This example computes chisquare tests and Fisher’s exact test to compare the probability of coronary heart disease for two types of diet. It also estimates the relative risks and computes exact confidence limits for the odds ratio.
The data set FatComp
contains hypothetical data for a casecontrol study of high fat diet and the risk of coronary heart disease. The data are
recorded as cell counts, where the variable Count
contains the frequencies for each exposure and response combination. The data set is sorted in descending order by the variables
Exposure
and Response
, so that the first cell of the table contains the frequency of positive exposure and positive response. The FORMAT procedure creates formats to identify
the type of exposure and response with character values.
proc format; value ExpFmt 1='High Cholesterol Diet' 0='Low Cholesterol Diet'; value RspFmt 1='Yes' 0='No'; run;
data FatComp; input Exposure Response Count; label Response='Heart Disease'; datalines; 0 0 6 0 1 2 1 0 4 1 1 11 ;
proc sort data=FatComp; by descending Exposure descending Response; run;
In the following PROC FREQ statements, ORDER=DATA option orders the contingency table values by their order in the input data
set.
The TABLES statement requests a twoway table of Exposure
by Response
. The CHISQ option produces several chisquare tests, while the RELRISK option produces relative risk measures. The EXACT
statement requests the exact Pearson chisquare test and exact confidence limits for the odds ratio.
proc freq data=FatComp order=data; format Exposure ExpFmt. Response RspFmt.; tables Exposure*Response / chisq relrisk; exact pchi or; weight Count; title 'CaseControl Study of High Fat/Cholesterol Diet'; run;
The contingency table in Output 3.5.1 displays the variable values so that the first table cell contains the frequency for the first cell in the data set (the frequency of positive exposure and positive response).
Output 3.5.1: Contingency Table
CaseControl Study of High Fat/Cholesterol Diet 


Output 3.5.2 displays the chisquare statistics. Because the expected counts in some of the table cells are small, PROC FREQ gives a warning that the asymptotic chisquare tests might not be appropriate. In this case, the exact tests are appropriate. The alternative hypothesis for this analysis states that coronary heart disease is more likely to be associated with a high fat diet, so a onesided test is desired. Fisher’s exact rightsided test analyzes whether the probability of heart disease in the high fat group exceeds the probability of heart disease in the low fat group; because this pvalue is small, the alternative hypothesis is supported.
The odds ratio, displayed in Output 3.5.3, provides an estimate of the relative risk when an event is rare. This estimate indicates that the odds of heart disease is 8.25 times higher in the high fat diet group; however, the wide confidence limits indicate that this estimate has low precision.
Output 3.5.2: ChiSquare Statistics
Statistic  DF  Value  Prob 

ChiSquare  1  4.9597  0.0259 
Likelihood Ratio ChiSquare  1  5.0975  0.0240 
Continuity Adj. ChiSquare  1  3.1879  0.0742 
MantelHaenszel ChiSquare  1  4.7441  0.0294 
Phi Coefficient  0.4644  
Contingency Coefficient  0.4212  
Cramer's V  0.4644  
WARNING: 50% of the cells have expected counts less than 5. (Asymptotic) ChiSquare may not be a valid test. 
Pearson ChiSquare Test  

ChiSquare  4.9597 
DF  1 
Asymptotic Pr > ChiSq  0.0259 
Exact Pr >= ChiSq  0.0393 
Fisher's Exact Test  

Cell (1,1) Frequency (F)  11 
Leftsided Pr <= F  0.9967 
Rightsided Pr >= F  0.0367 
Table Probability (P)  0.0334 
Twosided Pr <= P  0.0393 
Output 3.5.3: Relative Risk
Odds Ratio and Relative Risks  

Statistic  Value  95% Confidence Limits  
Odds Ratio  8.2500  1.1535  59.0029 
Relative Risk (Column 1)  2.9333  0.8502  10.1204 
Relative Risk (Column 2)  0.3556  0.1403  0.9009 
Odds Ratio  

Odds Ratio  8.2500 
Asymptotic Conf Limits  
95% Lower Conf Limit  1.1535 
95% Upper Conf Limit  59.0029 
Exact Conf Limits  
95% Lower Conf Limit  0.8677 
95% Upper Conf Limit  105.5488 