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.
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
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.
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
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.
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
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.
Contrast Test Results Wald Contrast DF Chi-Square Pr > ChiSq Pairwise 3 17.9164 0.0005
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.
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