PROC LIFEREG enables you to make modelbased inferences. This example uses the larynx cancer data (Klein and Moeschberger, 1997) to illustrate usage of the LSMEANS, LSMESTIMATE, and EFFECTPLOT statements for model postfitting analysis.
The survival time is modeled by a proportional odds model with two covariates: patient age and cancer stage (1, 2, 3, 4). The following statements use PROC LIFEREG to fit this model:
ods graphics on; proc sort data=Larynx; by DESCENDING Stage; run; proc lifereg data=Larynx order=data; class Stage; model Time*Death(0) = Age Stage / dist = llogistic; lsmeans Stage / diff adjust=Sidak; effectplot / noobs; run;
The LSMEANS statement compares pairwise differences in survival times among the four different cancer stages, while adjusting for age. The ADJUST=SIDAK option uses the Sidak method to control the overall Type I error rate of these comparisons. Results are displayed in Output 55.8.1.
Output 55.8.1: LSMeans Differences between Disease Stages
Differences of Stage Least Squares Means Adjustment for Multiple Comparisons: Sidak 


Stage  _Stage  Estimate  Standard Error  z Value  Pr > z  Adj P 
4  3  0.9604  0.4379  2.19  0.0283  0.1581 
4  2  1.6404  0.4931  3.33  0.0009  0.0053 
4  1  1.7661  0.4257  4.15  <.0001  0.0002 
3  2  0.6800  0.4316  1.58  0.1151  0.5199 
3  1  0.8057  0.3539  2.28  0.0228  0.1292 
2  1  0.1257  0.4152  0.30  0.7621  0.9998 
All the LSmeans differences and their significance are displayed by the meanmean scatter plot in Output 55.8.2.
Suppose you want to jointly test whether the effects of stages 2, 3, and 4 are different from stage 1. The following LSMESTIMATE statement contrasts the LSmeans of stages 2, 3, and 4 against the LSmeans of stage 1:
proc lifereg data=Larynx order=data; class Stage year; model Time*Death(0) = Age Stage / dist = llogistic; lsmestimate Stage 'Stage 4 vs 1' 1 0 0 1, 'Stage 3 vs 1' 0 1 0 1, 'Stage 2 vs 1' 0 0 1 1 / cl adjust=Sidak; run;
The CL option produces 95% confidence limits, including both unadjusted ones and those adjusted for multiple comparisons according to the ADJUST= option. Results are displayed in Output 55.8.3.
Output 55.8.3: Custom LSMeans Tests and Relative Odds
Least Squares Means Estimates Adjustment for Multiplicity: Sidak 


Effect  Label  Estimate  Standard Error  z Value  Pr > z  Adj P  Alpha  Lower  Upper  Adj Lower  Adj Upper 
Stage  Stage 4 vs 1  1.7661  0.4257  4.15  <.0001  0.0001  0.05  2.6004  0.9319  2.7825  0.7498 
Stage  Stage 3 vs 1  0.8057  0.3539  2.28  0.0228  0.0668  0.05  1.4993  0.1122  1.6507  0.03921 
Stage  Stage 2 vs 1  0.1257  0.4152  0.30  0.7621  0.9865  0.05  0.9395  0.6881  1.1171  0.8657 
As displayed in Output 55.8.4, the EFFECTPLOT statement generates a plot of age effects on survival time on a natural logarithm scale by four disease stages.
You can also perform the preceding analysis for a Bayesian model. The following statements generate posterior samples from a Bayesian model and request an LSmeans analysis to compare the stage effects:
proc lifereg data=Larynx order=data; class Stage; model Time*Death(0) = Age Stage / dist = llogistic; bayes seed=100 nmc=500 nbi=500 diagnostic=none outpost=OOO; lsmeans Stage / diff exp; lsmestimate Stage 'Stage 4 vs 1' 1 0 0 1, 'Stage 3 vs 1' 0 1 0 1, 'Stage 2 vs 1' 0 0 1 1 / cl plots=boxplot(orient=horizontal); run;
Because no prior distributions for the regression coefficients were specified, the default uniform improper distributions shown in the “Uniform Prior for Regression Coefficients” table in Output 55.8.5 are used. The specified gamma prior for the scale parameter is also shown in Output 55.8.5.
Output 55.8.5: Model Parameter Priors
Uniform Prior for Regression Coefficients 


Parameter  Prior 
Intercept  Constant 
Age  Constant 
Stage4  Constant 
Stage3  Constant 
Stage2  Constant 
Independent Prior Distributions for Model Parameters  

Parameter  Prior Distribution  Hyperparameters  
Scale  Gamma  Shape  0.001  Inverse Scale  0.001 
Under the Bayesian framework, the LSmeans differences are treated as random variables for which posterior samples are readily available according to the linear relationship of LSmeans and the regression coefficients. Output 55.8.6 lists the sample mean, standard deviation, and percentiles for each LSmeans difference.
Output 55.8.6: LSMeans Differences between Disease Stages
Sample Differences of Stage Least Squares Means  

Stage  _Stage  N  Estimate  Standard Deviation  Percentiles  Exponentiated  Standard Error of Exponentiated 
Percentiles for Exponentiated 

25th  50th  75th  25th  50th  75th  
4  3  500  0.9307  0.4752  1.2743  0.9446  0.6086  0.4426  0.232690  0.2796  0.3888  0.5441 
4  2  500  1.6591  0.5327  2.0161  1.6573  1.2861  0.2181  0.115808  0.1332  0.1907  0.2763 
4  1  500  1.8001  0.4321  2.0951  1.7943  1.5491  0.1815  0.082975  0.1231  0.1663  0.2124 
3  2  500  0.7284  0.4828  1.0488  0.7219  0.3975  0.5410  0.268735  0.3504  0.4858  0.6720 
3  1  500  0.8694  0.3727  1.1199  0.8541  0.6149  0.4488  0.168055  0.3263  0.4257  0.5407 
2  1  500  0.1410  0.4413  0.4126  0.1417  0.1363  0.9585  0.462376  0.6619  0.8679  1.1461 
The LSMESTIMATE statement produces summary statistics of the posterior samples for the specified LSmeans contrasts. Results are presented in Output 55.8.7; they are very similar to the results based on maximum likelihood in Output 55.8.3.
Output 55.8.7: Summary Statistics of Custom LSMeans Differences
Sample Least Squares Means Estimates  

Effect  Label  N  Estimate  Standard Deviation  Percentiles  Alpha  Lower HPD  Upper HPD  
25th  50th  75th  
Stage  Stage 4 vs 1  500  1.8001  0.4321  2.0951  1.7943  1.5491  0.05  2.6279  0.8897 
Stage  Stage 3 vs 1  500  0.8694  0.3727  1.1199  0.8541  0.6149  0.05  1.6033  0.2031 
Stage  Stage 2 vs 1  500  0.1410  0.4413  0.4126  0.1417  0.1363  0.05  1.1401  0.6252 
The PLOTS= option uses ODS Graphics to display the Bayesian samples. A box plot is presented in Output 55.8.8.