This review covers Bayesian analyses of two-treatment crossover studies. The main emphasis is placed on the analysis of continuous data although we also consider dichotomous responses. Studies discussed include (1) the simple two-period, two-treatment crossover, (2) the two-period crossover with one baseline measurement, (3) the two-period crossover with two baselines and (4) the extra-period design with two treatment sequences.
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References
1.
Jones B., Kenward MGDesign and analysis of cross-over trials. London: Chapman-Hall, 1989.
2.
Senn SJCrossover trials in clinical research. London: Wiley, 1993.
3.
Ratkowsky DA, Evans MA, Alldredge JRCross-over experiments: design, analysis and application. New York: Marcel Dekker, 1993.
4.
Naylor JC, Smith Afm.Application of a method for the efficient computation of posterior distributions . Applied Statistics1982; 31: 214-25.
5.
Tierney L., Kadane J.Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association1986; 81: 82-86.
6.
Shaw Jeh.A quasirandom approach to integration in Bayesian statistics. Annals of Statistics1988; 16: 895-914.
7.
Gelfand AE, Smith Afm.Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association1990; 85: 972-85.
8.
Racine A., Grieve AP, Flühler H., Smith Afm.Bayesian methods in practice: experiences in the pharmaceutical industry (with discussion). Applied Statistics1986; 35: 93-150.
9.
Breslow N. Biostatistics and Bayes(with discussion). Statistical Science1990 ; 5: 269-98.
10.
Rodda BE, Davis RLDetermining the probability of an important difference in bioavailability . Clinical Pharmacology and Therapeutics1980 ; 28: 247-52.
11.
Selwyn MR, Dempster AR, Hall NRA Bayesian approach to bioequivalence for the 2×2 changeover design. Biometrics1981; 37: 11-21.
12.
Mandallaz D. , Mau J.Comparison of different methods for decision-making in bioequivalence assessment. Biometrics1981 ; 37: 213-22.
13.
Flühler H., Grieve AP, Mandallaz D., Mau J., Moser HAOn Bayesian methods for bioequivalence. Journal of PharmaceuticalSciences1983; 72: 1178-81.
14.
Racine-Poon A., Grieve AP, Flühler H., Smith Afm.A two-stage procedure for bioequivalence studies. Biometrics1987; 43: 847-56.
Hews RJA further note on the interpretation of results from the two-period cross-over clinical trial. PSINewsletter1987; 3(2).
17.
Geisser S.Estimation in the uniform covariance case. Journal of the Royal Statistical Society, Series B1964; 26: 477-83.
18.
Grieve APExtending a Bayesian analysis of the two-period crossover to allow for baseline measurements. Statistics in Medicine1944; 13: 905-29.
19.
Grieve APA Bayesian analysis of the two-period crossover design for clinical trials . Biometrics1985; 41: 979-90.
20.
Grieve APCorrection. Biometrics1986; 42: 459.
21.
Racine A., Grieve AP, Flühler H., Smith Afm.Bayesian methods in practice: experiences in the pharmaceutical industry (with discussion). Applied Statistics1986; 35: 93-150.
22.
Patil VMApproximation to the Behrens-Fisher distributions. Biometrika1965; 52: 267-71.
23.
Grieve APA note on the analysis of the two-period crossover design when the period-treatment interaction is significant. Biometrical Journal1987; 29: 771-75.
24.
Grieve APCrossover versus parallel designs. In: Berry DA ed., Statistical methodology in the pharmaceutical sciences . New York: Marcel Dekker, 1990: 239-70.
25.
Grizzle JEThe two-period change-over design and its use in clinical trials. Biometrics1965: 21: 467-80.
26.
Spiegelhalter DJ, Smith Afm.Bayes factors for linear and log-linear models with vague prior information. Journal of the Royal Statistical Society, Series B1982; 44: 377-87.
27.
Jeffreys H.Theory of probability. Oxford: Clarendon Press, 1983.
28.
Spiegelhalter DJ. In discussion of Racine et al.21.
29.
Brown BWThe crossover experiment for clinical trials. Biometrics1980; 36: 69-79.
30.
Kenward MG, Jones B.The analysis of data from 2 x 2 crossover trials with baseline measurements . Statistics in Medicine1987; 6: 911-26.
31.
Nicholls DP , Moles K., Gleadhill Dns, Booth K., Rowan J., Morton P.Comparison of transiderm nitrate and isosorbide dinitrate in chronic stable angina. British Journal of Clinical Pharmacology1986; 22: 15-20.
32.
Grieve APImplementation of Bayesian methods in the pharmaceutical industry. Unpublished Ph.D. thesis, University of Nottingham, 1992.
33.
Grieve APApplications of Bayesian software: two examples. The Statistician1987; 36: 283-88.
34.
Grieve APExtending a Bayesian analysis of the two-period crossover to accommodate missing data. Biometrika. In press.
35.
Gelfand AE, Hill SE, Racine-Poon A., Smith Afm.Illustration of Bayesian inference in normal data models using Gibbs sampling . Journal of the American Statistical Association1990; 85: 972-85.
36.
Dunsmore IRAnalysis of preferences in crossovers. Biometrics1981; 37: 575-78.
37.
Altham Pme.Exact Bayesian analysis of a 2 x 2 contingency table, and Fisher's 'exact' signifiance test. Journal of the Royal Statistical Society, Series A1969; 31: 261-69.
38.
Altham Pme.The analysis of matched proportions. Biometrika1971; 58: 561-76.
39.
Forster JJA Bayesian approach to the analysis of binary crossover data. The Statistician1994; 43: 61-68.
40.
Kenward MG, Jones B.A log-linear model for binary cross-over data. Applied Statistics1987; 36: 192-204.
41.
Polasek W., Pötzelberger K.Robust Bayesian methods in simple ANOVA models. Theory of Probability and its Applications1992; 37: 163-66.
42.
Farrow M., Goldstein M.Bayes linear methods for grouped multivariate repeated measurement studies with application to crossover trials. Biometrika1993; 80: 39-59.