Statistics is fun because there many paths. Most studies using the microbiome uses the easy, but naïve, path of computing averages and standard deviation. As my dataset has grown, I have been travelling some less traveled path, for example: Visual Exploration of Odds Ratios, and a patent pending method termed “Kaltoft-Moltrup”.

One of the frequent decisions that I see in studies is to limit examination of bacteria that have a high frequency in the samples. This allows the researchers to keep to familiar and classic statistics. Using frequency of observation in the control group and the condition group is one of these much less travelled paths. It usually require big sample sizes and many studies have a sample size of 30 (sufficient for the mean and standard deviation approach).

I just completed code to compute Chi2 using Biomesight data for users reporting Autism.

• Control Population: 3525
• Autism: 88

Chi2 can be converted to probability (p) of happening at random with the following table

Seen too Rarely(Want to increase)

We see one bacteria available as a probiotic Bifidobacterium adolescentis. The rest would need to be altered by diet.

tax_name	TAX_RANK	Chi2	Observed	Expected	Shift
Butyricimonas synergistica	species	10	17	36	Under-Represented
Bifidobacterium adolescentis JCM 15918	strain	9.8	9	24	Under-Represented
Dehalobacterium	genus	9.7	18	37	Under-Represented
Pelotomaculum isophthalicicum	species	8	17	33	Under-Represented
Ammonifex thiophilus	species	7.3	17	32	Under-Represented

Seen too Often (Want to decrease)

We see 32 bacteria over a Chi2 of 6.635 ( P < 0.01 or 1 change in 100 of being a false detection). One very striking feature is that there are many, many different species of Bifidobacterium that are over represented while one species is under represented. This is not a simple situation to address.

tax_name	TAX_RANK	Chi2	Observed	Expected	Shift
Bifidobacterium catenulatum subsp. kashiwanohense	subspecies	43.5	54	23	Over-Represented
Bifidobacterium angulatum	species	33	39	16	Over-Represented
Staphylococcus pseudolugdunensis	species	23.6	20	7	Over-Represented
Clostridium cellulovorans	species	22.9	20	7	Over-Represented
Bifidobacterium catenulatum PV20-2	strain	19.5	58	33	Over-Represented
Streptococcus mutans	species	19	23	10	Over-Represented
Hungateiclostridium	genus	18.3	30	14	Over-Represented
Hungateiclostridiaceae	family	18.1	30	14	Over-Represented
Streptococcus intermedius	species	17.5	23	10	Over-Represented
Bifidobacterium catenulatum	species	16.9	58	34	Over-Represented
Absiella	genus	16.7	22	10	Over-Represented
Clostridium chartatabidum	species	16.7	43	23	Over-Represented
Bifidobacterium gallicum	species	15.4	73	47	Over-Represented
Prevotella veroralis	species	13	15	6	Over-Represented
Corynebacterium durum	species	12.6	14	6	Over-Represented
Bifidobacterium thermacidophilum	species	11.3	18	8	Over-Represented
Parascardovia	genus	10.5	32	18	Over-Represented
Klebsiella oxytoca	species	10.5	27	15	Over-Represented
Bifidobacterium scardovii	species	10	30	17	Over-Represented
Bifidobacterium cuniculi	species	9.9	31	18	Over-Represented
Candidatus Blochmanniella camponoti	species	9.8	21	11	Over-Represented
Abiotrophia	genus	9.2	12	5	Over-Represented
Enterococcus gilvus	species	9.1	14	6	Over-Represented
Megamonas funiformis	species	8.8	21	11	Over-Represented
Segatella oulorum	species	8.6	22	12	Over-Represented
Ralstonia	genus	7.9	14	7	Over-Represented
Bifidobacterium indicum	species	7.7	67	48	Over-Represented
Candidatus Blochmanniella	genus	7.2	35	22	Over-Represented
ant endosymbionts	clade	7.2	35	22	Over-Represented
unclassified Bacteroidetes Order II.	order	7.2	75	55	Over-Represented
Enterobacter hormaechei	species	6.9	36	23	Over-Represented
Moorella group	norank	6.7	66	48	Over-Represented

Bottom Line

The next step is to compute similar tables for all symptoms and incorporate these findings into a new algorithm. I say new, because I do not know if it is better than the existing ones. Conceptually, it would be added as a 5th set of suggestions to the existing consensus view on Microbiome Prescription.