Zero-event studies¶

Zero cells in 2-by-2 tables affect OR, RR, RD, and Mantel-Haenszel estimators in different ways. PyMetaAnalysis therefore separates study-level effect corrections from the pooled Mantel-Haenszel correction.

Default study-level correction¶

For study-level OR/RR effects, the default settings are:

continuity_correction=0.5
correction_scope="only_zero_studies"

The correction is added to every cell of an included study containing at least one zero cell. Non-zero studies are not changed.

Available scopes are:

Scope	Behavior
only_zero_studies	Correct each included study that contains a zero cell
if_any_zero	Correct every included study if any included study has a zero
all_studies	Correct every included study
none	Do not correct study-level tables

Setting the correction to zero or the scope to none is rejected when it leaves an OR/RR undefined or an effect variance non-positive.

Double-zero and double-all studies¶

A study with no events in either group, or events in every participant in both groups, contains no relative-effect information for OR or RR. Such studies are excluded before effect pooling, heterogeneity statistics, and weights are calculated. They remain visible in result.study_results with included=False and a structured exclusion_reason.

RD has a different estimand. Any study in which both arms are at a boundary (zero events or events in every participant) has zero uncorrected RD sampling variance. This includes double-zero, double-all, and opposite-boundary tables.

The default policy retains these studies:

rd_zero_variance="correct"

The RD itself remains the raw treatment risk minus control risk. Corrected counts are used only to form a positive sampling variance. To exclude all such studies before pooling, Q, tau-squared, and weight calculations, use:

rd_zero_variance="exclude"

Excluded rows remain in result.study_results with exclusion_reason="zero uncorrected risk-difference variance". The policy is RD-specific; setting exclude for OR or RR is rejected.

Mantel-Haenszel correction is separate¶

Exact common-effect Mantel-Haenszel OR/RR pooling uses raw tables by default:

mh_continuity_correction=None
mh_correction_scope="only_zero_studies"

continuity_correction still controls the study-level effects used for display and heterogeneity. It does not silently alter the pooled Mantel-Haenszel estimator. If an exact pooled estimator is undefined, choose an explicit positive mh_continuity_correction and report that decision.

Inspect what happened¶

columns = [
    "study",
    "included",
    "exclusion_reason",
    "continuity_corrected",
    "rd_zero_variance",
    "mh_continuity_corrected",
    "normalized_weight",
]

result.study_results[columns]

Resolved correction values and scopes also appear in dict(result.method.options). RD analyses additionally record the resolved zero-variance policy and affected row IDs in provenance. This makes it possible to distinguish a corrected analysis from an exact or exclusion-based one after fitting.