My design is that of repeated measures (within-subject design). That is, the subjects (name) are the same through the groups (group). This implies that there is dependency between the data, which is why we cannot use one-way ANOVA. The alternative, then, is to use one-way repeated-measures ANOVA (RANOVA) - this ANOVA accounts for the dependence between the data in its variance calculations. However, other problems appear: normality and sphericity.
Some metabolites are not normally distributed. Therefore, we cannot apply RANOVA to them. In addition, the other assumption of sphericity needs to be satisfied. The method I used to calculate RANOVA automatically checks the assumption and corrects it, if necessary. This method also returns the size of the generalized effect, which enriches our adjustment.
But, how to solve the problem of non-normal metabolites? We can apply ANOVA to those normally distributed, certainly, but for those others we can use the Friedman test: nonparametric equivalent to RANOVA. However, it is not that robust. Instead, it would be interesting to use mixed models.
As the design is dependent, so mixed models apply well, at first.
See what metabolomics data can be transformed into a long format:
name group metabolite value 1 S1 1 1-Methylnicotinamide 0.0190 2 S1 1 2-Aminoadipate 0.410 3 S1 1 2-Hydroxyisobutyrate 0.114 4 S1 1 2-Oxoglutarate 0.266 5 S1 1 3-Hydroxybutyrate 0.0579 6 S1 1 3-Hydroxyisobutyrate 0.303 7 S1 1 3-Hydroxyisovalerate 0.106 8 S1 1 3-Hydroxyphenylacetate 0.0445 9 S1 1 3-Indoxylsulfate 0.615 10 S1 1 4-Hydroxyphenylacetate 0.256
We can see them in a certain hierarchy:
group
name
metabolite
From what I have studied, in order to verify that metabolites have changed significantly over time (of the groups), we first created a baseline model and a main model. Next, we compare whether the main model significantly improved the fit. How is this done in practice?
In the first model, baseline, we considered only the group average as a predictor of metabolites. Imagine a regression where only the intercept varies. We expect the fit to be poor, right? A straight line (without slope) is not able to predict much. On the other hand, in the second, main model, the regression also has the group as a predictor. Compared to the baseline, if this model improves the fit for the metabolites, then we have evidence that the variable group has a significant effect.
What follows this comparison between models is a multiple comparison. What is the most robust method suggested in this case?
In the hierarchy I made above, we can say that metabolites vary across individuals and across groups. But I'm not sure it is a correct model. It could be: metabolites vary for each individual, and individuals vary in each group. It makes more sense, right?
Which treatment structure is the most suitable for this case? Is there any script available for R that can be used?
Is your hypothesis about some metabolites change differently across groups by time? This is a generic research question I confront with. If your hypothesis is like this, you can check group*time interaction.
When you find the interaction significant, you can perform lsmeans comparisons to find where the difference lies.
To do the interaction check, just add the interaction term into your model.
Jochen Wilhelm
- we have no way to insert an interaction: our data are 82 metabolites, measured 7 times over time, for msms 15 individuals
- the way I did it was:
baseline %
select(metabolite, AIC, BIC, deviance, logLik, statistic, df, p.adj)
Can you help us?
Where is the "time" in your analysis? This seems to be completely ignored?
---
another point:
Have you checked the residual diagnostics of the models?
Have you visualized the data in a heatmap and in a PCA biplot?
---
PS: a note on performance:
You fit two models, "baseline" and "main", where "baseline" is nested within main, lacking the factor "group". It is more efficient and clearer to fit the "main" model and create the "baseline" model by updating "main":
baseline
Mehmet Sinan Iyisoy, thanks for you answer!
Is your hypothesis about some metabolites change differently across groups by time? This is a generic research question I confront with. If your hypothesis is like this, you can check group*time interaction.
My hypothesis is that some metabolites change differently across groups--groups is the time variable here. We took a urine sample for each participant in seven (7) different times. With each sample we then performed a MRS (Magnetic Resonance Spectroscopy) analysis.
When you find the interaction significant, you can perform lsmeans comparisons to find where the difference lies.
I used the emmeans method to inspect the comparisons, but I didn't inspect the results yet--mainly because my doubts concerning the validity my lmm model.
To do the interaction check, just add the interaction term into your model.
Unfortunately I can not add the interaction term because of the experiment's design: 82 metabolites obtained from 15 participants in 7 specific moments.
Daniel Wright, thank you for your answer!
Try having the data in "long" format rather than "wide" format.
I already have it:
|name |group |metabolite | value|
|:----|:-----|:--------------------|---------:|
|S1 |1 |1-Methylnicotinamide | 0.0189781|
|S1 |1 |2-Aminoadipate | 0.4099270|
|S1 |1 |2-Hydroxyisobutyrate | 0.1135766|
|S1 |1 |2-Oxoglutarate | 0.2656934|
|S1 |1 |3-Hydroxybutyrate | 0.0579075|
|S1 |1 |3-Hydroxyisobutyrate | 0.3032603|
...
|S15 |7 |Xanthosine | 0.0050495|
|S15 |7 |Xylose | 0.0600000|
|S15 |7 |cis-Aconitate | 0.0246535|
|S15 |7 |o-Cresol | 0.0015842|
|S15 |7 |sn-Glycero-3-phosphocholine | 0.0125743|
|S15 |7 |trans-Aconitate | 0.0096040|
Jochen Wilhelm, thanks again for your help!
Where is the "time" in your analysis? This seems to be completely ignored?
The "time" variable is the "group" variable--it is just a naming thing. My design is a repeated measures design: 15 individuals measured in 7 different moments in time; for each one a urine sample was taken and a MRS analysis was performed to obtain the 82 metabolites. It is a crossed design, if I understand it correctly.
Have you checked the residual diagnostics of the models?
Yes. Some residuals were not "OK". That is, not random in the residual plot or normally distributed as indicated by the qqplot. I got about 15-20 bad residuals (i.e., clusters in the residual plot). Can I show you somehow? Bad residuals implies that I should not trust the model, right? My data was insufficient, in that case, for a linear model.
Have you visualized the data in a heatmap and in a PCA biplot?
Actually, no, but I didn't relate them to this LMM analysis. Can you tell me, please, what do I need to understand here? Also, if it is useful to know, I performed an OPLS-DA analysis and obtained good Q2Y and R2Y metrics (>0.8 and >0.9 in average, respectively), with 2000 permutations.
PS: a note on performance: ...
That is good! I didn't know the drop1 function. I used it when you cited in your first answer. Now I know that it should be used for its simplicity and performance. Thanks!
Ok, you just measured 82 different metabolites over time in 15 subjects, and there are no "groups" to compare concentrations... (Note: comparing concentrations of the same metabolite between the 7 time-points is not a really sensible thing to do; and the values are not independent between time-points).
What you may want is to analyze the time course (as a whole, over the entire time-span, not time point by time point). With only 7 differenttime points this may not be really feasable with your data. But you can still look for patterns of "common time courses" for subsets of your metabolites, and that's just what you will see in a heatmap when you cluster by row (metabolite) and not by column (time, what is given from 1 through 7). You may choose a correlation coefficient as distance measure instead of the commonly used Euclidean distance to better group metabolites that show the same changes even if these happen at different scales.
You may then (hopefully) find some metabolites showing a common time course pattern, you this may (hopefully) help you to generate hypotheses about metabolism and/or its kinetic that are testable in future planned experiments. As far as I understoodyour design now, think this is a hypothesis-generating (explorative) design, I don't think that any formal hypothesis tests make sense here.
Diego Salgueiro OK, now your analysis became clearer. So there is no group but only a time variable. Therefore the interaction is out of consideration.
You can check validity of your models by analysing residuals. You can try different variance-covariance matrice types like AR1, Toeplitz etc. A LMM model would be always superior to a RANOVA or Friedman model if it's done correctly.
Jochen Wilhelm
Ok, you just measured 82 different metabolites over time in 15 subjects, and there are no "groups" to compare concentrations... (Note: comparing concentrations of the same metabolite between the 7 time-points is not a really sensible thing to do; and the values are not independent between time-points).
I see. Why that would not be a sensible thing to do? LMM with the subjects as a random effect doesn't account for the dependency in the data? Or actually the 7 time-points is too little to fit a good model?
What you may want is to analyze the time course (as a whole, over the entire time-span, not time point by time point). ...
Thanks! I will certainly look into that. If I understood you correctly, you are suggesting something like this: https://www.datanovia.com/en/blog/clustering-using-correlation-as-distance-measures-in-r/
... cluster by row (metabolite) and not by column (time, what is given from 1 through 7).
Can you please explain what you mean here? Should I reshape my data somehow? Or am I missing some concept related to cluster analysis?
Mehmet Sinan Iyisoy, thanks for the tip! If I recall correctly, I have tried the AR(1) as pointed by [1] in Chapter 19. I will certainly pay more attention to this now.
[1] Field, Andy P., Jeremy Miles, and Zoë Field. "Discovering statistics using R/Andy Field, Jeremy Miles, Zoë Field." (2012).
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