/* PubH 7450
Exampel 8.2 (continued): fitting a PHM using the larynx cancer data
             and conducting local tests; 
             see Tables 8.3-8.4 on p.270-271. 
NOTE: coding for Satge is now the same as that in the textbook!
*/

options ls=80 center pagesize=60 number label;
goptions device = PS;  
         /* graphs are saved in a file names sasgraph.ps */

data larynx;
infile '/home/merganser/weip/public_html/course/7450/data/larynx.txt'
       firstobs=19;
input stage time age year status ;
  if stage=2 then Z1=1;
     else Z1=0;
  if stage=3 then Z2=1;
     else Z2=0;
  if stage=4 then Z3=1;
     else Z3=0;

/* To test for interactions b/w stage and age:*/
/*full model: covb requests to give Cov(b) */
proc phreg;
Z5=Z1*Age; Z6=Z2*Age; Z7=Z3*Age;
model time*status(0) = Z1 Z2 Z3 age Z5 Z6 Z7 / covb;
title 'Full model with 3 interaction terms';

/*reduced model:*/
proc phreg;
Z5=Z1*Age; Z6=Z2*Age; Z7=Z3*Age;
model time*status(0) = Z1 Z2 Z3 age Z5;
title 'Reduced model with only 1 interaction term';

/* alternatively, a Wald test can be specified by TEST statement: */
proc phreg;
Z5=Z1*Age; Z6=Z2*Age; Z7=Z3*Age;
model time*status(0) = Z1 Z2 Z3 age Z5 Z6 Z7 ;
test1: test Z6=Z7=0;

/* In the reduced model, how to calculate RR(Stage II vs Stage I)? */
*****************************
                      Full model with 3 interaction terms                      1

                             Model Fit Statistics
                                     Without           With
                    Criterion     Covariates     Covariates

                    -2 LOG L         394.426        370.155
                    AIC              394.426        384.155
                    SBC              394.426        397.539

                    Testing Global Null Hypothesis: BETA=0
 
            Test                 Chi-Square       DF     Pr > ChiSq

            Likelihood Ratio        24.2709        7         0.0010
            Score                   28.5852        7         0.0002
            Wald                    24.1136        7         0.0011

                    Analysis of Maximum Likelihood Estimates
 
                   Parameter     Standard                               Hazard
  Variable   DF     Estimate        Error   Chi-Square   Pr > ChiSq      Ratio

  Z1          1     -7.94614      3.67821       4.6670       0.0307      0.000
  Z2          1     -0.12250      2.46833       0.0025       0.9604      0.885
  Z3          1      0.84702      2.42571       0.1219       0.7270      2.333
  age         1     -0.00256      0.02605       0.0096       0.9218      0.997
  Z5          1      0.12025      0.05231       5.2853       0.0215      1.128
  Z6          1      0.01135      0.03745       0.0919       0.7618      1.011
  Z7          1      0.01367      0.03597       0.1445       0.7038      1.014

                          Estimated Covariance Matrix
 
Variable                Z1                Z2                Z3               age
Z1             13.52924052        2.93236220        2.95628293        0.04489138
Z2              2.93236220        6.09266544        2.95717875        0.04411237
Z3              2.95628293        2.95717875        5.88408080        0.04417708
age             0.04489138        0.04411237        0.04417708        0.00067864
Z5             -0.19073359       -0.04382437       -0.04421827       -0.00068777
Z6             -0.04386625       -0.09147457       -0.04420681       -0.00067504
Z7             -0.04504689       -0.04424959       -0.08588510       -0.00068052
         Variable                Z5                Z6                Z7

         Z1             -0.19073359       -0.04386625       -0.04504689
         Z2             -0.04382437       -0.09147457       -0.04424959
         Z3             -0.04421827       -0.04420681       -0.08588510
         age            -0.00068777       -0.00067504       -0.00068052
         Z5              0.00273606        0.00067091        0.00069054
         Z6              0.00067091        0.00140243        0.00067714
         Z7              0.00069054        0.00067714        0.00129362
*********************************
                   Reduced model with only 1 interaction term                  3
                             Model Fit Statistics
                                     Without           With
                    Criterion     Covariates     Covariates

                    -2 LOG L         394.426        370.316
                    AIC              394.426        380.316
                    SBC              394.426        389.876

                    Testing Global Null Hypothesis: BETA=0
 
            Test                 Chi-Square       DF     Pr > ChiSq
            Likelihood Ratio        24.1097        5         0.0002
            Score                   27.9849        5         <.0001
            Wald                    23.7747        5         0.0002

                    Analysis of Maximum Likelihood Estimates
 
                   Parameter     Standard                               Hazard
  Variable   DF     Estimate        Error   Chi-Square   Pr > ChiSq      Ratio
  Z1          1     -7.38147      3.40279       4.7056       0.0301      0.001
  Z2          1      0.62156      0.35581       3.0516       0.0807      1.862
  Z3          1      1.75350      0.42394      17.1084       <.0001      5.775
  age         1      0.00597      0.01488       0.1610       0.6882      1.006
  Z5          1      0.11166      0.04767       5.4855       0.0192      1.118
*********************************
                       Linear Hypotheses Testing Results
                                   Wald
                    Label    Chi-Square      DF    Pr > ChiSq
                    test1        0.1613       2        0.9225