Hello, I am looking for an advice regarding my experimental design and what statistics I should do.
My experimental design:
I have 3 cell lines (A, B, C) and from each I do 3-4 differentiations into cardiac myocytes (A1-A4, B1-B4, C1-C3). Then each differentiation is treated with the same 3 concentrations of a chemical (T1, T2, T3). And for each treatment, I measure the calcium concentration (y). So I have one continuous dependent variable (y), two categorical independent variables (x1 for cell line and x2 for treatment) and a random error which I want to correct for (e for differentiation).
I want to investigate the impact of the cell line (x1, main effect) on the cell response to the treatment (x2).
Many thanks in advance !
I don't get what the different "differentiations" should be and if and how you like to consider these in your model (afaiks you did not yet consider this at all).
Then it will be important to know if these differentiations are comparable between the cell lines, and if you want to analyze the treatment effect in the changes that happen between these differentiations, and if you plated cells that underwent these differentiations and during this process you took the measurement (possibly sacrifices parts of those cells to get the measurement while the rest continues to differentiate.
Once again I agree with Jochen, I will ask it another way.
What do these differentiations in myocytes imply?
Is it possible that the "3-4" differentiations cause a differentiation in calcium concentration?
if you don't know, it is possible that it is a third variable.
Thank you both for your answers. The cells I'm using are pluripotent stem cells which I then differentiate into cardiac myocytes. The differentiation protocol leads to various levels of purity (some fibroblasts or endothelial cells can emerge, the cardiac cells can be more or less ventricular or atrial-like, more or less mature,...) and this causes differences in the cardiac cells calcium handling (my measurement). The different differentiations are different batches of cells treated together to become cardiac myocytes. You can consider each differentiation like a single animal and I'm therefore using cells from 3-4 different "animals" per genetic background. I know there is a random variability coming from the differentiations and I want to control for it (I'm not interested in its effect). I hope this makes sense!
A few comments on the software. My opinion. YMMV.
- Don't use aov(). It just makes life more difficult for mixed effects models. [In a graduate school class we had to figure out the error terms for mixed effects model by hand, and sometimes that got pretty wiggy. That's what you need to do with aov() if the model gets at all complex.]
- Use lm() for OLS models, and either nlme or lme4 packages for mixed effects model.
- The choice between nlme or lme4 depends somewhat on what model you need to specify. lme4 is newer, and is probably the default. You'll want to use the lmerTest package if you want p-values for you effects. Or you can use car::Anova. But lmerTest also has a test for the effect of the random effects, and probably a bunch of other useful options and functions. The last I looked, nlme had some additional options for models, but you probably won't be needing them.
- My opinions on the differences between nlme and lme4 may be out-of-date. I haven't looked at this question in a while.
- For lm() or nlme model, you can use car::Anova for p-values.
- Any of these models is supported by the emmeans package. As long as your model is fit appropriately, the estimated marginal means are the universal way to compare among factors in post-hoc analysis.
- emmeans also has the joint_tests function will give you p-values for your factors. The result is usually just slightly different than that from car::Anova.
Sal Mangiafico Thank you for your advice, it's really helpful. I noticed aov was not the best for this and switched to lmer from the lme4 package. I will have a look to the emmeans package for the p-values.
A slightly different approach than "emmeans" has the "marginaleffects" package, which has a lot of very useful applications. Maybe you can give it a try https://marginaleffects.com/
I found a set of packages to perform all of this : easystats. It has two functions, one to compute standard errors, confidence intervals, and p-values based on various covariance matrices from the model (model_parameters, based on sandwich package) and another one to perform marginal mean contrast estimation (estimate_contrasts, based on emmeans package). I used both on my model but I get very different p-values (see pictures). Does anyone know why ? Which one should I trust more ?
Camille Charriere ,
From what I can see, the two outputs you show are different things.
- One is showing the summary of model, testing if the coefficients are different from zero. Like summary() of lm() models in base R.
- The other is comparing the groups, like emmeans would.
Sal Mangiafico you are right, but this seems to be a dummy coded variable with 3 levels. Therefore, the differences/slopes are the same, but the first model uses uncorrected test statistics to compare slopes/differences, whereas the "post hoc" test uses Holm adjusted p-values. Camille Charriere maybe it is possible to change the correction option to "none"? Then it should be the same.
Rainer Duesing It is indeed a dummy coded variable with 3 levels, that's why I was expecting comparable results. I switched to uncorrected p-value for the marginal contrast analysis and now I see the p-values are comparable.
Many thanks for your help !
Camille Charriere
One question, how many replications of differentiation*concentration do you have for each cell line?
John
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