Biostatistics

638 CHAPTER 12 THE CHI-SQUARE DISTRIBUTION AND THE ANALYSIS OF FREQUENCIES
b, A a, and B b are all greater than or equal to 5. Alternatively, when sample sizes are
sufficiently large, we may test the null hypothesis by means of the chi-square test.
Further Reading The Fisher exact test has been the subject of some controversy
among statisticians. Some feel that the assumption of fixed marginal totals is unrealistic in
most practical applications. The controversy then centers around whether the test is
appropriate when both marginal totals are not fixed. For further discussion of this and other
points, see the articles by Barnard (13–15), Fisher (16), and Pearson (17).
Sweetland (18) compared the results of using the chi-square test with those obtained
using the Fisher exact test for samples of size A þ B ¼ 3toA þ B ¼ 69. He found close
agreement when A and B were close in size and the test was one-sided.
Carr (19) presents an extension of the Fisher exact test to more than two samples of
equal size and gives an example to demonstrate the calculations. Neave (20) presents the
Fisher exact test in a new format; the test is treated as one of independence rather than of
homogeneity. He has prepared extensive tables for use with his approach.
The sensitivity of Fisher’s exact test to minor perturbations in 2 2 contingency
tables is discussed by Dupont (21).
EXAMPLE 12.6.1
The purpose of a study by Justesen et al. (A-12) was to evaluate the long-term efficacy of
taking indinavir/ritonavir twice a day in combination with two nucleoside reverse
transcriptase inhibitors among HIV-positive subjects who were divided into two groups.
Group 1 consisted of patients who had no history of taking protease inhibitors (PI Na€ıve).
Group 2 consisted of patients who had a previous history taking a protease inhibitor (PI
Experienced). Table 12.6.2 shows whether these subjects remained on the regimen for the
120 weeks of follow-up. We wish to know if we may conclude that patients classified as
group 1 have a lower probability than subjects in group 2 of remaining on the regimen for
120 weeks.
TABLE 12.6.2 Regimen Status at 120 Weeks for
PI Na€ıve and PI Experienced Subjects Taking
Indinavir/Ritonavir as Described in Example 12.6.1
Remained in
the Regimen
for 120 Weeks
Total Yes No
1 (PI Na€ıve) 9 2 7
2 (PA Experienced) 12 8 4
Total 21 10 11
Source: U.S. Justesen, A. M. Lervfing, A. Thomsen, J. A. Lindberg,
C. Pedersen, and P. Tauris, “Low-Dose Indinavir in Combination with
Low-Dose Ritonavir: Steady-State Pharmacokinetics and Long-Term
Clinical Outcome Follow-Up,” HIV Medicine, 4 (2003), 250–254.