LOG FOR A MANTEL-HAENSZEL STATISTIC FOR POLYNESIAN ISLAND DATA
  (making use of FORMATs for categorization)
================================================== 2/25/09

 libname  SAS "SASdat";
   data poly;
     set SAS.polynest; run;  * 80 obs, 16 variables ;

 options nodate nocenter linesize=80;

proc format;
    value  DEFOR  LOW - 3 = 1          
                   3.5 - 5 = 2 ;
         * Must use numeric format with  numeric variable ;
    value  LAT    LOW - 12 = 0
                   12.1 - 50 = 1 ;
    value  RAIN    LOW - 1800 = 1
                   1801 - 3500 = 2
                   3501 - HIGH = 3 ;

proc freq data=poly ;
      tables Deforstn LatitS Rain Deforstn * LatitS
                  / chisq nocum norow nocol nopercent;
      format Deforstn DEFOR. LatitS LAT. rain RAIN. ;
   run;

The FREQ Procedure

Table of Deforstn by LatitS

Deforstn     LatitS

Frequency|0       |1       |  Total
---------+--------+--------+
1        |     23 |     26 |     49
---------+--------+--------+
2        |     12 |     18 |     30
---------+--------+--------+
Total          35       44       79

Frequency Missing = 1



Statistics for Table of Deforstn by LatitS

Statistic                     DF       Value      Prob
------------------------------------------------------
Chi-Square                     1      0.3631    0.5468
Likelihood Ratio Chi-Square    1      0.3644    0.5461
...
Mantel-Haenszel Chi-Square     1      0.3585    0.5494


* SO NOT MUCH APPEARS TO BE GOING ON IN THE WHOLE POPULATION 
   OF 79 POLYNESIAN ISLANDS (EXCLUDING THE 1 MISSING DEFORSTN)
  BUT THIS POPULATION IS NOT AT ALL HOMOGENEOUS !!  ;


 proc freq data=poly ;
         tables  Rain * Deforstn * LatitS /    
                /* NOTE the first variable is the "Styratifier" */
            ALL   nocum norow nocol nopercent;
         format Deforstn DEFOR. LatitS LAT. rain RAIN. ;
      run;

* Not much going on in the 1 and 2 Rainfall categories, but in the
  high rainfall category (logically enough) we find low
  deforestation. ;

Table 3 of Deforstn by LatitS
Controlling for Rain=3

Deforstn     LatitS

Frequency|0       |1       |  Total
---------+--------+--------+
1        |      7 |      1 |      8
---------+--------+--------+
2        |      0 |      0 |      0
---------+--------+--------+
Total           7        1        8

/* The next set of statistics gives estimates of RR and OR and CI's
   separately under the assumption that (each of) these is contant
   over all of the separate Rain 2x2 tables Deforstn x LatitS */

            Estimates of the Common Relative Risk (Row1/Row2)

Type of Study     Method                  Value     95% Confidence Limits
-------------------------------------------------------------------------
Case-Control      Mantel-Haenszel        1.5238       0.5101       4.5522
  (Odds Ratio)    Logit **               0.8579       0.2291       3.2116

Cohort            Mantel-Haenszel        1.2619       0.6630       2.4017
  (Col1 Risk)     Logit **               0.7992       0.4417       1.4461

Cohort            Mantel-Haenszel        0.8701       0.6291       1.2034
  (Col2 Risk)     Logit                  0.7108       0.5441       0.9285


/* But finally, we also have a test of whether there are
differencesamong the odds ratios ! */


Summary Statistics for Deforstn by LatitS
Controlling for Rain

     Breslow-Day Test for
Homogeneity of the Odds Ratios
------------------------------
Chi-Square              7.1393
DF                           1
Pr > ChiSq              0.0075


Effective Sample Size = 78
Frequency Missing = 2