6a.3  Example: Discarding Ineffective Treatment
6a.3  Example: Discarding Ineffective TreatmentAn approach for discarding an ineffective treatment in an SE study, based on the exact binomial method, is as follows. Suppose that the lowest success rate acceptable to an investigator for the treatment is 0.20. Suppose that the investigator decides to administer the treatment consecutively to a series of patients. When can the investigator terminate the SE trial if he continues to find no treatment successes?
SASĀ® Example
Determine when the exact confidence interval for p no longer contains a certain value
SAS Example: Modifications to the exact confidence interval program used earlier can be made to determine when the exact confidence interval for p no longer contains a certain value.
***********************************************************************
* This is a program that illustrates the use of PROC FREQ in SAS for *
* determining an exact confidence interval for a binomial proportion. *
***********************************************************************;
proc format;
value succfmt 1='yes' 2='no';
run;
data Example_1;
input success count;
format success succfmt.;
cards;
1 03
2 16
;
run;
proc freq data=Example_1;
tables success/binomial alpha=0.05;
weight count/zeros;
title "Exact and Asymptotic 95% Confidence Intervals for a Binomial Proportion";
run;
SAS PROF FREQ (trialanderror) indicates that the exact onesided 95% upper confidence limit for p, when 0 out of 14 successes are observed, is 0.19. Thus, if the treatment fails in each of the first 14 patients, then the study is terminated.
Did you get 45% with the exact limits?
Notice also how clearly wrong the asymptotic limit is in this situation.
The FREQ Procedure  

Positive  Frequency  Percent  Cumulative Frequency  Cumulative Percent 
yes  0  0.00  0  0.00 
no  5  100.00  5  100.00 
Binomial Proportion 


Proportion  0.0000 
ASE  0.0000 
90% Lower Conf Limit  0.0000 
90% Upper Conf Limit  0.0000 
Exact Conf Limits  
90% Lower Conf Limit  0.0000 
90% Upper Conf Limit  0.4507 
Test of H0: Proportion = 0.5 


ASE Under H0  0.2236 
Z  2.2361 
OneSided Pr < Z  0.0127 
TwoSided Pr > Z  0.0253 
Sample Size = 5
The answer is 9 ...
The FREQ Procedure  

Positive  Frequency  Percent  Cumulative Frequency  Cumulative Percent 
yes  0  0.00  0  0.00 
no  9  100.00  9  100.00 
Binomial Proportion 


Proportion  0.0000 
ASE  0.0000 
90% Lower Conf Limit  0.0000 
90% Upper Conf Limit  0.0000 
Exact Conf Limits  
90% Lower Conf Limit  0.0000 
90% Upper Conf Limit  0.2831 
Test of H0: Proportion = 0.5 


ASE Under H0  0.1667 
Z  3.0000 
OneSided Pr < Z  0.0013 
TwoSided Pr > Z  0.0027 
Sample Size = 9