Source: https://guthlabs.ai/docs/instruments/relative-risk-odds-ratio-calculator/
instrument / verified-with-binding-errata
# Relative Risk / Odds Ratio Calculator
The current ledger marks this instrument verified with errata that must be applied at binding time.
Status: **VERIFIED_WITH_ERRATA**Lifecycle: **verified-with-binding-errata**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified with errata that must be applied at binding time.
**Area**: Biology, Medicine & Pharmacology (educational estimates only — every panel labeled not-medical-advice)
**Tranche**: tranche-6
**Evidence ID**: t6-103
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The core RR and OR point-estimate formulas are standard, but the instrument is not implementation-complete because the CI and p-value algorithms are underspecified and zero-cell behavior is absent. Keep the educational/not-medical-advice label, and explicitly state the cell orientation, count-only input requirement, CI formulas, z critical value, chi-square variant, and zero-cell policy before release.
### Formula and scope findings
- The RR formula is standard for a=exposed outcome, b=exposed no outcome, c=unexposed outcome, and d=unexposed no outcome, but the table orientation must be explicitly enforced.
- The OR formula is standard under the same cell definitions.
- The log-SE confidence-interval method is underspecified: it must state whether the interval is the Wald interval, the z critical value (normally 1.96 for 95%), and the exact SE formulas. Standard choices are SE(log RR)=sqrt(1/a-1/(a+b)+1/c-1/(c+d)) and SE(log OR)=sqrt(1/a+1/b+1/c+1/d), followed by exponentiation of the log-scale limits.
- The p-value method is underspecified. Chi-square must specify Pearson versus likelihood-ratio chi-square, continuity correction, degrees of freedom, and one-sided versus two-sided reporting. The vectors below use uncorrected two-sided Pearson chi-square with df=1.
- No zero-cell policy is specified. Without a continuity correction or exact method, log-SE confidence intervals are undefined when any required cell is zero.
- A normal-distribution z-table alone is insufficient to calculate a chi-square p-value unless the implementation explicitly uses the df=1 identity p=2(1-Phi(sqrt(chi-square)).
### Unit assumptions
- a, b, c, and d are nonnegative integer counts, not percentages, proportions, rates, or person-time measurements.
- The table is a mutually exclusive 2x2 table: a=exposed with outcome, b=exposed without outcome, c=unexposed with outcome, d=unexposed without outcome.
- RR and OR are dimensionless. Counts must refer to the same observation unit and time/risk period.
- For the nonzero-cell vectors, 95% CIs use natural logarithms, z=1.96, the standard Wald log-SE formulas, and exponentiation back to the original scale.
- The chi-square p-values use the uncorrected Pearson statistic with df=1 and a two-sided upper-tail probability.
## Boundary hardening
**BREAK_CLAIMED** · SELF_FLAGGED
Zero cells expose undefined or infinite odds ratios and log-based confidence intervals. The specification does not state zero-cell handling, continuity corrections, table-orientation validation, or a literal formula branch. Several intermediate chi-square arithmetic checks also require careful denominator handling; an implementation should validate the Pearson formula and reject or explicitly label undefined results.
## Errata and corrections
### Tranche errata
**RR_95_CI** · vector 2
[0.1774, 1.4091]
[0.1772, 1.4106]
micro: 1.96*0.529150=1.037134, she wrote 1.036135
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"inputs": {
"a": 30,
"b": 70,
"c": 10,
"d": 90,
"ci_method": "Wald log scale, 95%, z=1.96",
"p_method": "uncorrected two-sided Pearson chi-square, df=1"
},
"expected_outputs": {
"RR": 3,
"RR_95_CI": [
1.5508,
5.8034
],
"OR": 3.8571428571,
"OR_95_CI": [
1.7666,
8.4216
],
"pearson_chi_square": 12.5,
"p_value_approximately": 0.000407
},
"working": "Risk exposed = a/(a+b)=30/(30+70)=30/100=0.30. Risk unexposed = c/(c+d)=10/(10+90)=10/100=0.10. RR=0.30/0.10=3.00. SE(log RR)=sqrt(1/30-1/100+1/10-1/100)=sqrt(0.0333333-0.0100000+0.1000000-0.0100000)=sqrt(0.1133333)=0.336650. log(RR)=log(3)=1.098612. Limits on log scale=1.098612 +/- 1.96(0.336650)=1.098612 +/- 0.659834, giving [0.438778,1.758447]. Exponentiating gives RR CI [exp(0.438778),exp(1.758447)]=[1.5508,5.8034]. OR=(a*d)/(b*c)=(30x90)/(70x10)=2700/700=27/7=3.8571428571. SE(log OR)=sqrt(1/30+1/70+1/10+1/90)=sqrt(0.1587302)=0.398410. log(OR)=log(27/7)=1.349927. Limits=1.349927 +/- 1.96(0.398410)=1.349927 +/- 0.780883, so [0.569044,2.130810]. Exponentiating gives [1.7666,8.4216]. Pearson chi-square=n(ad-bc)^2/[(a+b)(c+d)(a+c)(b+d)]=200(30x90-70x10)^2/(100x100x40x160)=200(2000)^2/64000000=12.5. With df=1, p=2[1-Phi(sqrt(12.5))]=2[1-Phi(3.53553)] approximately 0.000407."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_WITH_ERRATA`
- `evidence-tranche6/tranche6-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`