1) Matching increases the power if there is a strong correlation in the response between the matched individuals.

2) RM ANOVA is really outdated. Using a hierarchical/mixed model (as I proposed) is the better way to account for such correlations, for the reasons I explained above.

I gave reasons and explanations. Instead of just citing old papers, I would be grateful if you could argue why the approach I proposed is not ok. If it is because there are papers giving other advice, well, then why do you ask? The papers you referenced are not comparing pros and cons of RM ANOVA and mixed model approaches.

PS: Interestingly, Festing is a well-known author in this field of animal research, much involved in 3R. However, he is not a statistician (he studied agriculture and has a PhD in genetics - that's not the problem), and his publications are obviousely not made in cooperation with any statistician (this I consider a problem). It is undoubtfully good that he tries to promote methods to improve power and reduce the need of animals, also that he sensitizes researchers for possible (statistical) issues in animal experiments. Very good. The problematic part is that he is very much influenced by the standard textbook stats. It would be nice to see that this massive competence in animal research and experimental design would be complemented with a similarily well-founded competence in statistics. No need that all this is unified in a single person.

The best option is to use "litter" as a random effect (random intercept term).

If can house them in different cages (I don't know if this is ok for the mice; but if housing littermates together comes with some problems [like social stress or whatever], you don't need to do this). In this case you can also include "cage" as a random effect (crossed with "litter").

I did not understand why you make a point of "using 3 pups of one sex" to split over the treatment groups. If you assume that there might be differences between the sexes, better include "sex" as a factor in your analysis, possibly with the sex:treatment interaction. There is also no reason to "throw away" a littermate that happens to have less than two sisters or brothers.

Finally, I have a gut feeling that using 2 doses makes everything overly complicated and is a waste of mice. If you need a dose-finding, then perform a proper experiment for that. Otherwise use a dose where you are quite sure that it should work sufficiently well (and if it turns out that it does not work, you can still kill another round of animals treated with a different dose).

Dear Jochen, thank you for your answer. I think I have to clarify my question.

Mice are social animals. They should not be single housed. To minimize the possibility of male aggression it is best to keep them in the same groups from weaning (separation from mother). Therefore it is the easiest way to keep siblings together. As siblings are more similar to each other than to other mice from the same strain because of conditions during pregnancy and mother care "litter effect" is a well known phenomenon. By keeping littermates toghether I would avoid adding new factor of cage-effect.

Average litter size of C57 mice is 7.5 (5 - 11). This way I can assume that in a majority of litters I will get at least 3 males and 3 females. I plan to treat 3 pups of each sex from each litter. I initially planned to analyze males and females separately, as it had been reported, that compounds I plan to use may act in a sex-dependent manner. If I decide to use repeated measures ANOVA, then indeed I will have to discard pups of one sex from too small litters. It was my initial major point of concern. However, I do not expect it to happen frequently. On the other hand, if I have missing "n" because of too small litter, I think I would still need to replace the whole litter. I cannot just simply add it from another, bigger litter because in this case 2 pups from the same litter would obtain the same treatment. In this case, due to litter effect, I would have to average their response and use as n=1. If each pup from a certain litter obtains the same treatment, then one pup is an experimental unit. If whole litter, or a group within this litter obtains the same treatment, then the whole litter or its part is considered one experimental unit. I just cannot combine for example 12 male pups from 3-4 litters into one group, because in this case n=3-4.

" Finally, I have a gut feeling that using 2 doses makes everything overly complicated and is a waste of mice ". Not in the case of within-litter design. I can of course use only 1 dose and do a t-test. But in this casue I would have to waste more mice, as if I treat more than 1 littermates with the same dose, it is still n=1 after averaging.

" you can still kill another round of animals treated with a different dose ". In this case I would also have to repeat control group, because of litter effect, discussed before.

Dear Jakub,

thank you for your clarification. I know that mice are social animals and that the should not be kept isolated. I just did not know if it is better to keep siblings together or better keep non-siblings together. If there would be a higher stress-level when siblings are kept together (what is not the case, as you said), then it yould be worthwhile to mix non-siblings in the cages. This couöld be accounted for by introducing "cage" as random effect, and any disadvantage by this would be outweighted by the advantage of a more adequate or comfortable life situation for the mice.

I don't completely understand your problems with the distribution of the pups. You keep litters together, and treat them differently. Some of the pups are females, others are males. You use all the pups available, and you analyze the data including a sex:treatment interaction and "litter" as random factor. There is no problem with n=1 cases or whatever. And as a result you can infere the effects of the treatment in males as well as in females, and also the difference in the treatment effects between males and females (that is, the interaction).

Your planned design has (statistical) the disadvantage that you have to decide which 3 animals you are going to "pair". This is arbitrary and costs 2 d.f. per pairing (a huge loss of power). Additionally, you have the problem that you always need "full pairings", with the problem that you may have some mice left over that you can not use.

My advice is: discard the deliberate "pairing". Just include "litter" as a random effect in your model (not as a fixed effect). This takes account of the correlation between litter-mates, it saves you the d.f. for the analysis, and it is possible to have unequal sample sizes (so you can use all the pups available, always)*

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You just need to take care that for each litter you have roughly similar numbers of males and females in the same treatment group. If you would -in the worst case possible- put all females in the control group and all males in the treatment group, treatment and sex would be (fully) confounded and you (or the model) could not say the treatment-effect from the sex-difference. The more equally you distribute the sexes across the groups, the better. But the distribution does not need to be perfercly equal.

Dear Jochen,

the design is based on principles covered in the publications:

Article Design and Statistical Methods in Studies Using Animal Model...

Article Multiparous species present problems (and possibilities) to ...

Say we have 12 litters, each culled to 3 males and 3 females before treatment, so we can name them:

Litter 1: M1, M1, M1 and F1, F1, F1

Litter 2: M2, M2, M2 and F2, F2, F2

Litter 3: M3, M3, M3 and F3, F3, F3

and so on...

Within each litter I randomly assign treatments to control (C), treatment X (X), treatment Y (Y), so we have:

Litter 1: M1C, M1X, M1Y and F1C, F1X, F1Y

Litter 2: M2C, M2X, M2Y and F2C, F2X, F2Y

Litter 3: M3C, M3X, M3Y and F3C, F3X, F3Y

and so on...

According to developmentalists (cited papers) littermates are not independent replicates. So my initial question was whether I can do RM ANOVA with matching within litters so M1C is matched to M1X and M1Y, F1C is matched to F1X and F1Y, M2C is matched to M2X and M2Y and so on? This matching is based on the mentioned finding that siblings are not independent. I don't think this is deliberate decision which triads of animals to match. Treatment assignments are random and belonging to the same litter is also not my decision.

If each C, X, Y are results of the same animal on 3 distinct time points and treatments, it will be no brainer to use RM ANOVA.

If I understood paper by Zorrilla well, matching within litters increases power of statistical analysis in this case.

1) Matching increases the power if there is a strong correlation in the response between the matched individuals.

2) RM ANOVA is really outdated. Using a hierarchical/mixed model (as I proposed) is the better way to account for such correlations, for the reasons I explained above.

I gave reasons and explanations. Instead of just citing old papers, I would be grateful if you could argue why the approach I proposed is not ok. If it is because there are papers giving other advice, well, then why do you ask? The papers you referenced are not comparing pros and cons of RM ANOVA and mixed model approaches.

PS: Interestingly, Festing is a well-known author in this field of animal research, much involved in 3R. However, he is not a statistician (he studied agriculture and has a PhD in genetics - that's not the problem), and his publications are obviousely not made in cooperation with any statistician (this I consider a problem). It is undoubtfully good that he tries to promote methods to improve power and reduce the need of animals, also that he sensitizes researchers for possible (statistical) issues in animal experiments. Very good. The problematic part is that he is very much influenced by the standard textbook stats. It would be nice to see that this massive competence in animal research and experimental design would be complemented with a similarily well-founded competence in statistics. No need that all this is unified in a single person.

Dear Jochen,

thank you for response. I think, now I get your point.

To begin, I am not a statistician. I am looking for best solution for my problem. I found cited papers, so I assumed I can do RM-ANOVA in GraphPad Prism (which my institution has) for this project. But in the back of my head I had doubts, so I asked a question here.

Now, you convinced me that mixed model with two fixed effects (sex and treatment) and one random effect (litter) will do best for my project. Ability to analyze "not full" litter is one of its advantages over RM-ANOVA. This problem had been my concern, but I was planning to deal with it in other way (by in-fostering missing pups from litters born on the same day).

I have never said that solution you proposed had any disadvantages. I just wanted to be sure that my within-litter study design was clearly stated.

My initial assumption was that I could analyze this kind of data with Prism, but I don't think it is capable of doing this type of analysis (https://www.graphpad.com/guides/prism/8/statistics/stat_anova-approach-vs_-mixed-model.htm).

Any suggestions which software can do it?

Once again, thank you for your help.

See Prof Marie Davidian's course notes on longitudinal models at her NCSU. Website. This is the best reference I know of and it supports prof Wilhelm. Best, D. Booth

This is a useful site especially as it has links to different software

Longitudinal Analysis: Modeling Within-Person Fluctuation and Change

https://www.pilesofvariance.com/

SAS, S, SPSS, R and surely many other software can handle mixed models. The advantage of R is that it is completely free and that you will find a lot of free resources (the disatvantage is that R is a programming language you would need to learn/understand, what is quite demanding, but also extremely revarding in the longer term!).

I agree with dear Kelvyn Jones

Now there are a lot of software products that will do all the calculations for you. The main thing is to enter correctly into the database.

Regards, Pushkin Sergey Viktorovich

I am also thinking in the direction of Prof. @Jochen. Using a mixed model with "litter" as a random effect in your model will be really ideal, and each "sex" systematicaly represented in the groups: control, low and high treatment doses. Also, "measurements" taken at three "time points" respectively. Honestly, is RM ANOVA really outdated? I will be grateful for direction or references on the pitfalls, and what alternative approach addressed that specifically please. . Thanks

Abiodun Christian Ibiloye the Prof Marie Davidian's course notes that David Eugene Booth pointed to are very good on the comparison of traditional and random effects ANOVA and you may be interested in Article Contextual Models of Urban House Prices: A Comparison of Fix...