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I have a set of age matched patients (40males and 40females).

I am measuring the drug dose effect on their hormone outcome.

They are treated for 4 weeks, each week we increase the drug dose starting from baseline (So BL followed by 4 weeks with increase in dose). We measure their hormone level twice a day, everyday (2 hormones in total) from blood and cerebrospinal fluid.

So variables are:

Sex, hormone level, drug dose, and time (every 12 hours), fluid type.

I thought of using rmANOVA to check each point difference from baseline, but I want to also see 1- is there a significant difference between the female and male hormone curves measured? 2- how rapid is the hormone increasing with respect to dose increase? 3-is there a difference between the 2 hormones curves?

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You need a model of hormone-level observations that incorporates all of your predictors while taking the associations of measurements within individual participants into account. Each observation of the hormone concentration would be represented by a different row in the data matrix, with the measured value, the participant ID, and all the covariate values corresponding to that observation, including the time.

An appropriately structured linear model should provide what you need. Time could be incorporated as a flexible continuous predictor, for example via restricted cubic splines. Drug dose, sex and fluid type (cerebrospinal fluid, CSF, vs blood) would also be included. Even though you have age-matched patients, you might also include age as a predictor to provide more precision. If you expect different time-courses for blood and CSF measurements, you need to include an interaction term between the fluid type and the Time modeling.

There might be other interactions among predictors that you need to include, based on your knowledge of the subject matter. However you work through those details, tests on the coefficients will help answer the questions about sex differences, drug-dose/hormone-response relationships, etc.

The question is then how to deal with the lack of independence among observations within each participant. There are a few general approaches.

One is a mixed model of the hormone measurements, calling your other predictors "fixed effects" and modeling the participants with some form of random effect. The form of the random effect(s) depends on just what types of differences among participants you need to correct for.

The simplest is a random intercept, effectively adjusting for differences among individuals in the estimated baseline hormone concentration while having the same associations of predictors with differences from that individualized baseline. Again, depending on your understanding of the subject matter, you might want to include additional differences among individuals as random effects, for example in the CSF/blood difference or the drug-dose/hormone-response relationship.

Chapter 7 of Harrell's course notes deals extensively with longitudinal measurements from a different perspective of generalized least squares, with a worked-through example. That chapter has a helpful table comparing the relative advantages of repeated-measures ANOVA, mixed-effect models, generalized least squares, and generalized estimating equations for this type of situation.

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  • $\begingroup$ Oh, no! I can't upvote you yet because I don't have 15 reputations, but will do when I have that. Thank you kindly for your comprehensive answer. Much appreciated! $\endgroup$
    – Daveyin
    Commented May 10, 2021 at 0:14

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