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I begin exposing the context of my work, and the main doubt or approach about. My project is based in a clinical trial in which I have 3 groups of intervention (OO, NTS, LFD). The individuals (n = 151) are almost equally distributed in the 3 groups, and teh variables to measure are genes: these genes are measured at baseline and 12 months after the intervention (a combination of diet, physical activity, therapy...).

The idea of using PCA is to observe clusters according to the upregulation or downregulation of these genes. Until now I have done PCA in just the genes, expressed in a numeric and continuous variable, and normalized/standardized (not in statistical sense, but I will standardize/scale the data before running PCA) relative to control genes. However I came across the FAMD modality (Factomine package), and theoretically combines categorical variables with continuous quantitative variables. The most intuitive and coherent idea would be the observation of clusters according to the groups (if there are in whichever way)

My database would be made up by 151 individuals (as rownames) and 51 variables ( 1 categorical and 50 continuous). I have missing values across my database (NOT in the categorical variable) which I intend to impute. Would be FAMD the optimal approach? Is there any modification in PCA that let include a categorical variable? About the imputation process, would you recommend me to impute with missMDA::imputePCA or missMDA::imputeFAMD?

Thank you so much!

head(PCA)
          grup_int ppara ppard pparg nr1h3 nr1h2  rxra  rxrb cyp27a1
50109018      LFD 3.761 1.575 2.201 1.550 0.861 1.402 0.987   1.058
50109019      LFD 1.276 1.096 1.171 1.451 1.744 1.280 0.938   1.079
50109025      LFD 0.918 1.278 1.330 1.046 0.824 1.076 1.882   1.152
50109026     NTS    NA 1.303 1.303 1.294 0.665 1.105 1.506   0.743
50109027      LFD    NA 1.282 0.991 0.797 0.913 1.400 2.067   1.803
50118001       OO    NA 1.954 1.471 1.602 1.355 1.327 1.526   1.157

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  • $\begingroup$ There is a wiki page about MCA. But probably you don't need this. You might be more interested in applying the PCA to your continuous data only. (It is actually not clear to me how gene expression can be a continuous variable; Isn't this a dichotomous case like expressed or not expressed?). $\endgroup$ Dec 21, 2022 at 18:01
  • $\begingroup$ @SextusEmpiricus gene expression is quantified by the cycle in which fluorescence reach a certain threshold. After, several mathematical operation (to normalize) you get an scalar called fold-change (meaning the expression relative to the baseline). MCA as far as I know is for categorical variable, my doubt lies between PCA without the group categorical variable (or embedded somehow in the data base) or using FAMD (Factor Analysis for Mixed Data). $\endgroup$ Dec 21, 2022 at 18:47
  • $\begingroup$ MCA is what I remember from the FactoMineR package, but I never used it (Is this package still active anyway?). Anyway, the point is that your case with only a single categorical variable might be treated without the categorical variable. You can apply the PCA on only the continuous variables and continue analysis with the clusters formed based on the analysis without the categorical variables. $\endgroup$ Dec 21, 2022 at 19:07

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