By Kenneth Lassesen, B.Sc.(Statistics), M.Sc.(Operations Research)

Odds Ratio and Chi2 are two sides of the same coin. The worth of this coin is far more than the fourrées seen with studies using averages.

The simplest case is how often is a specific bacteria reported with the control versus study groups. This is easy computed and can be placed in a table such as the one below

	Control (without Symptom)	Study (or with Symptom)
Bacteria Seen	300	90
Bacteria Not Seen	600	700

Just looking at the table, it is obvious that this bacteria is less likely to be seen in a study group. We can just drop these numbers in a page like this one, and get the results.

Converting to odds ratio is simple:

• Compute odds for study group: $\frac{300}{90}=3.333$90300=3.333.
• Compute odds for control group: $\frac{600}{700}\approx 0.857$700600≈0.857.
• Odds ratio: $OR=\frac{3.333}{0.857}\approx 3.89$ that seeing this bacteria put you likely not in the study group
  • Or 1/3.89 = 0.257 if seeing this bacteria, places you in the study group

Second Tier: The amount

This is identical to the above, except there is a little mathematics needed to compute the best range of bacteria for odds ratio.

At 0.04%	Control (without Symptom)	Study (or with Symptom)
Above or Equal	100	60
Below	200	30

Again a simple computation with great statistical significant.

And again the Odds Ratio is calculated the same as above.

• 100/60 = 1.66
• 200/30 = 6.66
• OR = 1.66 / 6.66 = 0.25 (or 4.00 for the reverse.

We have a tri-state odds ratio

• Bacteria not seen: 0.257 of having symptom (i.e. bacteria is rarely seen with symptom)
• Bacteria see but above or equals to 0.04%: 3.89 * 4 =15.56
• Bacteria see but below 0.04%: 3.89 * .25 = 0.9725, almost no effect.

In this example, we used above or below 0.04%; we could have also used in the range (0.03 to 0.07) or not in the range.

Key points

• Use only bacteria with P < 0.001 or better
  • Check Present or not Present
  • There is a finite enumeration of possible ranges when a bacteria present.
    • With today’s powerful computers, this is not a challenge
• Check all bacteria that satisfies the minimum size constraint for the function used for the 2×2 table

For some symptoms we have:

• over 450 bacteria with significant odds ratios for some conditions.
• Highest Odds ratio over 92 for some bacteria

Performance

This data is based on self-declared symptoms from users. Often the symptoms entered are incomplete (some users had over 100 symptoms entered). While not rigorous, this appears to work for getting sample annotations entered in a citizen science context and for demonstration of the concept. There was enough consistency of data to get results.

The best news: The following had the Odds Ratio > 1.0, over a dozen in the sampling and agreement with entered symptoms.

Source	SymptomName	Ratio
BiomeSight	Official Diagnosis: Mood Disorders	100
Thryve	DePaul University Fatigue Questionnaire : Frequently get words or numbers in the wrong order	100
Thryve	Autism: More Repetitive Movements	100
Thryve	Autonomic Manifestations: cardiac arrhythmias	100
Thryve	Condition: Acne	100
Thryve	DePaul University Fatigue Questionnaire : Pain in Multiple Joints without Swelling or Redness	100
Thryve	DePaul University Fatigue Questionnaire : Feeling like you have a temperature	100
Thryve	Official Diagnosis: Diabetes Type 1	100
Thryve	Neurological: Spatial instability and disorientation	100
Thryve	Condition: Type 1 Diabetes	100
Thryve	Neuroendocrine Manifestations: abnormal appetite	100
BiomeSight	Autonomic Manifestations: delayed postural hypotension	100
Thryve	Physical: Long term antibiotics(over 6 months)	100
Thryve	Comorbid: Electromagnetic Sensitivity (EMF)	100
BiomeSight	Physical: Bad Air Quality	100
BiomeSight	Neuroendocrine Manifestations: marked diurnal fluctuation	100
Thryve	Physical: Amalgam fillings	100
BiomeSight	Comorbid: Reactive Hypoglicemia	100
Thryve	Comorbid: Sugars cause sleep or cognitive issues	100
BiomeSight	Official Diagnosis: Dermatitis (all types)	100
Thryve	Physical: Steps Per Day 2000-4000	100
Thryve	Neuroendocrine Manifestations: Painful menstrual periods	100
Thryve	General: Anhedonia (inability to feel pleasure)	100
BiomeSight	Virus: Parvovirus positive (B19)	100
BiomeSight	Blood Type: FUT2 secretor	100
Thryve	Official Diagnosis: High Blood Pressure (Hypertension)	100
Thryve	DePaul University Fatigue Questionnaire : Poor hand to eye coodination	100
Thryve	Infection: Coxsackie	100
Thryve	Neuroendocrine Manifestations: marked diurnal fluctuation	100

Looking at the biggest sets. we see very good performance for some symptoms and poor performance for items like gender. Unrefreshing Sleep is interesting:

• Unrefreshed sleep: 88.6% accurate
• Unrefreshing Sleep, that is waking up feeling tired: 36.7% accurate

Is the cause, the fineness of definition (and lack of clarity by users entering) or some other issues?

Source	Symptom	% Correct	Size
BiomeSight	General: Fatigue	98.70317	694
BiomeSight	Neurocognitive: Brain Fog	98.18182	660
BiomeSight	Sleep: Unrefreshed sleep	88.57616	604
BiomeSight	Neurocognitive: Difficulty paying attention for a long period of time	75.54113	462
BiomeSight	Immune Manifestations: Bloating	90.13761	436
BiomeSight	DePaul University Fatigue Questionnaire : Fatigue	85.96491	399
BiomeSight	Gender: Male	59.79644	393
BiomeSight	Comorbid: Histamine or Mast Cell issues	88.0102	392
BiomeSight	Official Diagnosis: COVID19 (Long Hauler)	97.87798	377
BiomeSight	DePaul University Fatigue Questionnaire : Unrefreshing Sleep, that is waking up feeling tired	36.66667	360
BiomeSight	Neurocognitive: Can only focus on one thing at a time	63.76404	356
BiomeSight	Neuroendocrine Manifestations: worsening of symptoms with stress.	70.26239	343
BiomeSight	Neurological-Audio: Tinnitus (ringing in ear)	60.71429	336
BiomeSight	Neurocognitive: Problems remembering things	47.00599	334
BiomeSight	Age: 30-40	97.14286	315
BiomeSight	DePaul University Fatigue Questionnaire : Post-exertional malaise, feeling worse after doing activities that require either physical or mental exertion	92.33227	313
BiomeSight	Neurocognitive: Absent-mindedness or forgetfulness	62.7907	301
BiomeSight	Sleep: Daytime drowsiness	69.33333	300
BiomeSight	Post-exertional malaise: General	85.95318	299
BiomeSight	Immune Manifestations: Constipation	83.22148	298

Lab Performance

Identification by Age exhibits the reality of all labs are not equal. If Odds Ratios from the microbiome was not statistically significant for estimating age, we would see 14% for accuracy. We far exceed that.

Lab	Symptom	Accuracy	Size
BiomeSight	Age: 0-10	86.2	29
Ombre	Age: 0-10	76.3	59
BiomeSight	Age: 10-20	80	25
Ombre	Age: 10-20	94.7	19
BiomeSight	Age: 20-30	58.5	135
Ombre	Age: 20-30	64.7	34
BiomeSight	Age: 30-40	97.1	315
Ombre	Age: 30-40	66.3	104
BiomeSight	Age: 40-50	22.2	203
Ombre	Age: 40-50	71.4	63
BiomeSight	Age: 50-60	29.7	111
Ombre	Age: 50-60	61.7	47
BiomeSight	Age: 60-70	52.5	59
Ombre	Age: 60-70	18.1	83
BiomeSight	Age: 70-80	90	20

This difference of labs is seen with other symptoms — some of which has associations reported in the literature.

Source	SymptomName	Ratio	Size
BiomeSight	General: Depression	67.7	195
Ombre	General: Depression	13.9	108
BiomeSight	General: Fatigue	98.7	694
Ombre	General: Fatigue	20.8	149
BiomeSight	General: Headaches	71.6	197
Ombre	General: Headaches	15.5	103

Summary

The use of odds ratios provides statistically significant evidence for identifying probable symptoms. While not definitive—acknowledging that few diagnostic tests achieve complete certainty—the results demonstrate that both the selected testing method and its interpretation (for example, in relation to bacterial associations) materially influence diagnostic accuracy.

In clinical contexts, reliance on odds ratios offers greater methodological rigor than studies reporting merely “higher or lower levels of certain bacteria with $P<0.05$.” A notable clinical strength of this approach lies in its capacity to generate a structured list of potential symptoms for further inquiry, including those that patients may not have initially disclosed.

Nota Bene: It should be noted that the observed error rate is likely attributable, at least in part, to underreporting of symptoms. Patients often disclose only the symptoms they perceive as most severe, thereby introducing reporting bias into the dataset.

The table below shows the accuracy from 4 different labs. It is not a surprise that Shotgun data is more accurate than 16s tests.

Source	Ratio	Size
BiomeSight – 16s	60.8	45069
Thorne – Shotgun	80.7	491
Ombre/Thryve – 16s	40.8	17123
uBiome – 162	47.6	13071