The data set Pain
contains hypothetical data for a clinical trial of a drug therapy to control pain. The clinical trial investigates whether
adverse responses increase with larger drug doses. Subjects receive either a placebo or one of four drug doses. An adverse
response is recorded as Adverse
='Yes'; otherwise, it is recorded as Adverse
='No'. The number of subjects for each drug dose and response combination is contained in the variable Count
.
data pain; input Dose Adverse $ Count @@; datalines; 0 No 26 0 Yes 6 1 No 26 1 Yes 7 2 No 23 2 Yes 9 3 No 18 3 Yes 14 4 No 9 4 Yes 23 ;
The following PROC FREQ statements provide a trend analysis. The TABLES statement requests a table of Adverse
by Dose
. The MEASURES option produces measures of association, and the CL option produces confidence limits for these measures. The
TREND option tests for a trend across the ordinal values of the variable Dose
with the CochranArmitage test. The PLOTS= option requests a mosaic plot of Adverse
by Dose
.
The EXACT statement produces exact pvalues for this test, and the MAXTIME= option terminates the exact computations if they do not complete within 60 seconds. The TEST statement computes an asymptotic test for Somers’ .
ods graphics on; proc freq data=Pain; tables Adverse*Dose / trend measures cl plots=mosaicplot; test smdrc; exact trend / maxtime=60; weight Count; title 'Clinical Trial for Treatment of Pain'; run; ods graphics off;
Output 3.8.1 through Output 3.8.4 display the results of the analysis. The “Col Pct” values in Output 3.8.1 show the expected increasing trend in the proportion of adverse effects with the increasing dosage (from 18.75% to 71.88%). The corresponding mosaic plot (Output 3.8.2) also shows this increasing trend.
Output 3.8.1: Contingency Table
Clinical Trial for Treatment of Pain 


Output 3.8.2: Mosaic Plot
Output 3.8.3 displays the measures of association produced by the MEASURES option. Somers’ measures the association treating the row variable (Adverse
) as the response and the column variable (Dose
) as a predictor. Because the asymptotic 95% confidence limits do not contain zero, this indicates a strong positive association.
Similarly, the Pearson and Spearman correlation coefficients show evidence of a strong positive association, as hypothesized.
The CochranArmitage test (Output 3.8.4) supports the trend hypothesis. The small leftsided pvalues for the CochranArmitage test indicate that the probability of the Row 1 level (Adverse
='No') decreases as Dose
increases or, equivalently, that the probability of the Row 2 level (Adverse
='Yes') increases as Dose
increases. The twosided pvalue tests against either an increasing or decreasing alternative. This is an appropriate hypothesis when you want to determine
whether the drug has progressive effects on the probability of adverse effects but the direction is unknown.
Output 3.8.3: Measures of Association
Statistic  Value  ASE  95% Confidence Limits 


Gamma  0.5313  0.0935  0.3480  0.7146 
Kendall's Taub  0.3373  0.0642  0.2114  0.4631 
Stuart's Tauc  0.4111  0.0798  0.2547  0.5675 
Somers' D CR  0.4427  0.0837  0.2786  0.6068 
Somers' D RC  0.2569  0.0499  0.1592  0.3547 
Pearson Correlation  0.3776  0.0714  0.2378  0.5175 
Spearman Correlation  0.3771  0.0718  0.2363  0.5178 
Lambda Asymmetric CR  0.1250  0.0662  0.0000  0.2547 
Lambda Asymmetric RC  0.2373  0.0837  0.0732  0.4014 
Lambda Symmetric  0.1604  0.0621  0.0388  0.2821 
Uncertainty Coefficient CR  0.0515  0.0191  0.0140  0.0890 
Uncertainty Coefficient RC  0.1261  0.0467  0.0346  0.2175 
Uncertainty Coefficient Symmetric  0.0731  0.0271  0.0199  0.1262 
Somers' D RC  

Somers' D RC  0.2569 
ASE  0.0499 
95% Lower Conf Limit  0.1592 
95% Upper Conf Limit  0.3547 
Test of H0: Somers' D RC = 0  

ASE under H0  0.0499 
Z  5.1511 
Onesided Pr > Z  <.0001 
Twosided Pr > Z  <.0001 
Output 3.8.4: Trend Test
CochranArmitage Trend Test  

Statistic (Z)  4.7918 
Asymptotic Test  
Onesided Pr < Z  <.0001 
Twosided Pr > Z  <.0001 
Exact Test  
Onesided Pr <= Z  7.237E07 
Twosided Pr >= Z  1.324E06 