/******************************************************************
CHAPTER 11, EXAMPLE 1
Fit a logistic regression model to the myocardial infarction
data.
******************************************************************/
options ls=80 ps=59 nodate; run;
/******************************************************************
The data look like (first 10 records)
   Obs    id    oral    age    smoke    mi

                      1     1      1      33      1       0
                      2     2      0      32      0       0
                      3     3      1      37      0       1
                      4     4      0      36      0       0
                      5     5      1      50      1       1
                      6     6      1      40      0       0

...
[Discard Obs]
column 1 subject id
column 2 oral contraceptive indicator (0=no,1=yes)
column 3 age (years)
column 4 smoking indicator (0=no,1=yes)
column 5 binary response -- whether MI has been suffered
(0=no,1=yes)
******************************************************************/
data mi; infile 'infarc.dat';
	input id oral age smoke mi;
run;
proc print data=mi; run;

/******************************************************************
Simple model,with 1 covariate (Age)
	Model: logit(P(MI_j=1)) = beta_0 +beta_1 Age_j 
******************************************************************/
proc genmod data=mi descending;
	model mi = age  / dist = binomial link = logit;
	estimate "age log odds ratio" int 1 age 34 / exp;
run;

/******************************************************************
            Analysis Of Maximum Likelihood Parameter Estimates

                          Standard       Wald 95%             Wald
 Parameter  DF  Estimate     Error   Confidence Limits  Chi-Square  Pr > ChiSq

 Intercept   1   -6.9987    1.4226   -9.7869   -4.2106       24.20      <.0001
 age         1    0.1586    0.0384    0.0835    0.2338       17.11      <.0001
 Scale       0    1.0000    0.0000    1.0000    1.0000

NOTE: The scale parameter was held fixed.

## Write down the estimated logistis regression:
 
Label                     Estimate    Confidence Limits    Estimate      Error

 age log odds ratio          0.1673     0.1173     0.2330    -1.6049     0.2109
 Exp(age log odds ratio)                                      0.2009     0.0424

                           Contrast Estimate Results

                                            L'Beta           Chi-
  Label                      Alpha    Confidence Limits    Square   Pr > ChiSq

  age log odds ratio          0.05    -2.0182    -1.1916    57.93       <.0001
  Exp(age log odds ratio)     0.05     0.1329     0.3037

******************************************************************/

/******************************************************************
Full model,with all covariates
	Model: logit(P(MI_j=1)) = beta_0 +beta_1 Age_j + beta_2 OralC_j+beta_3 Smoke_j
******************************************************************/


/*****************************************************************
Fit the logistic regression model using PROC GENMOD.
We do not use a CLASS statement here, as the covariates are
either continuous (AGE) or already in "dummy" form (ORAL, SMOKE).
The model statement with the LINK=LOGIT option results in the
logistic regression model in equation (10.21). The DIST=BINOMIAL
specifies the Bernoulli distribution, which is the simplest case
of a binomial distribution.
In versions 7 and higher of SAS, PROC GENMOD will model by
default the probability that the response y=0 rather than
the conventional y=1! To make PROC GENMOD model probability
y=1, as is standard, one must include the DESCENDING option in
the PROC GENMOD statement. In earlier versions of SAS, the
probability y=1 is modeled by default, as would be expected.
If the user is unsure which probability is being modeled, one
can check the .log file. In later versions of SAS, an explicit
statement about what is being modeled will appear. PROC GENMOD
output should also contain a statement about what is being
modeled.
******************************************************************/
proc genmod data=mi descending;
	model mi = oral age smoke / dist = binomial link = logit;
	estimate "smk log odds ratio" int 0 oral 0 age 0 smoke 1 / exp;
run;


/*****************************************************************


              Analysis Of Maximum Likelihood Parameter Estimates

                          Standard       Wald 95%             Wald
 Parameter  DF  Estimate     Error   Confidence Limits  Chi-Square  Pr > ChiSq

 Intercept   1   -9.1140    1.7571  -12.5579   -5.6702       26.90      <.0001
 oral        1    1.9799    0.4697    1.0593    2.9005       17.77      <.0001
 age         1    0.1626    0.0445    0.0753    0.2498       13.32      0.0003
 smoke       1    1.8122    0.4294    0.9706    2.6538       17.81      <.0001
 Scale       0    1.0000    0.0000    1.0000    1.0000

Write down the estimated logistic regression model
Interpret the parameters

*****************************************************************/