To improve the power of a parallel groups design and reduce the time length of a crossover trial, we may consider an incomplete block crossover design. Under a distribution-free random effects logistic regression model, we derive an exact test and a Mantel-Haenszel Type of summary test procedure for testing non-equality in binary data when comparing three treatments. We employ Monte Carlo simulation to evaluate the performance of these test procedures. We find that both test procedures developed here can perform well in a variety of situations. We use the data taken as a part of the crossover trial comparing the low and high doses of an analgesic with a placebo for the relief of pain in primary dysmenorrhea to illustrate the use of the proposed test procedures.
SmithSJMarkanduNDSagnellaGAet al.Moderate potassium chloride supplementation in essential hypertension: is it additive to moderate sodium restriction?Brit Med J1985; 290: 110–113.
2.
RhindGBConnaughtonJJMcFieJet al.Sustained release choline theophyllinate in nocturnal asthma. Brit Med J1985; 291: 1605–1607.
3.
FleissJL. The design and analysis of clinical experiments, New York: Wiley, 1986.
4.
HillsMArmitageP. The two-period cross-over clinical trial. Brit J Clin Pharmacol1979; 8: 7–20.
5.
GrizzleJE. The two-period change-over design and its use in clinical trials. Biometrics1965; 21: 467–480.
JonesBKenwardMG. Design and analysis of cross-over trials, 3rd ed. Boca Raton, FL: CRC Press, Taylor and Francis, 2014.
8.
SennS. Cross-over trials in statistics in medicine: the first ‘25’ years. Stat Med2006; 25: 3430–3442.
9.
KochGGAmaraIABrownBWJr.et al.A two-period crossover design for the comparison of two active treatments and placebo. Stat Med1989; 8: 487–504.
10.
LuiK-J. Test equality between three treatments under an incomplete block crossover design. J Biopharm Stat2015; 25: 795–811.
11.
LuiK-JChangK-C. Sample size determination for testing nonequality under a three-treatment two-period incomplete block crossover trial. Biomet J2015; 57: 410–421.
12.
LuiK-JChangK-C. Test and estimation in binary data analysis under an incomplete block crossover design. Comput Stat Data Anal2015; 81: 130–138.
13.
Lui K-J. Estimation of the treatment effect under an incomplete block crossover design in binary data – a conditional likelihood approach. Stat Methods Med Res 2017; 26: 2197–2209.
14.
EzzetFWhiteheadJ. A random effects model for binary data from crossover clinical trials. Appl Stat1992; 41: 117–126.
15.
FleissJL. Statistical methods for rates and proportions, New York: Wiley, 1981.
16.
LuiK-J. Statistical estimation of epidemiological risk, New York: Wiley, 2004.
17.
AgrestiA. Categorical data analysis, New York: Wiley, 1990.
18.
JonesBKenwardMG. Modelling binary data from a three-period cross-over trial. Stat Med1987; 6: 555–564.
19.
FleissJL. A critique of recent research on the two-treatment crossover design. Controlled Clin Trials1989; 10: 237–243.
20.
SennSJ. Is the simple carry-over model useful?Stat Med1992; 11: 715–726.
21.
SchoutenHKesterA. A simple analysis of a simple crossover trial with a dichotomous outcome measure. Stat Med2010; 29: 193–198.
22.
SAS Institute Inc. SAS language, reference version 6, 1st ed. Cary, NC: SAS Institute Inc, 1990.
