/*
Peter H. Van Ness
November 10, 2008
This program provides SAS code to calculate the probabilstic index from both a Wilcoxon Rank Sum
Statistic and from a Somers' D Correlation Coefficient.  See: Acion, Laura, Peterson, John J.,
Temple, Scott, and Arndt, Stephen, Probabilistic index: an intuitive, non-parametric approach
to measuring the size of treatment effects. Statistics in Medicine; 2006:591-602.

Note that the above authors speak of Kendall's Tau-b Correlation Coefficient.  In some
circumstances it yields the same value as Somers' D.  From the SAS output it is the
Somers' D value that should be generally used.
*/

*This presents the structure of the data.  Treatment leads to higher, more positive scores;

data p_index;
	input treatment score;
datalines;
1 -5
1  0
1  1
1  0
1  1
1  0
1  3
1  5
0 -5
0 -4
0 -1
0 -1
0 -1
0  0
0  0
0  -1
0  4
;
run;

proc print data=p_index; var score; run;


/*******************Probabilistic Index Calculation********************/

*Wilcoxon Rank Sum Test Version;

*This code calculates the probabilistic index P(treatment>control);

proc npar1way data=p_index wilcoxon;
	class treatment;
	var   score;
run; 

*From the PROC NPARIWAY output the w is the rank sum total for treatment and n is the sample
of this treatment group, while m is the sample size of the other control group ;

%let w = 90.50;
%let n = 8;
%let m = 9;

%put &w &n &m;

data wilcoxon_calc;
p_index = (&w - .5*&n*(&n+1))/ (&n*&m);
run;

proc print data=wilcoxon_calc; 
	title  'Probabilistic Index from the Wilcoxon Rank Sum Statistic';
run;

*The value of the probabilistic index represents that probability that the score for a patient
in the treatment group is greater than the score for a randomly chosen patient from the control group;

*The Somers' D Version;

proc freq data=p_index;
	tables treatment*score / measures;
run;

*From the PROC FREQ output somers_d is given the value of the Somers' D Correlation Coefficient
in the column given row (C!R) version. n is the sample size of the treatment group and 
m is the sample size of the control group;

%let somers_d = 0.5139;
%let n = 8;
%let m = 9;
%let s = (&n + &m);

%put &somers_d &n &m &s;

data somers_calc;

v =(0.5*(&n*(&n-1))) + (0.5*(&m*(&m-1)));

t = 0.5*(((&n)*(&m))-(&somers_d)*sqrt((&n)*(&m)*((.5*(&s)*(&s-1))-v)));

u = ((&n)*(&m)) - t;

p_index = u / ((&n)*(&m));

run;

proc print data=somers_calc; 
	title  'Probabilistic Index from the Somers D Correlation Coefficient';
run;

*The value of the probabilistic index represents that probability that the score for a patient 
in the treatment groupis greater than the score for a randomly chosen patient from the control group;