[R] testing correlated proportions

[Yuelin Li]

A question about comparing symptom reduction over time and across 
treatment groups.  Each respondent is asked twice if they 
experience symptoms (coded 1), at baseline and then at 6 months 
later.  They are randomly assigned to either the control or the 
intervention group.  The 2x2x2 table below shows the frequency 
counts.

As can be seen in the margins of the table, 21% of the control 
group show symptoms at baseline, then it reduced to 7% six months 
later; and 48% of the intervention group show symptoms at 
baseline, then only 4% at 6 month.  

The question is, given the information below, how do I test if 
the intervention group has a better improvement?

Intuitively, I imagine that a difference of 44% should be better 
than a 14% difference in a sample of about 30 respondents.  But 
it is no so according to Levin & Serlin's method (J. of Stats 
Education, 8 (2), 2000).

Levin and Serlin say that correlated proportions between two 
groups can be tested by a simple 2x2 table using the frequency of 
changes:

			Control		Intervention
		------------------------------------
0 --> 1 (worse)		2		0
1 --> 0 (better)	6		12
----------------------------------------------------

A fisher.test(matrix(c(2,6,0,12), ncol=2)) shows a p-value of 
0.15.  

I'd appreciate suggestions to alternative methods, perhaps a test 
of conditional independence in loglin()?  But I am not sure how 
to do that.

Yuelin Li.

---------  Table  -------------

Control Group

(baseline by 6 months)
Frequency|
Percent  |
Row Pct  |       0|       1|  Total
---------+--------+--------+
       0 |     20 |      2 |     22
         |  71.43 |   7.14 |  78.57
         |  90.91 |   9.09 |
---------+--------+--------+
       1 |      6 |      0 |      6
         |  21.43 |   0.00 |  21.43
         | 100.00 |   0.00 |
---------+--------+--------+
Total          26        2       28
            92.86     7.14   100.00

Intervention Group

(baseline by 6 months)
Frequency|
Percent  |
Row Pct  |       0|       1|  Total
---------+--------+--------+
       0 |     14 |      0 |     14
         |  51.85 |   0.00 |  51.85
         | 100.00 |   0.00 |
---------+--------+--------+
       1 |     12 |      1 |     13
         |  44.44 |   3.70 |  48.15
         |  92.31 |   7.69 |
---------+--------+--------+
Total          26        1       27
            96.30     3.70   100.00