Multivariate analysis for a data with different metric units

Question

I have some weird data that I don’t know how to treat them!

I have a data of metabolite measurements in different groups of samples with 5 replicate in each group:

Groups      treatment   diet
Group1:     yes         A
Group2:     NO          A
Group3:     yes         B
Group4:     No          B

Each sample has been measured for 500 different metabolites. but the measurement values are so weird since:

1. The measured values are the signals and not the concentration, which means the metric units are different (i.e. value 2 means totally different in metabolite 1 comparing to metabolite 2).

2. There are some missing values, which means that it wasn’t possible to detect those metabolites in that specific sample but it doesn’t mean it is zero! E.x. as below.

   samples         metabolite1
   Group1          12374
   Group1          NA
   Group1          NA
   Group1          NA
   Group1          46091
   Group2          128025
   Group2          90689
   Group2          129950
   Group2          76813
   Group2          66439
   

What I want to do:

1. First, I would like to do a principle component analysis to see if there is any clear separation between the groups.
2. And then I would like to study if any of the factors: treatment or diet or the interaction has any effect on each metabolite.

What do you suggest me to do with this data?

P.S. I analyze my data in R!

Answer 1

Missing values

As @gung says, a first step would be to go and find out why there are NAs:

• concentrations are below LOD/LOQ/signal below critical value: ask for the uncensored values. At the very least make sure that in future data is not censored and instead you are provided with the critical values/LOD/LOQ in addition to the data.
  Btw: known LOD and LOQ implies that a calibration is available.

• Obviously, if NAs are not due to censoring but mean that for some reason measurement was not possible, you'll have to go on with missing values.

• Whether the NAs come from (left) censoring or other reasons is important for dealing with them.

• Ivana Stanimirova from Katowice has done a lot of work about data analysis with missing values both completely at random (CAR) and/or due to censoring.
  I. Stanimirova: Practical approaches to principal component analysis for simultaneously dealing with missing and censored elements in chemical data, Analytica Chimica Acta, 796 (2013) 27–37.
  DOI: 10.1016/j.aca.2013.08.026
  may be a good starting point.

Signals instead of concentrations and scaling

• are not very problematic:
  different metabolites come at vastly varying concentrations as well, so you'd anyways need to think about scaling
• if all signals are physically the same unit and don't vary in their order of magnitude, you may keep them as they are
• see also: Variables are often adjusted (e.g. standardised) before making a model - when is this a good idea, and when is it a bad one?
• Sometimes it is possible to set up scaling according to some control group.

Study factors

ASCA (ANOVA Simultaneous Component Analysis), PCA-ANOVA and rMANOVA (regularized MANOVA) could be starting points.