*==================================================;
* Example of an exponential regression            *;
*==================================================;

options ls=75;
data one; input y x cen;
***** you do not need to say [ly = log(y)] because it does log for you; 
***** cannot have 0's in the responses, since log(0) is a no-no;
cards;
15  2  0
13  3  1
9   1  1
19  3  1
12  2  1
;
proc lifereg data=one;
model y = /dist=exponential;  ***ignor censoring!! and no covariate ***;
run;
* the output is actually for an extreme value distribution estimates *;
* Homework: Use the output, give the fitted hazard function of the weibull.*;
* To force intercept=0, say  noint  as in  /dist=weibull noint;
* To force scale=1, use exp as dist. ;

proc lifereg data=one;
     model y*cen(0)= /dist=exponential;
run;

** To predict the median and other quantiles, i.e.
** the median of the dist by fitted model, try this example.

proc lifereg data=one;
     model y*cen(0)= /dist=exponential;
     output out=new p=perc quantiles=0.1 0.5 0.9;
run;

proc print data=new;
     var  _prob_  perc;
run;


*==========================================================;
* Example of a Weibull (exponential) regression with a    *;
*       doubly and interval censored data set: double     *;
*==========================================================;

data double;
input upper lower x;
cards;
12 12 55
14 .  59
16 .  48
14 14 39
.  8  44
13 9  48
9  9  45
;
run;

proc lifereg data=double;
   model (lower,upper)= / dist=weibull;
run;

*** To fix the intercept or scale at a given value, we can do ***; 

proc lifereg data=double;
  model (lower,upper)= / dist=weibull scale=0.5 noscale intercept=1 noint;
run;

*** if "noscale" is ommited then sas just use scale=0.5 as initial value in*;
*** iteration of maximumization *; 
*** how to fix a covariate, like R offset() ??? ***; 

For similar effect to R function survreg() offset(), may be we can
substract from the responses y the amount b*age and then do the
fit use y-b*age as the new responses.