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Table Analysis |

After the pilot study on the new ouchless bandaids, the investigators decided to continue their research by conducting a clinical trial in which children at five clinics were tested with the test and regular bandaids. Instead of a single table, the clinical trial produces five tables. In order to assess whether the test bandaids produced fewer complaints than the regular bandaids, you need to assess the association in sets of tables instead of the association in a single table.

Extended Mantel-Haenszel statistics, also known as Cochran-Mantel-Haenszel statistics, provide a way of assessing association between two variables that determine a table while controlling for, or adjusting for, the variables that determine the sets of tables. These variables are also known as stratification variables. In this instance, the statistics can provide a way to assess the association between bandaid type and complaint status while controlling for clinic.

In the first section, the odds ratio was presented as a measure of association. You can also compute an overall odds ratio for a set of tables that has been adjusted for the stratification variables.

The Studybandaid data set contains the information collected in this clinical trial and includes data that constitute tables for each of the five clinics.

- Select
**Tools****Sample Data**... - Select Studybandaid.
- Click
**OK**to create the sample data set in your Sasuser directory. - Select
**File****Open By SAS Name**... - Select Sasuser from the list of
**Libraries**. - Select Studybandaid from the list of members.
- Click
**OK**to bring the Studybandaid data set into the data table.

Figure 9.15 displays the data table containing these data. Note that the data are in frequency form, with the variable count containing the frequencies of the profile contained in each row of the table. The column corresponding to the variable clinic contains the values for the five clinics.

- Select
**Statistics****Table Analysis**... - Select type from the candidate list as the
**Row**variable. - Select outcome from the candidate list as the
**Column**variable. - Select clinic from the candidate list as the
**Strata**variable. - Select count from the candidate list as the
**Cell Counts**variable.

Figure 9.16 displays the resulting dialog.

- Click on the
**Statistics**button. - Select
**Chi-square statistics**. - Select
**Mantel-Haenszel Statistics**. - Click
**OK**.

Note that the Tables dialog specifications (see Figure 9.5) made previously remain in effect. Therefore, both frequencies and row percentages are produced for this analysis.

Click **OK** in the Table Analysis dialog to perform the analysis.

Figure 9.17 contains the frequency table for clinic A.
Figure 9.18 contains the table statistics for clinic A.
The Pearson chi-square statistic has the value 2.8505 and
a *p*-value of 0.091 with 1 degree of freedom.

Figure 9.19 contains the frequency table for clinic B.
Figure 9.20 contains the associated table statistics.
The Pearson chi-square statistic has a value of 9.9475
and a corresponding *p*-value of 0.0016.

The other individual tables, not printed here, show varying degrees of evidence of association. Clinic C and clinic E appear to have no evidence of association, while clinic D does appear to show evidence of association.

Figure 9.21 displays the results of the CMH analysis.

**Figure 9.21:** CMH Summary Table

Three versions of the CMH statistic are printed; all have the
value 14.2206 and a *p*-value of 0.0002 with 1 degree of freedom.
Your choice of statistic depends on the scale of variables that
determine the rows and columns.
The General Association statistic always applies. If the
columns can be considered ordered, or ordinal, then the
Row Mean Score statistic is appropriate as well and is
directed at location shifts. If both the columns and rows
are ordered, then the Correlation statistic is also appropriate
and is directed at linear association. The degrees of freedom
of these statistics vary. For more details, refer to
Stokes, Davis, and Koch (1995). Note that the sample size requirement
for the CMH statistics is that the total (tables combined) sample size
be adequate.

In the case of the 2 ×2 table, all of these statistics are equivalent. Here, you can conclude that type of bandaid is significantly associated with complaint status, controlling for clinic. Figure 9.22 displays the overall relative risk and odds ratios and their confidence bounds.

The odds ratio for this study has the value 2.1597 with a confidence bound of (1.4420, 3.2348). This means that those children with the regular bandaid are twice as likely to have complaints as those with the test bandaid or, conversely, that those children with the test bandaid are half as likely to have complaints as those children with the regular bandaid. Since the 95 percent confidence bounds don't include the value 1, this odds ratio is considered to be significantly different from 1.

Note that another test called the Breslow-Day test for Homogeneity
of Odds Ratio is also printed. Since the test has a *p*-value
of 0.3455, you would conclude that the hypothesis is not rejected.
The sample size requirement for this test is that each individual
table has to have sufficient sample size unlike the sample size
requirement for the CMH statistics. In this case, since all tables
have totals greater than 25, this condition is met.

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