Binary outcomes¶

Use meta_binary() for independent treatment and control groups described by event counts and total sample sizes.

Mantel-Haenszel common-effect analysis¶

The default binary workflow is a Mantel-Haenszel common-effect risk ratio:

import pandas as pd
import meta_analyze as ma

studies = pd.DataFrame(
    {
        "events_t": [12, 8, 15, 6],
        "total_t": [120, 95, 140, 80],
        "events_c": [18, 11, 19, 10],
        "total_c": [118, 100, 145, 82],
    },
    index=["Trial A", "Trial B", "Trial C", "Trial D"],
)

result = ma.meta_binary(
    studies,
    event_treat="events_t",
    n_treat="total_t",
    event_control="events_c",
    n_control="total_c",
    measure="RR",
    method="MH",
    model="common",
)

print(result.summary())

Mantel-Haenszel pooling currently supports OR and RR with model="common" and ci_method="normal".

Random-effects analysis¶

Use inverse-variance pooling for a random-effects binary analysis:

result = ma.meta_binary(
    studies,
    event_treat="events_t",
    n_treat="total_t",
    event_control="events_c",
    n_control="total_c",
    measure="OR",
    method="IV",
    model="random",
    tau2_method="REML",
    ci_method="hartung_knapp_adhoc",
)

method="IV" first calculates one effect and variance per study, then passes them to the generic inverse-variance model.

Effect measures and scales¶

Measure	Model scale	Display scale	Direction
OR	log odds ratio	odds ratio	treatment relative to control
RR	log risk ratio	risk ratio	treatment relative to control
RD	risk difference	risk difference	treatment minus control

For OR and RR, result.estimate and result.ci stay on the log model scale. Use display_estimate and display_ci for exponentiated ratios.

RD is available through inverse-variance pooling:

result = ma.meta_binary(
    studies,
    event_treat="events_t",
    n_treat="total_t",
    event_control="events_c",
    n_control="total_c",
    measure="RD",
    method="IV",
    model="common",
    rd_zero_variance="correct",
)

rd_zero_variance="correct" is the default. It retains boundary studies with their raw RD and uses corrected counts only for sampling variance. Use "exclude" for a protocol that excludes these studies before all synthesis calculations. See zero-event studies for details.

Input validation¶

Event counts and sample sizes must be finite, integer-valued, and non-negative; events cannot exceed their group total, and totals must be positive. Missing rows raise by default. With missing="drop", they remain in the result table with included=False and an exclusion reason.

Sparse tables require additional decisions. Read zero-event studies before changing continuity-correction settings.

See statistical methods for the OR/RR/RD and Mantel-Haenszel equations, and validation for cross-software coverage.