I recently read a book by T.J. Cleophas titled "Statistics Applied to Clinical Trials". It is interesting that the author em phased the importance that the crossover study should not be used to test treatments with different chemical class.
"..Clinical trials comparing treatments with a totally different chemical class/mode of action are at risk of negative correlation between treatment responses. Such negative correlations have to be added to the standard errors in a cross-over trial, thus reducing the sensitivity of testing differences, making the design a flawed method for evaluating new treatments. "
"So far, statisticians have assumed that a negative correlation in cross-over studies was virtually non-existent, because one subject is used for comparison of two treatments. For example, Grieve recently stated one should not contemplate a cross-over design if there is any likelihood of correlation not being positive. The examples in the current paper show, however, that with completely different treatments, the risk of a negative correlation is a real possibility, and that it does give rise to erroneously negative studies. It makes sense, therefore, to restate Grieve's statement as follows: one should not contemplate a cross-over design if treatments with a totally different chemical class/mode of action are to be compared."
"At the same time, however, we should admit that the cross-over design is very sensitive for comparing treatments of one class and presumably one mode of action. The positive correlation in such treatment comparisons adds sensitivity, similarly to the way it reduces sensitivity with negative correlations: the pooled SEM is approximately sqrt(1-r) times smaller with positive correlation than it would have been with a zero correlation (parallel-group study), and this increases the probability level of testing accordingly. This means that the cross-over is a very sensitive method for evaluating studies with presumable positive correlation between treatment responses, and that there is, thus, room left for this study design in drug research."
One example the author mentioned is Ferrous sulphate and folic acid used for improving hemoglobin. There was an inverse correlation between the two treatments: Ferrous sulphate was only beneficial when folic acid was not, and so was folic acid when ferrous sulphate was not.