Period effect in crossover design I am confused with period effect, secular change, temporal trends in crossover design.
In this article it is stated that

The randomization of the treatment sequence helps to account for
temporal trends (such as seasonal variation).

But for example, in Stephen Senn's book on cross-over trials, he says:

Alternatively, during the time in which the cross-over trial is run
the condition of the patients might suffer a secular change (some
factors other than treatment might be slowly be affecting the
condition of most patients) and then the benefit (or otherwise) of one
drug compared to the other might be dependent on the current state of
the patient. This would provide a case of period by treatment
interaction.

So does the first link roughly say randomization can solve the issue? Or am I confused between period effect and period by interaction effect?

The first quote talks about a period main effect with a consistent difference between the treatments across the periods. E.g. something like these means:




Treatment
Period
Mean outcome




A
1
0


B
1
1


A
2
5


B
2
6




In the second case, we would have a treatment by period interaction (and probably also a period main effect) meaning that the treatment effect is not the same across periods. E.g. something like these means




Treatment
Period
Mean outcome




A
1
0


B
1
1


A
2
5


B
2
10




The first case is not really a problem, at all, while the second one is trickier to deal with. In particular, it may be hard to figure out why a period by treatment interaction occurs (e.g. it could be a carry-over effect of the period 1 treatment, it could be the sort of thing Senn described with patients getting more - or less - benefit from a treatment based on some underlying state that changed over time etc.).
