Statistical Methods in Medical Research 4ed

Example 15.10
In Example 15.7 (Table 15.7) the exact test gives the following results.
The sum of P rAi over the three strata is 29. The exact probability that this sum would
be greater than or equal to 29 if there were no association between mortality and
treatment, subject to the marginal totals in each of the three age groups, is 0 0327 from
StatXact. The probability that P rAi ˆ 29 is 0 0237, so that the exact one-sided mid-P
value is 0 0327 1
2
15.8 Exact tests for contingency tables 527
…0 0237† ˆ0 0208. The two-sided tests, based on doubling the one-
sided values, are 0 042 and 0 065 for the mid-P and P values, respectively. From Example
15.7, using XMH and XMHc, the corresponding levels are 0 037 and 0 067.
The tests based on x 2 statistics proved acceptable approximations to the exact values.
This is in accord with the earlier comment that the Mantel±Haenszel test is likely to be
valid if the smallest of the expected cell frequencies summed over strata is at least 5. In this
example, the smallest such expected cell frequency is 13.1.
Exact tests have been discussed above as significance tests. However, the
methodology may be used to estimate a confidence interval for a parameter. For
example, the odds ratio (4.25) is often used as a measure of association in a 2 2
table in epidemiological studies and an estimate may be obtained of the common
odds ratio after combining over strata (§19.5). Exact limits for this estimate
follow the rationale illustrated, for a simpler situation, in Fig. 4.8. The exact
limits are conservative, due to the discreteness of the data, and mid-P limits are
more satisfactory (§4.4); StatXact produces mid-P limits.