Table 3.1 on page 78 using the actg320 dataset. The z value and confidence intervals are not provided in the proc phreg output, but the confidence interval can be calculated manually. For example, the lower confidence interval limit will be -.68425 – .21492*1.96 = -1.1054.
proc phreg data = actg320; model time*censor(0) = tx; run;
The PHREG Procedure
Model Information
Data Set WORK.ACTG320
Dependent Variable TIME
Censoring Variable CENSOR
Censoring Value(s) 0
Ties Handling BRESLOW
Number of Observations Read 1151
Number of Observations Used 1151
Summary of the Number of Event and Censored Values
Percent
Total Event Censored Censored
1151 96 1055 91.66
Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
Without With
Criterion Covariates Covariates
-2 LOG L 1316.931 1306.236
AIC 1316.931 1308.236
SBC 1316.931 1310.800
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 10.6952 1 0.0011
Score 10.5399 1 0.0012
Wald 10.1365 1 0.0015
Analysis of Maximum Likelihood Estimates
Parameter Standard Hazard
Variable DF Estimate Error Chi-Square Pr > ChiSq Ratio
TX 1 -0.68425 0.21492 10.1365 0.0015 0.504
Table 3.2, page 83 using the actg320 dataset.
NOTE: The formula for z is on page 79 and the formula for CI is on page 80.
NOTE: The standard error for age is different than that shown in the text.
ods output ParameterEstimates=out1; proc phreg data = actg320; model time*censor(0) = tx age sex cd4 priorzdv; run;
The PHREG Procedure
Model Information
Data Set WORK.ACTG320
Dependent Variable TIME
Censoring Variable CENSOR
Censoring Value(s) 0
Ties Handling BRESLOW
Number of Observations Read 1151
Number of Observations Used 1151
Summary of the Number of Event and Censored Values
Percent
Total Event Censored Censored
1151 96 1055 91.66
Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
Without With
Criterion Covariates Covariates
-2 LOG L 1316.931 1237.651
AIC 1316.931 1247.651
SBC 1316.931 1260.473
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 79.2798 5 <.0001
Score 63.1500 5 <.0001
Wald 55.7066 5 <.0001
Analysis of Maximum Likelihood Estimates
Parameter Standard Hazard
Variable DF Estimate Error Chi-Square Pr > ChiSq Ratio
TX 1 -0.65899 0.21529 9.3695 0.0022 0.517
AGE 1 0.02836 0.01127 6.3353 0.0118 1.029
SEX 1 0.09727 0.28412 0.1172 0.7321 1.102
CD4 1 -0.01658 0.00255 42.4134 <.0001 0.984
PRIORZDV 1 -0.0002931 0.00369 0.0063 0.9367 1.000
data out2;
set out1;
z = sqrt(chisq);
z2 = estimate /stderr;
lb = estimate-1.96*stderr;
ub = estimate+1.96*stderr;
run;
proc print data = out2;
var variable estimate stderr z z2 probchisq lb ub;
format estimate z z2 probchisq lb ub f8.3;
format stderr f8.4;
run;
ProbChi
Variable Estimate StdErr z z2 Sq lb ub
TX -0.659 0.2153 3.061 -3.061 0.002 -1.081 -0.237
AGE 0.028 0.0113 2.517 2.517 0.012 0.006 0.050
SEX 0.097 0.2841 0.342 0.342 0.732 -0.460 0.654
CD4 -0.017 0.0025 6.513 -6.513 0.000 -0.022 -0.012
PRIORZDV -0.000 0.0037 0.079 -0.079 0.937 -0.008 0.007
Table 3.3, page 84 using the actg320 dataset.
proc phreg data = actg320; model time*censor(0) = tx age cd4; run;
The PHREG Procedure
Model Information
Data Set WORK.ACTG320
Dependent Variable TIME
Censoring Variable CENSOR
Censoring Value(s) 0
Ties Handling BRESLOW
Number of Observations Read 1151
Number of Observations Used 1151
Summary of the Number of Event and Censored Values
Percent
Total Event Censored Censored
1151 96 1055 91.66
Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.
Model Fit Statistics
Without With
Criterion Covariates Covariates
-2 LOG L 1316.931 1237.771
AIC 1316.931 1243.771
SBC 1316.931 1251.464
Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 79.1602 3 <.0001
Score 63.0400 3 <.0001
Wald 55.5635 3 <.0001
Analysis of Maximum Likelihood Estimates
Parameter Standard Hazard
Variable DF Estimate Error Chi-Square Pr > ChiSq Ratio
TX 1 -0.65871 0.21504 9.3827 0.0022 0.518
AGE 1 0.02777 0.01115 6.2071 0.0127 1.028
CD4 1 -0.01656 0.00254 42.5390 <.0001 0.984
Table 3.4, page 87 using the whas100 dataset. We convert time to from years to quarters to increase the number of ties and better display the differences in methods for handling ties. These do not match the book exactly.
data whas100_q; set whas100; time=foltime/30.44 /* divide by days per month */; time=round(time/3) /* divide by months per quarter */; if time=0 then time=.5 /* event can't occur at time zero */; run; title "Exact"; proc phreg data = whas100_q; model foltime*folstatus(0) = bmi gender / ties = exact; run;
Exact
The PHREG Procedure
Analysis of Maximum Likelihood Estimates
Parameter Standard Hazard
Variable DF Estimate Error Chi-Square Pr > ChiSq Ratio
BMI 1 -0.09265 0.03348 7.6594 0.0056 0.912
GENDER 1 0.53408 0.28287 3.5650 0.0590 1.706
title "Breslow"; proc phreg data = whas100_q; model foltime*folstatus(0) = bmi gender / ties = breslow; run;
Breslow
The PHREG Procedure
Analysis of Maximum Likelihood Estimates
Parameter Standard Hazard
Variable DF Estimate Error Chi-Square Pr > ChiSq Ratio
BMI 1 -0.08850 0.03299 7.1988 0.0073 0.915
GENDER 1 0.51836 0.28303 3.3543 0.0670 1.679
title "Efron"; proc phreg data = whas100_q; model foltime*folstatus(0) = bmi gender / ties = efron; run; title;
Efron
The PHREG Procedure
Analysis of Maximum Likelihood Estimates
Parameter Standard Hazard
Variable DF Estimate Error Chi-Square Pr > ChiSq Ratio
BMI 1 -0.09459 0.03391 7.7829 0.0053 0.910
GENDER 1 0.53815 0.28256 3.6272 0.0568 1.713