Factorial design - dropping factors and conditions

research methods design
1

Assume a factorial design with three factors with two levels each. At interim analyses it is found that one factor is associated with severe harm (or strong positive effect), and thus it seems redundant to collect more data with respect to this factor (thinking in terms of Bayesian sequential design). What would the implications be if this factor was dropped and the number of allocation conditions reduced?

If we consider that the analysis consists of a normal regression model with each factor represented as a covariate, I see no concern for dropping one factor when I have the data I need to shape the uncertainties in ways that is important to me. It may of course reduce the power available to me for interactions - but it would also mean that I can allocate participants to the other conditions at a quicker pace and close out the trial earlier.

2

I don’t see any problem with that way of thinking. But frequentist operating characteristics (since data probabilities are relevant unlike Bayes which uses parameter probabilities) are altered in complex ways and it may be difficult to define p-values and confidence intervals. The very meaning of “observing data more extreme than mine” may be tricky to pin down. I’d like to get pointers from others from existing literature. There may be something useful from “drop the loser” designs in clinical trials.