Generic effects¶

Use meta_analysis() when each study already has an effect estimate and its sampling variance or standard error. This is the generic inverse-variance workflow; it does not calculate an outcome-specific effect size.

The pooling, tau-squared, confidence-interval, prediction-interval, and heterogeneity equations are specified under statistical methods.

DataFrame input¶

import pandas as pd
import meta_analyze as ma

data = pd.DataFrame(
    {
        "label": ["A", "B", "C", "D"],
        "yi": [0.18, 0.31, -0.04, 0.22],
        "vi": [0.025, 0.041, 0.030, 0.036],
    }
)

result = ma.meta_analysis(
    data,
    effect="yi",
    variance="vi",
    study="label",
    model="random",
    tau2_method="PM",
)

String arguments select DataFrame columns. The study column is optional; the DataFrame index is used when it is omitted.

Array input¶

result = ma.meta_analysis(
    effect=[0.18, 0.31, -0.04, 0.22],
    variance=[0.025, 0.041, 0.030, 0.036],
    study=["A", "B", "C", "D"],
    model="common",
)

All array-like arguments must be one-dimensional and have equal lengths. Generated row labels start at zero when no study labels are supplied.

Variance or standard error¶

Supply exactly one of variance= or standard_error=. Both must contain finite, strictly positive values. A reported standard-error column can be used directly:

result = ma.meta_analysis(
    data,
    effect="yi",
    standard_error="standard_error",
)

PyMetaAnalysis squares standard errors internally, retains both uncertainty columns in the study table, and records the conversion in provenance. Do not pass confidence-interval widths or study sample standard deviations as standard errors; they describe different quantities.

Missing values¶

The default missing="raise" rejects missing effects or values in the selected uncertainty input. To retain incomplete rows as structured exclusions:

result = ma.meta_analysis(
    data,
    effect="yi",
    variance="vi",
    study="label",
    missing="drop",
)

result.excluded_studies[["study", "exclusion_reason"]]

Dropped rows do not enter the pooled estimate, heterogeneity statistics, or weights.

Subgroups¶

Pass a column name or array through subgroup=:

subgroups = ma.meta_analysis(
    data,
    effect="yi",
    variance="vi",
    subgroup=["North", "North", "South", "South"],
)

See result objects for the returned structure.

For shared DataFrame/array, row identity, and exclusion rules, see input data and row decisions.