Pairwise Ma Methodology

Pairwise Meta-Analysis Methodology

Comprehensive methodological guidance for conducting rigorous pairwise meta-analysis following Cochrane and PRISMA guidelines.

When to Use This Skill

• Planning a pairwise meta-analysis
• Choosing between fixed and random effects models
• Interpreting heterogeneity statistics
• Assessing publication bias
• Designing sensitivity analyses
• Reviewing pairwise MA code or results

Fixed vs Random Effects

Decision Framework

Are studies functionally identical?
├── Yes → Fixed-effect model appropriate
│   - Same population, intervention, comparator, outcome
│   - Estimating single "true" effect
│
└── No (usually the case) → Random-effects model
    - Studies differ in ways that affect true effect
    - Estimating mean of distribution of effects
    - More generalizable inference

When to Use Fixed-Effect

• Studies are very similar (rare in practice)
• Want to estimate effect in "identical" studies
• Very few studies (75% | Considerable heterogeneity |

Caution: These thresholds are rules of thumb, not strict cutoffs.

τ² (Tau-squared)

• Absolute between-study variance
• On scale of effect measure
• Used for prediction intervals
• Compare to typical effect sizes for context

H²

• Relative excess heterogeneity
• H² = Q/(k-1) where k = number of studies
• H² = 1 means no heterogeneity

Prediction Intervals

Critical: Always report prediction intervals alongside confidence intervals.

• CI: Uncertainty in mean effect estimate
• PI: Range where 95% of true study effects would lie

# In meta package
metabin(..., prediction = TRUE)

If PI includes null but CI doesn't:

• Mean effect is statistically significant
• But future studies might show no effect or opposite effect
• Heterogeneity is clinically important

Investigation of Heterogeneity

Subgroup Analysis

# Categorical moderator
update(ma_result, subgroup = risk_of_bias)

# Requirements:
# - Pre-specified in protocol
# - Limited number of subgroups
# - Biological/clinical rationale
# - Report within and between subgroup heterogeneity

Meta-Regression

# Continuous moderator
rma(yi, vi, mods = ~ year + sample_size, data = es_data)

# Requirements:
# - Minimum 10 studies per moderator
# - Pre-specified moderators
# - Avoid overfitting
# - Use Knapp-Hartung adjustment
# - Permutation test for multiple moderators

Rule of Thumb for Investigation

• Need ≥10 studies for meaningful subgroup analysis
• Meta-regression requires even more studies
• Pre-specify investigations in protocol
• Report all investigated moderators (avoid selective reporting)

Publication Bias Assessment

Visual Assessment: Funnel Plot

funnel(ma_result)
# Look for:
# - Asymmetry (small studies with large effects)
# - Missing studies in certain regions
# - Outliers

Statistical Tests

Egger's Test (Continuous Outcomes)

metabias(ma_result, method.bias = "linreg")
# P  0.05, so use fixed-effect"
- Right: Choose based on study similarity, report both

### 2. Ignoring Prediction Intervals
- CI shows precision of mean estimate
- PI shows variability in true effects
- Both are clinically important

### 3. Over-interpreting I²
- I² has wide CI with few studies
- Context matters (clinical significance)
- Don't use arbitrary thresholds mechanically

### 4. Selective Subgroup Analysis
- Pre-specify in protocol
- Report all, not just significant ones
- Adjust for multiple testing

### 5. Publication Bias Assessment with Few Studies
- Tests unreliable with < 10 studies
- State this limitation, don't perform test

## Quick Reference Code

```r
library(meta)

# Basic random-effects MA (binary)
ma <- metabin(
  event.e, n.e, event.c, n.c,
  studlab = study,
  data = dat,
  sm = "OR",
  method = "MH",
  method.tau = "REML",
  hakn = TRUE,           # Knapp-Hartung adjustment
  prediction = TRUE      # Prediction interval
)

# Forest plot
forest(ma, sortvar = TE, prediction = TRUE)

# Funnel plot and Egger's test
funnel(ma)
metabias(ma, method.bias = "linreg")

# Influence analysis
metainf(ma)

# Subgroup analysis
update(ma, subgroup = risk_of_bias)

Resources

• Cochrane Handbook: https://training.cochrane.org/handbook
• PRISMA Statement: http://www.prisma-statement.org/
• Higgins & Green: Cochrane Handbook for Systematic Reviews
• Borenstein et al.: Introduction to Meta-Analysis

Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

• Author: choxos
• Source: choxos/BiostatAgent
• License: MIT

Install and usage instructions live in the source repository linked above.