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 ME/CFS.

• Total Population: 3525
• ME/CFS: 280

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
Segatella oulorum	species	13.9	16	38	Under-Represented
Bifidobacterium cuniculi	species	10.8	33	57	Under-Represented
Brenneria	genus	10.5	1	12	Under-Represented
Bifidobacterium adolescentis	strain	10.3	50	77	Under-Represented
Prevotella veroralis	species	10.3	6	20	Under-Represented
Aggregatibacter	genus	10.1	46	72	Under-Represented
Hoylesella shahii	species	10.1	12	28	Under-Represented
Segatella paludivivens	species	9.6	40	64	Under-Represented
Actinobacillus pleuropneumoniae	species	8.6	33	54	Under-Represented
Slackia heliotrinireducens	species	8.2	8	20	Under-Represented
Prevotella micans	species	8.1	3	13	Under-Represented
Actinobacillus	genus	8	123	157	Under-Represented
[Actinobacillus] rossii	species	7.1	79	105	Under-Represented
Pasteurellaceae incertae sedis	no rank	7.1	79	105	Under-Represented
[Pasteurella] aerogenes-[Pasteurella] mairii-[Actinobacillus] rossii complex	species group	7.1	79	105	Under-Represented
Aggregatibacter aphrophilus	species	7	4	13	Under-Represented
Mitsuokella multacida	species	6.8	3	12	Under-Represented

Seen too Often (Want to decrease)

We see 118 bacteria over a Chi2 of 6.635 ( P < 0.01 or 1 change in 100 of being a false detection). The list below are for genus and higher taxonomy orders.

Tax Name	Rank	Chi2	Observed	Expected	Shift
Dethiobacteraceae	family	20.9	75	45	Over-Represented
Hungateiclostridiaceae	family	16.1	71	45	Over-Represented
Tepidimicrobiaceae	family	14.6	16	7	Over-Represented
unclassified Burkholderiales	family	12.6	29	16	Over-Represented
Corynebacteriaceae	family	11.2	159	123	Over-Represented
Halanaerobiaceae	family	10.1	76	54	Over-Represented
Alcanivoracaceae	family	9.6	53	35	Over-Represented
Halanaerobiales	order	9.6	81	58	Over-Represented
Desulfonatronovibrionaceae	family	9.1	58	40	Over-Represented
Acetobacteraceae	family	8.7	124	96	Over-Represented
Hyphomonadaceae	family	8	29	18	Over-Represented
Tissierellaceae	family	7.5	20	11	Over-Represented
Rhizobiaceae	family	7.1	98	76	Over-Represented
Nannocystineae	suborder	6.9	36	24	Over-Represented
Rubritaleaceae	family	6.9	124	99	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.