All Times EDT
Keywords: cross-over, carry-over, Bayesian, model averaging
The best advice to apply a 2x2 cross-over design is to do all that is possible to reduce the potential of a differential carryover effect. However, a small differential carryover effect may still be noticed during the analysis. In the literature, various reasons may induce a carryover effect such as an inadequate washout period, a change in the physiological or psychological state of the patients caused by the treatment in the first period, or the treatment differences induced by the period mean level.
The frequentist approaches such as the adjusted two-stage approach and Willan maximum test are discussed in Wang, et al. 1997. In a Bayesian setting, the uncertainty of the carryover effect may be incorporated through model selection or model averaging. In Grieve, et al 1998, two Bayesian approaches are discussed, the first is a discrete model averaging approach by weighting with Bayes factor on the likelihood model with or without carryover effect; the second approach is to get the marginal posterior distribution of the treatment effect by integrating out the carryover effect from the model.
Reference: 1) Wang, Sue-Jane, and HM James Hung. "Use of two-stage test statistic in the two-period crossover trials." Biometrics (1997): 1081-1091. 2) Grieve, Andrew, and Stephen Senn. "Estimating treatment effects in clinical crossover trials." Journal of Biopharmaceutical Statistics 8, no. 2 (1998): 191-233.
Questions/Concerns: 1. What are the reasons for a carryover effect you have experienced and what measures have you implemented to mitigate it? 2. What are the pros and cons of the frequentist and Bayesian approaches in this setting? 3. What Bayesian approach - including prior distributions- would you recommend on the carryover and treatment effect?