Technical Note: An Eubiosis Index for the Microbiome

This note in a continuation of an earlier note:

I am a statistician and operations research person by training and experience. I tend to take novel approaches to many issues based on mathematics. These are recorded in this series of notes

I have some 4,600 different unique microbiome samples uploaded to my citizen science site. Most of these are from people with gut issues. Some are from health hackers (i.e. no issues).

A simple Chi2 experiment using percentages of percentiles is done. I bucketized the genus data into 10% percentile ranges resulting in 10 buckets, compute the chi2 and thus we have 9 degree of freedom.

Genus has adequate counts per sample. Species reporting is often very sparse for some tests (depending on the number of reads that the lab set as a threshold, etc.). Genus gives the highest count for a specific taxonomy rank in this dataset.

I then proceeded to plot the values to see what the data looks like. Note the significance levels for 9 degree of freedom below

  • 14.7 is 0.1
  • 16.9 is 0.05
  • 19.02 is 0.025
  • 21.7 is 0.01
  • 27.9 is 0.001

Over all of the values, we do see some extreme values

But let us look a less extreme values

We now need to do a little math assuming there was no significance, i.e. the numbers were happening random.

  • 0.1 (aka 10%) means that 90% of the samples would be expected to have a chi2 value of 14.7 or less. We have 1130/4600 or 24% of the samples

We could start working to lower values, but using 14.7 means that 1/4 of the samples at this value may not have dysbiosis. Taking 0.1 and this ratio, we can estimate that we have around a 97% chance of correctly identifying dysbiosis

General conclusion is that a gut without dysbiosis would have a chi2 value of 15 or below for genus.

The Challenge of Getting a “Health Index” for the Microbiome

Looking at a variety of microbiome testing sites I see a lot of “flying by the seats of their pants” being tossed out. IMHO, these sites are soiling their pants — somewhat appropriate for this business :-).

I believe we can create a statistically valid index that works solely off the numbers and not some idealized concept of what a healthy gut should be. We use the above analysis to create this index.

People like have a percentage number for a healthy gut, then the following is suggested (which is actually a percentile ranking):

  • Under 15: 100% good
  • Over 15: 100 – (Percentile over those over 15)

For lack of a better name (and keeping with naming practices for indices), I will call this the Lassesen Eubiosis Index with 100% being no apparent sign of dysbiosis and good eubiosis.

From the set of samples used above, I extracted a reference table (which may vary according to the test used and the population used). Since I know that the majority of samples have dysbiosis issues, this is likely a reasonable guideline.

Eubiosis IndexChi2
9018
8021.3
7024.5
6029.1
5035.6
4045.2
3065.3
20106
10168
5248

The joy of this approach is that it simple, statistically valid and is taxonomy agnostic. No judgement calls are being made on good or bad bacteria.

Example of 100% Eubiosis

We see a dip at the 50-59%ile range but this minor disturbance does not register as a likely dysbiosis.

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