*-----------------------------------------------------------------------------------------* compute the confidence interval of two binomial proportions difference
潘建红
jinruchouru@163
2012年08月08日
*-----------------------------------------------------------------------------------------* PARAMETERS:
trial:the original clinical dataset
var:the number of four cells in the 2 by 2 table
*-----------------------------------------------------------------------------------------*; %macro pr_diff(trial,var);
proc transpose data=&trial out=dataset(drop=_name_) prefix=a; ***the cells named a1-a4;
var &var;
run;
***one sample binomial proportion confidence interval---wilson score method;
data _null_;
call symput("z",-probit(0.025)); **confidence limit ;
run;
***two samples:unpaired case---Newcombe method;
data unpaired;
set dataset;
n1=a1+a2; p1=a1/n1;
n2=a3+a4; p2=a3/n2;
l1=(2*a1+&z.**2-&z.*sqrt(&z.**2+4*a1*a2/n1))/(2*(n1+&z.**2));
*lower confidence interval for one sample;
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u1=(2*a1+&z.**2+&z.*sqrt(&z.**2+4*a1*a2/n1))/(2*(n1+&z.**2));
*upper confidence interval for one sample;
l2=(2*a3+&z.**2-&z.*sqrt(&z.**2+4*a3*a4/n2))/(2*(n2+&z.**2));
u2=(2*a3+&z.**2+&z.*sqrt(&z.**2+4*a3*a4/n2))/(2*(n2+&z.**2));
d=p1-p2;
l_unpaired=d-sqrt((p1-l1)**2+(u2-p2)**2);
*lower confidence interval for the difference;
u_unpaired=d+sqrt((p2-l2)**2+(u1-p1)**2);
*upper confidence interval for the difference;
run;
data group_a;
帝国神话retain group a1 a2 n1 p1 d l_unpaired u_unpaired; format group $255.;
informat group $255.;
set unpaired;
group="A组";
rename
a1=positive
a2=negative
n1=sum
p1=proportion
d=difference;
keep group a1 a2 n1 p1 d l_unpaired u_unpaired;
run;
data group_b;
retain group a3 a4 n2 p2 ;
format group $255.;
informat group $255.;
set unpaired;
group="B组";
rename
a3=positive
a4=negative
n2=sum
p2=proportion;
keep group a3 a4 n2 p2 ;
run;
data unpaired_diff;
set group_a group_b;
label
group="分组"
positive="阳性"
2013诺贝尔文学奖获得者negative="阴性"
sum="合计"
proportion="阳性率"
difference="率差"
u_unpaired="率差可信区间上限" ;
run;
/*-----------------------------------------------------------------------------------------------*/
***two samples:paired case---Newcombe method;
data paired;
set dataset;
n=a1+a2+a3+a4;
n1=a1+a2; p1=n1/n;
n2=a1+a3; p2=n2/n;
l1=(2*n1+&z.**2-&z.*sqrt(&z.**2+4*n1*(n-n1)/n))/(2*(n+&z.**2));
*lower confidence interval for one sample;
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u1=(2*n1+&z.**2+&z.*sqrt(&z.**2+4*n1*(n-n1)/n))/(2*(n+&z.**2)); *upper confidence interval for one sample;
l2=(2*n2+&z.**2-&z.*sqrt(&z.**2+4*n2*(n-n2)/n))/(2*(n+&z.**2));
u2=(2*n2+&z.**2+&z.*sqrt(&z.**2+4*n2*(n-n2)/n))/(2*(n+&z.**2));
d=p1-p2;
q1=(a1+a2)*(a3+a4)*(a1+a3)*(a2+a4);
if q1=0 then
do;
coe=0; q2=.; q3=.;
end;
else do;
xtt
q2=a1*a4-a2*a3;
if q2>n/2 then q3=q2-n/2;
else if 0<=q2<=n/2 then q3=0;
else if q2<0 then q3=q2;
coe=q3/sqrt(q1);
end;
l_paired=d-sqrt((p1-l1)**2-2*coe*(p1-l1)*(u2-p2)+(u2-p2)**2);
*lower confidence interval for the difference;
u_paired=d+sqrt((p2-l2)**2-2*coe*(p2-l2)*(u1-p1)+(u1-p1)**2);
*upper confidence interval for the difference;
run;
proc format;
value fmt
1="阳性"
2="阴性" ;
run;
data group;
do i=1 to 2;
do j=1 to 2;
output;
end;
end;
run;
data group;
merge group &trial(keep=&var);
run;
data paired_1;
set group;
group_a=put(i,fmt.);
group_b=put(j,fmt.);
drop i j;
run;
data paired_2;
set paired;
keep p1 p2 d l_paired u_paired;
run;
data paired_diff;
retain group_a group_b &var p1 p2 d l_paired u_paired;
merge paired_1 paired_2;
label
group_a="A组"
group_b="B组"
&var="例数"
p1="A组阳性率"
p2="B组阳性率"
d="率差"
l_paired="率差可信区间下限"
u_paired="率差可信区间上限" ;
keep group_a group_b &var p1 p2 d l_paired u_paired; run;
%mend pr_diff;
run;
************Example*****************;
***generate two by two table;
data table;
do i=1to2;
do j=1to2;
input f @@;
output;
end;
汇率指数
end;
cards;
53 4 1 3
;
run;
%pr_diff(table,f);
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