ExactCIs

ExactCIs provides design-aware inference for sparse 2 × 2 tables in Python, with explicit sampling assumptions, documented interval constructions, and fail-closed numerical behaviour.

Version 1.0.0 does not claim universal exactness, unconditional coverage for conditional procedures, clinical validation, or formal verification.

Installation

ExactCIs supports Python 3.11 through 3.13 and has zero runtime dependencies. (The lower bound is intentional: the public API and typing assume 3.11+.)

python -m pip install exactcis

For a specific version:

python -m pip install exactcis==1.0.0

For development and documentation checks (from a source checkout):

uv sync --frozen --extra dev --extra docs

Quick start

The package-wide table orientation is defined before this first calculation:

             outcome +   outcome -
exposed +        a           b
exposed -        c           d

Declare the sampling design explicitly. A fixed-margin case-control table uses the conditional odds-ratio lane:

from exactcis import Design, compute_or_with_policy

result = compute_or_with_policy(
    10,
    2,
    5,
    20,
    design=Design.CASE_CONTROL_FIXED_MARGIN,
)

assert result.lower <= result.point <= result.upper
print(
    f"{result.method} ({result.construction}): "
    f"point={result.point:.6g}  ({result.lower:.6g}, {result.upper:.6g})"
)

The same four numbers must not be relabelled as a risk ratio under a fixed-margin case-control design. For two independent cohort groups, declare Design.COHORT_BINOMIAL and call compute_rr_with_policy.

Table orientation

Throughout the package:

             outcome +   outcome -
exposed +        a           b
exposed -        c           d

• The odds ratio is a d / (b c), where defined.
• The cohort risk ratio is [a / (a + b)] / [c / (c + d)], where identified.
• Cross-sectional use of the same row-proportion ratio is a prevalence ratio.

Counts must be finite, non-negative integers no larger than 10**12 per cell. Rows identify the two comparison groups; columns identify outcome status. Swapping either pair reciprocates the corresponding ratio and transforms finite interval endpoints accordingly.

Supported designs, estimands, and methods

The machine-readable source of truth is exactcis.estimands.method_registry(). The complete generated table, including construction, calibration statement, and limitations, is in Supported methods.

Design	Effect measure	Stable method keys	Default policy method
Fixed-margin case-control	odds ratio	conditional, midp, minlike, blaker	conditional
Cohort, two independent binomials	odds ratio	wald, wald_haldane	wald
Cohort, two independent binomials	risk ratio	score_rr, wald_rr	score_rr
Cross-sectional groups	prevalence odds ratio	wald, wald_haldane	wald
Cross-sectional groups	prevalence ratio	score_rr, wald_rr	score_rr
Prespecified independent strata	common odds ratio	mantel_haenszel	explicit compute_pooled_or call

Risk or prevalence ratios are not identified from fixed-margin retrospective case-control sampling. Same-study marginal pooling without participant-level union or dependence information is outside this release. compute_pooled_or accepts one or more strata; a single stratum is valid mathematically but is usually a modelling mistake when “pooled” was intended.

Statistical conventions and assumptions

alpha is the two-sided significance level, so alpha=0.05 requests a 95% confidence set. The numerically certified domain is the open interval 1e-12 < alpha < 1 - 1e-12; unsupported extremes raise ValidationError before quantile evaluation or inversion. Conditional methods use Fisher's noncentral-hypergeometric law and condition on both margins. conditional inverts inclusive equal tails; midp uses half the observed mass in each tail; minlike uses inclusive probability-mass ordering; and blaker uses the smaller inclusive tail as its acceptability ordering.

The Wald methods and the Mantel-Haenszel/Robins-Breslow-Greenland construction are asymptotic. score_rr inverts the Koopman-Nam score statistic for two independent binomial groups. Conditional and unconditional/asymptotic methods are not expected to agree by construction.

Edge cases and numerical behaviour

• Conditional support endpoints map to odds-ratio endpoints 0 and +∞.
• Singleton conditional support yields the full confidence set (0, +∞); the high-level policy refuses to invent a unique point estimate.
• Empty independent-binomial groups are invalid.
• A risk/prevalence ratio with zero events in both groups has confidence set (0, +∞) but no policy-level point estimate.
• ci_wald adds 0.5 to every cell only when a zero cell is present; ci_wald_haldane always applies that correction.
• Numerical inversion is bracketed and checked. Failure raises NumericalError; ExactCIs never returns another method as a fallback.
• A finite configured search-domain limit is never reported as an inferential endpoint. Unsupported significance levels fail validation instead.
• Algorithms sum the complete conditional support. Runtime grows with support width: tables with margins around 1e5–1e6 can take tens of seconds to minutes on a single core; above roughly 1e7 the solvers typically fail closed with NumericalError rather than hang forever. Prefer asymptotic methods when such scales are expected and exact conditioning is not required.

See API contract for return types, exceptions, and individual method examples.

Experimental and compatibility methods

This release has no retained experimental or compatibility-only method. Historical evidence-policy, unconditional, Bayesian-evidence, plotting, reporting, batch, accelerator, and clinical-adjudication routes are not imported or shipped. Unknown method keys fail explicitly and do not participate in automatic selection.

API documentation

The stable root API is listed in API contract. Only the package root exports (see exactcis.__all__) and exactcis.estimands are stable public surfaces. Other non-underscore implementation packages under exactcis.* have no compatibility promise. Lower-level registry inspection is available from exactcis.estimands; helpers beginning with an underscore are internal.

Validation and reproducibility

The release tests cover canonical interior and boundary tables, reciprocal transformations, confidence-level nesting, endpoint domains, explicit solver failure, and direct calls to every stable method. Independent fixtures record:

• 80-decimal mpmath finite-support calculations for central and Mid-P limits;
• R exact2x2 1.6.8 minimum-likelihood and Blaker results;
• R PropCIs 0.3-0 Koopman-Nam score limits; and
• statsmodels 0.14.5 Mantel-Haenszel/RBG results.

Every fixture records its function, options, orientation, definition, tolerance, generator or derivation, version, and source revision. The release workflow also executes this README example against source, wheel, and sdist.

Contributing

See CONTRIBUTING.md. Statistical changes require a stated mathematical definition, an independent oracle, focused boundary tests, and a separate explanation of any changed outputs.

Citation

See CITATION.cff and CITATION.txt. Cite the exact version and Git revision analysed. No DOI is assigned yet.

Licence

ExactCIs is distributed under the MIT License.