Chapter Contents Previous Next
 The FREQ Procedure

## Example 28.7: Computing the Cochran-Armitage Trend Test

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 TABLES statement in the following program produces a two-way table. 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 Dose variable with the Cochran-Armitage test. The EXACT statement produces exact p-values 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 Somer's D(C|R). These statements produce Output 28.7.1 through Output 28.7.3.

```   proc freq data=Pain;
weight Count;
tables Dose*Adverse / trend measures cl;
test smdcr;
exact trend / maxtime=60;
title1 'Clinical Trial for Treatment of Pain';
run;
```

Output 28.7.1: Contingency Table

 Clinical Trial for Treatment of Pain
 The FREQ Procedure
 Frequency Percent Row Pct Col Pct
 Table of Dose by Adverse Dose Adverse Total No Yes 0 26 16.15 81.25 25.49 6 3.73 18.75 10.17 32 19.88 1 26 16.15 78.79 25.49 7 4.35 21.21 11.86 33 20.50 2 23 14.29 71.88 22.55 9 5.59 28.13 15.25 32 19.88 3 18 11.18 56.25 17.65 14 8.70 43.75 23.73 32 19.88 4 9 5.59 28.13 8.82 23 14.29 71.88 38.98 32 19.88 Total 102 63.35 59 36.65 161 100.00

The "Row Pct" values in Output 28.7.1 show the expected increasing trend in the proportion of adverse effects due to increasing dosage (from 18.75% to 71.88%).

Output 28.7.2: Measures of Association

 Clinical Trial for Treatment of Pain
 The FREQ Procedure
 Statistics for Table of Dose by Adverse

 Statistic Value ASE 95% Confidence Limits Gamma 0.5313 0.0935 0.3480 0.7146 Kendall's Tau-b 0.3373 0.0642 0.2114 0.4631 Stuart's Tau-c 0.4111 0.0798 0.2547 0.5675 Somers' D C|R 0.2569 0.0499 0.1592 0.3547 Somers' D R|C 0.4427 0.0837 0.2786 0.6068 Pearson Correlation 0.3776 0.0714 0.2378 0.5175 Spearman Correlation 0.3771 0.0718 0.2363 0.5178 Lambda Asymmetric C|R 0.2373 0.0837 0.0732 0.4014 Lambda Asymmetric R|C 0.1250 0.0662 0.0000 0.2547 Lambda Symmetric 0.1604 0.0621 0.0388 0.2821 Uncertainty Coefficient C|R 0.1261 0.0467 0.0346 0.2175 Uncertainty Coefficient R|C 0.0515 0.0191 0.0140 0.0890 Uncertainty Coefficient Symmetric 0.0731 0.0271 0.0199 0.1262

 Somers' D C|R Somers' D C|R 0.2569 ASE 0.0499 95% Lower Conf Limit 0.1592 95% Upper Conf Limit 0.3547

 Test of H0: Somers' D C|R = 0 ASE under H0 0.0499 Z 5.1511 One-sided Pr > Z <.0001 Two-sided Pr > |Z| <.0001
 Sample Size = 161

Output 28.7.2 displays the measures of association produced by the MEASURES option. Somer's D(C|R) measures the association treating the column variable (Adverse) as the response and the row 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.

Output 28.7.3: Tests

 Clinical Trial for Treatment of Pain
 The FREQ Procedure
 Statistics for Table of Dose by Adverse

 Cochran-Armitage Trend Test Statistic (Z) -4.7918 Asymptotic Test One-sided Pr < Z <.0001 Two-sided Pr > |Z| <.0001 Exact Test One-sided Pr <= Z 7.237E-07 Two-sided Pr >= |Z| 1.324E-06
 Sample Size = 161

The Cochran-Armitage test (Output 28.7.3) supports the trend hypothesis. The small left-sided p-values for the Cochran-Armitage test indicate that the probability of the Column 1 level ( Adverse='No') decreases as Dose increases or, equivalently, that the probability of the Column 2 level (Adverse='Yes') increases as Dose increases. The two-sided p-value 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.

 Chapter Contents Previous Next Top