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name: data-extraction description: Extract and prepare study data for meta-analysis including effect size calculation, variance estimation, and handling missing data. Use when users need to convert reported statistics into analyzable format or calculate effect sizes from raw data. license: Apache-2.0 compatibility: Requires R with metafor and escalc functions metadata: author: meta-agent version: "1.0.0" category: data-preparation domain: evidence-synthesis difficulty: intermediate estimated-time: "15 minutes" prerequisites: meta-analysis-fundamentals

Data Extraction for Meta-Analysis

This skill teaches how to extract, convert, and prepare study data for meta-analysis.

Overview

Before running a meta-analysis, you need to extract effect sizes and their variances from each study. Studies report results in different formats, requiring conversion to a common metric.

When to Use This Skill

Activate this skill when users:

• Have study data in different formats
• Need to calculate effect sizes from raw data
• Ask about converting between effect size types
• Have missing standard deviations or standard errors
• Need to extract data from figures or tables

Data Requirements

Minimum Data Needed

Outcome Type	Required Data
Binary	Events and totals for each group, OR 2x2 table
Continuous	Means, SDs, and sample sizes for each group
Correlation	Correlation coefficient (r) and sample size
Pre-calculated	Effect size and SE (or CI or variance)

Effect Size Calculations

Binary Outcomes

From 2x2 Table

              Treatment    Control
Event            a           b
No Event         c           d
Total           n1          n2

Odds Ratio:

OR = (a/c) / (b/d) = (a*d) / (b*c)
log_OR = log(OR)
SE_log_OR = sqrt(1/a + 1/b + 1/c + 1/d)

Risk Ratio:

RR = (a/n1) / (b/n2)
log_RR = log(RR)
SE_log_RR = sqrt(1/a - 1/n1 + 1/b - 1/n2)

Risk Difference:

RD = (a/n1) - (b/n2)
SE_RD = sqrt((a*c/n1^3) + (b*d/n2^3))

Continuous Outcomes

Standardized Mean Difference (SMD/Hedges' g)

# Pooled SD
s_pooled = sqrt(((n1-1)*sd1^2 + (n2-1)*sd2^2) / (n1+n2-2))

# Cohen's d
d = (mean1 - mean2) / s_pooled

# Hedges' g (bias-corrected)
J = 1 - (3 / (4*(n1+n2-2) - 1))
g = J * d

# Variance
var_g = (n1+n2)/(n1*n2) + g^2/(2*(n1+n2))

Mean Difference (MD)

MD = mean1 - mean2
SE_MD = sqrt(sd1^2/n1 + sd2^2/n2)

R Code for Effect Size Calculation

Using escalc() Function

library(metafor)

# Binary outcomes - Odds Ratio
dat_binary <- escalc(measure = "OR",
                     ai = events_treat, bi = nonevents_treat,
                     ci = events_ctrl, di = nonevents_ctrl,
                     data = mydata)

# Binary outcomes - Risk Ratio
dat_rr <- escalc(measure = "RR",
                 ai = events_treat, bi = nonevents_treat,
                 ci = events_ctrl, di = nonevents_ctrl,
                 data = mydata)

# Continuous outcomes - SMD (Hedges' g)
dat_smd <- escalc(measure = "SMD",
                  m1i = mean_treat, sd1i = sd_treat, n1i = n_treat,
                  m2i = mean_ctrl, sd2i = sd_ctrl, n2i = n_ctrl,
                  data = mydata)

# Continuous outcomes - Mean Difference
dat_md <- escalc(measure = "MD",
                 m1i = mean_treat, sd1i = sd_treat, n1i = n_treat,
                 m2i = mean_ctrl, sd2i = sd_ctrl, n2i = n_ctrl,
                 data = mydata)

# Correlations
dat_cor <- escalc(measure = "ZCOR",  # Fisher's z
                  ri = correlation, ni = sample_size,
                  data = mydata)

From Pre-calculated Statistics

# From OR and 95% CI
log_or <- log(OR)
se_log_or <- (log(CI_upper) - log(CI_lower)) / (2 * 1.96)

# From SMD and 95% CI
se_smd <- (CI_upper - CI_lower) / (2 * 1.96)

# From p-value and sample size (approximate)
# For t-test
t_value <- qt(1 - p_value/2, df = n1 + n2 - 2)
d <- t_value * sqrt(1/n1 + 1/n2)

Handling Missing Data

Missing SDs

Option 1: Impute from other studies

# Use median SD from studies that report it
median_sd <- median(dat$sd, na.rm = TRUE)
dat$sd[is.na(dat$sd)] <- median_sd

Option 2: Calculate from CI or SE

# From 95% CI for mean
SD = sqrt(n) * (CI_upper - CI_lower) / (2 * 1.96)

# From SE
SD = SE * sqrt(n)

Option 3: Calculate from IQR (for skewed data)

# Wan et al. method
SD = IQR / 1.35

Missing Sample Sizes

Option 1: Use reported total N

# If only total N given, assume equal groups
n1 = n2 = N / 2

Option 2: Contact authors

• Always the best option for critical missing data

Zero Events

# Add continuity correction (0.5 to all cells)
dat_corrected <- escalc(measure = "OR",
                        ai = events_treat + 0.5,
                        bi = nonevents_treat + 0.5,
                        ci = events_ctrl + 0.5,
                        di = nonevents_ctrl + 0.5,
                        data = mydata)

# Or use Peto OR (handles zeros better)
dat_peto <- escalc(measure = "PETO",
                   ai = events_treat, bi = nonevents_treat,
                   ci = events_ctrl, di = nonevents_ctrl,
                   data = mydata)

Data Extraction Checklist

□ Study identifier (author, year)
□ Sample sizes (treatment and control)
□ Outcome data:
  □ Binary: events in each group
  □ Continuous: means and SDs
□ Effect size (if pre-calculated)
□ Confidence interval or SE
□ Follow-up duration
□ Subgroup information
□ Risk of bias assessment

Common Conversion Scenarios

Scenario 1: Only p-value reported

# Convert p-value to effect size (approximate)
# Requires sample sizes
z <- qnorm(1 - p_value/2)
d <- z * sqrt(1/n1 + 1/n2)

Scenario 2: Median and IQR reported

# Estimate mean and SD (Wan et al. 2014)
# For sample size n:
mean_est <- (q1 + median + q3) / 3
sd_est <- (q3 - q1) / 1.35

Scenario 3: Different scales across studies

# Use SMD to standardize
# This puts all studies on same scale
dat <- escalc(measure = "SMD", ...)

Teaching Framework

Step 1: Identify What's Reported

"What statistics does the study report?

• Raw data (means, SDs, events)?
• Effect size with CI?
• Just a p-value?"

Step 2: Determine Target Effect Size

"What effect size is appropriate for your research question?

• Binary outcome → OR or RR
• Continuous, same scale → MD
• Continuous, different scales → SMD"

Step 3: Calculate or Convert

"Now let's calculate the effect size and its variance..."

Step 4: Verify

"Let's double-check:

• Does the direction make sense?
• Is the magnitude plausible?
• Does the CI seem reasonable?"

Assessment Questions

1. Basic: "What data do you need to calculate an odds ratio?"

   • Correct: Events and non-events (or totals) for each group

2. Intermediate: "A study reports mean difference = 5, p = 0.03, n = 50 per group. How do you get the SE?"

   • Correct: Use p-value to get t-statistic, then SE = MD / t

3. Advanced: "Studies use different depression scales (BDI, HDRS). How do you combine them?"

   • Correct: Use standardized mean difference (SMD) to put on common scale

Related Skills

• meta-analysis-fundamentals - Understanding effect sizes
• r-code-generation - Automating calculations
• grade-assessment - Evaluating certainty of evidence

Adaptation Guidelines

Glass (the teaching agent) MUST adapt this content to the learner:

1. Language Detection: Detect the user's language from their messages and respond naturally in that language
2. Cultural Context: Adapt examples to local healthcare systems and research contexts when relevant
3. Technical Terms: Maintain standard English terms (e.g., "forest plot", "effect size", "I²") but explain them in the user's language
4. Level Adaptation: Adjust complexity based on user's demonstrated knowledge level
5. Socratic Method: Ask guiding questions in the detected language to promote deep understanding
6. Local Examples: When possible, reference studies or guidelines familiar to the user's region

Example Adaptations:

• 🇧🇷 Portuguese: Use Brazilian health system examples (SUS, ANVISA guidelines)
• 🇪🇸 Spanish: Reference PAHO/OPS guidelines for Latin America
• 🇨🇳 Chinese: Include examples from Chinese medical literature