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I have a few questions for help,

  1. One of my predictors is for treatment and control. Another predictor is dosage. Treatment group has 4 dose levels which control group only has one. Can I still use regression, and model treatment/control and dosage as two predictors? Is it better to include an interaction?

  2. Similarly, one predictor genotype has two levels: TG and WT. Both treatment and control can apply to TG animals, whereas WT animals only receive treatment. Should I use two predictors or merge them into one, e.g. TG treated, TG control, WT treated?

  3. are the standard sample size calculation from power analysis, or newly developed approaches e.g. Hsieh 1998, applicable to animal studies? Due to ethnical reasons, people try to lower the sample size for animal study as much as possible. The general rules from linear regressions, 10 observations per variable, should not apply to animals right?

Hsieh, F. Y., Bloch, D. A., & Larsen, M. D. (1998). A simple method of sample size calculation for linear and logistic regression. Statistics in medicine, 17(14), 1623–1634.

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  1. Yes, you can include them, and yes you should include an interaction if you have a theoretically justifiable reason to do so. Here it makes sense to do, as we would almost always expect there to be some difference between treatment and control based on dosage. Note that a typical two-way interaction like this will require around four times the sample size required for a main effect to have sufficient power (Gelman et al., 2022, p.301-302), but I discuss power considerations further below. I essence, you could still fit the data, but be wary of what that means with respect to your sample size.

  2. I think this would be somewhat sensible given that the WT group will just have a linear constant with respect to treatment, but it will be hard to argue against placebo effect or simply genotype-driven differences if there is no control group for this genotype to compare against.

  3. Sample size considerations are always context-specific. One can use rules of thumb, but these typically require ignoring a lot of features that drive power...standard error of each coefficient, magnitude of effect, etc. However, it appears your data is observed already, so you wouldn't need to conduct post-hoc power testing, as it is deemed bad practice anyway.

References

  • Gelman, A., Hill, J., & Vehtari, A. (2022). Regression and other stories. Cambridge University Press.
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