# OpenEpi, Version of December 1, 2003

## Test Results for TwoByTwo Module

Dataset # | Left Side | a,b,c,d | Compared with | Result
1 | Disease | 20,6,0,5 | ExactBB | Exact limits and p-values OK
2 | Disease | 2,2,4,6 6,4,2,0 3,0,1,1 8,4,1,1 19,10,8,8 | Martin, Austin, Epidemiology 1991; 2; p. 361 | CMLE odds ratio, Fisher and mid P results agree. MH chi is 0.374 vs. Mantel-Haenszel Summary Chi Square in OpenEpi of 0.1399.
3 | Exposure | 27,95,44,443 | SAS proc FREQ | Agreement
4 | Exposure | 23,74,20,134 4,21,24,309 | SAS | Agreement except that method of calculating 2-sided confidence limits from 1-sided seems to be different.
5 | Exposure | 451,39,1729,636 | ATFRAC | Agreement for OR based etiologic fraction and CLs.
6 | Disease | 451,1729,39,636 | Stat22 | Agreement, but OpenEpi unable to calculate Fisher and midP
7 | Disease | Same as 6 | ExactMA | Same result as 6
8 | Disease | 39,451,636,1729 | ExactMA | Calculations agree and OpenEpi can compute, but p values “mostly zeroes”.
9 | Disease | Same as 6 | Stats Direct | Same as 6
10 | Disease | Same as 8 | Stats Direct | Same as 8. Prevented fraction not available from Stats Direct.
11 | Disease | 72,20,684,553 | Walter, IJE 1978;7;2. Table 2 | Good agreement
12 | Disease | 4,386,4,1250 | Rothman, EpiSheet, Downloaded Nov 2003 | Good agreement. 2-sided confidence intervals calculated the same way as OpenEpi (doubling the minimum of the one-sided exact), and agree.
13 | Disease | 3,9,104,1059 1,3,5,86 | Rothman, EpiSheet, Downloaded Nov 2003 | Rothman values labeled RR and mhRR are actually odds ratios, and agree with OpenEpi odds ratios.
14 | Disease | 8,5,98,115 22,16,76,69 | Rothman, EpiSheet, Downloaded Nov 2003 | ok
15 | Disease | 32,2,52407,18790 104,12,43248,10673 206,28,28612,5710 186,28,12663,2585 102,31,5317,1462 | Rothman, EpiSheet, Downloaded Nov 2003 | Rothman’s RR and mhRR are really odds ratios. RDs and other parameters agree.
16 | Exposure | 27,95,44,443 | Epi Info 2002, Ver 2 | Good agreement
17 | Exposure | 1,2,3,4 | Epi Info, Ver 3 | Good agreement
18 | Exposure | 22,6,3,16 20,5,0,2 | Epi Info, Ver 3 | Good agreement
19 | Exposure | 43,11,3,18 | Epi Info, Ver 3 | Good agreement
20 | Exposure | 27,4,3,10 16,7,0,8 | Epi Info, Ver 3 | Good agreement
21 | Exposure | 1,0,2,3 | Epi Info, Ver 3 | Agreement.
22 | Exposure | 66,28,36,32 139,61,93,54 | Sullivan, Unpublished chapter, with hand-calculated results, downloadable with OpenEpi. Click HELP in TwobyTwo. | Agreement.

By Andy Dean with a great deal of help from Ray Simons, who kindly sent printouts of comparison materials, and Kevin Sullivan, whose excellent unpublished chapter on 2 x 2 tables and Person Time statistics is the source of the equations and the test examples for many of the functions. Agreement is considered satisfactory if the first two significant figures agree, when a number, such as a p-value, is small.

Conclusions: There are some issues to resolve about terminology for upper and lower one-sided exact confidence limits, and concerning whether to add 0.5 to each cell if a cell is 0, but otherwise TwoByTwo seems ready to release for serious use, although it is always a good idea to check important conclusions with more than one program.