'Pairwise' cell 1  0  0, /* adeno vs large    */   cell 0  1  0, /* small vs large    */   cell 0  0  1, /* squamous vs large */   cell 1 -1  0, /* adeno vs small    */   cell 1  0 -1, /* adeno vs squamous */   cell 0  1 -1  /* small vs squamous */   / estimate=exp;   run;  

The output of PROC TPHREG is very similar to that of PROC PHREG, with additional tables for displaying the parameterization of the CLASS variables, the multiparameter tests for the model effects, and the analysis results of the specified contrasts.

Coding of the CLASS variables is displayed in Output 73.1.1. There is one dummy variable for Prior and one for Therapy , since both variables are binary. The dummy variable has a value of 0 for the reference category ( Prior =no, Therapy =standard). The CLASS variable Cell has four categories and are represented by three dummy variables. Note that the reference category, Cell =large, has a value of 0 for all three dummy variables.

Output 73.1.1: Reference Coding of CLASS Variables
start example
  The TPHREG Procedure   Class Level Information   Class       Value        Design Variables   Prior       no            0   yes           1   Cell        adeno         1      0      0   large         0      0      0   small         0      1      0   squamous      0      0      1   Therapy     standard      0   test          1  
end example
 

The test results of individual model effects are shown in Output 73.1.2. There is a strong prognostic effect of the Karnofsky performance status on patient survival ( p< . 0001), and the survival times in the various cell-type groups differ significantly ( p = 0 . 0005). However, there is a lack of evidence that the test chemotherapy differs from the standard therapy ( p = 0 . 1617) after accounting for the prognostic effects of other variables.

Output 73.1.2: Wald Tests for Individual Model Effects
start example
  Type 3 Tests   Wald   Effect        DF    Chi-Square    Pr > ChiSq   Kps            1       35.1124        <.0001   Duration       1        0.0001        0.9920   Age            1        0.8443        0.3582   Prior          1        0.0971        0.7554   Cell           3       17.9164        0.0005   Therapy        1        1.9579        0.1617  
end example
 

In the Cox proportional hazards model, the effects of the covariates are to act multiplicatively on the hazard of the survival time, and therefore it is a little easier to interpret the corresponding hazards ratios than the regression parameters. For a parameter that corresponds to an continous variable, the hazard ratio is the ratio of hazard rates for a increase of one unit of the variable. From Output 73.1.3, the hazard ratio estimate for Kps is 0.968, meaning that an increase of 10 units in Karnofsky performance scale will shrink the hazard rate by 1 ˆ’ (0 . 968) 10 =28%. For a CLASS variable parameter, the hazard ratio is the ratio of the hazard rates between the given category and the reference category. The hazard rate of Cell =adeno is 220% that of Cell =large, the hazard rate of Cell =small is 158% that of Cell =large, and the hazard rate of Cell =squamous is only 67% that of Cell =large.

Output 73.1.3: Inference about the Regression Parameters
start example
  Analysis of Maximum Likelihood Estimates   Parameter      Standard   Parameter            DF      Estimate         Error    Chi-Square    Pr > ChiSq   Kps                   1   0.03262       0.00551       35.1124        <.0001   Duration              1   0.0000916       0.00913        0.0001        0.9920   Age                   1   0.00855       0.00930        0.8443        0.3582   Prior     yes         1       0.07232       0.23213        0.0971        0.7554   Cell      adeno       1       0.78867       0.30267        6.7899        0.0092   Cell      small       1       0.45686       0.26627        2.9438        0.0862   Cell      squamous    1   0.39963       0.28266        1.9988        0.1574   Therapy   test        1       0.28994       0.20721        1.9579        0.1617   Analysis of Maximum Likelihood Estimates   Hazard   Parameter               Ratio    Variable Label   Kps                     0.968    Karnofsky performance scale   Duration                1.000    months from diagnosis to randomization   Age                     0.991    age in years   Prior     yes           1.075    prior therapy yes   Cell      adeno         2.200    cell type adeno   Cell      small         1.579    cell type small   Cell      squamous      0.671    cell type squamous   Therapy   test          1.336    type of treatment test  
end example
 

Although there are six pairwise comparisons for the four types of tumor cells in the CONTRAST statement, the overall test has only 3 degrees of freedom (Output 73.1.4). In fact this is the very same testing of no prognostics effect between the cell-type groups as shown in Output 73.1.2.

Output 73.1.4: Overall Test for All Paired Cell-type Groups
start example
  Contrast Test Results   Wald   Contrast      DF    Chi-Square    Pr > ChiSq   Pairwise       3       17.9164        0.0005  
end example
 

Output 73.1.5 is generated by the ESTIMATE=EXP option in the CONTRAST statement. Values of the Estimate column are the estimated hazard ratios: 2.200 for ˜adeno' vs ˜large', 1.579 for ˜small' versus ˜large', 0.671 for ˜squamous' versus ˜large', 1.394 for ˜adeno' versus 'small', 3.282 for ˜adeno' versus ˜squamous', and 2.355 for ˜small' versus ˜squamous'. Note that the first three hazard ratio estimates are already given in the parameter estimate table (Output 73.1.3), and therefore there is no need to specify those first three rows in the CONTRAST statement.

Output 73.1.5: Hazards Ratios for All Paired Cell-type Groups
start example
  Contrast Rows Estimation and Testing Results   Standard   Contrast   Type        Row   Estimate      Error    Alpha    Confidence Limits   Pairwise   EXP           1     2.2005     0.6660     0.05     1.2159     3.9824   Pairwise   EXP           2     1.5791     0.4205     0.05     0.9370     2.6611   Pairwise   EXP           3     0.6706     0.1895     0.05     0.3853     1.1669   Pairwise   EXP           4     1.3935     0.3840     0.05     0.8119     2.3916   Pairwise   EXP           5     3.2815     0.9870     0.05     1.8200     5.9167   Pairwise   EXP           6     2.3549     0.6480     0.05     1.3732     4.0384   Contrast Rows Estimation and Testing Results   Wald   Contrast   Type        Row   Chi-Square    Pr > ChiSq   Pairwise   EXP           1       6.7899        0.0092   Pairwise   EXP           2       2.9438        0.0862   Pairwise   EXP           3       1.9988        0.1574   Pairwise   EXP           4       1.4497        0.2286   Pairwise   EXP           5      15.6101        <.0001   Pairwise   EXP           6       9.6866        0.0019  
end example
 



SAS.STAT 9.1 Users Guide (Vol. 6)
SAS.STAT 9.1 Users Guide (Vol. 6)
ISBN: N/A
EAN: N/A
Year: 2004
Pages: 127

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