Meta Analysis for Binary Outcome in SPSS

1. Introduction

Meta-analysis of binary outcomes is a crucial tool in evidence-based medicine, enabling researchers to combine effect sizes from multiple studies to determine the overall treatment effect for dichotomous (yes/no) variables. SPSS, especially version 28 and higher, now offers a dedicated feature for binary meta-analysis, making it more accessible for researchers without coding skills.

2. What is Binary Meta-Analysis?

Binary meta-analysis refers to the statistical synthesis of results from studies with dichotomous outcomes, such as event/no-event, success/failure, or improved/not improved. Instead of focusing on means or continuous scores, this approach aggregates odds ratios, risk ratios, or risk differences across studies.

In addition to binary outcomes, meta-analysis can be applied to other data types depending on the study design and reported results. Common types include:

• Continuous Outcome Meta-Analysis: Used when studies report means and standard deviations (e.g., blood pressure, symptom scores). Effect sizes include
• Meta-Regression: Meta-regression examines whether study-level variables (e.g., sample size, year, dosage) explain variation in effect sizes. It’s ideal when heterogeneity is present.
• Proportional Meta-Analysis: Used to pool proportions or prevalence data (e.g., infection rates). Logit transformation is often applied to stabilize variance. This method is common in epidemiology and can be implemented in SPSS .

3. When to Use Meta-Analysis of Binary Outcomes?

Binary meta-analysis is used when studies report results in binary format. This is common in clinical trials reporting adverse events, mortality, treatment response, or disease remission. It is also relevant for observational studies assessing exposure-outcome relationships in a dichotomous framework.

4. What Effect Size for Binary Outcome in Meta Analysis?

In SPSS, you can choose from several effect sizes for binary outcome meta-analysis. Here’s a breakdown with guidance:

• Log Odds Ratio (LOR): The logarithmic transformation of odds ratios; often used due to its statistical properties in modeling.

• Odds Ratio (OR): Measures the odds of an event occurring in the treatment versus control group. Ideal when outcomes are rare.

• Log Risk Ratio (Log RR): Used when synthesizing risk ratios, helpful when interpreting relative risk is preferable.

• Risk Ratio (RR): Indicates how many times more (or less) likely the event is in the treatment group.

• Risk Difference (RD): Represents the absolute difference in event proportions. Easier to interpret but less commonly used in random-effects models.

Best Practice: Log Odds Ratio is generally preferred for rare events, while Risk Ratio may be favored when interpretability is key in clinical decisions.

5. What is the Difference Between Fixed and Random effects in Meta Analysis of Binary outcomes?

• Fixed-Effect Model assumes one true effect size shared across all studies. Use this when heterogeneity is negligible.

• Random-Effects Model allows for between-study variability. It assumes study-specific effects vary around a population mean.

Best Option: Random-effects is more realistic in medical research where heterogeneity is expected.

6. What Estimator Type of Meta Analysis of Binary Outcome?

SPSS allows choosing from several estimators to calculate the pooled effect under a random-effects model:

• REML (Restricted Maximum Likelihood): Offers stable and unbiased estimates; widely preferred.

• ML (Maximum Likelihood): Can underestimate variance; less ideal for small samples.

• Empirical Bayes: Shrinks extreme estimates toward the mean; useful with prior distributions.

• Hunter-Schmidt: Corrects for measurement error; used in psychometric contexts.

• Hedges: Adjusts for small sample bias.

• DerSimonian-Laird: Common default, though may overestimate precision.

• Sidik-Jonkman: More robust under high heterogeneity.

Best Choice: For most binary outcome meta-analyses, use REML for more stable estimates of heterogeneity and pooled effects.

7. Which Standard Error Adjustment Should You Set?

SPSS allows adjusting the standard error (SE) of the pooled estimate to correct for small sample bias:

• No Adjustment: Assumes normality and homogeneity; less conservative.

• Knapp-Hartung (KH): Provides more conservative standard errors; better with few studies.

• Truncated Knapp-Hartung: A modified version to avoid excessively wide CIs.

Best Practice: Knapp-Hartung is advised when dealing with fewer than 10 studies or high heterogeneity.

8. Heterogeneity in Meta Analysis of Binary Outcome

Heterogeneity assesses variation among study results and is quantified using:

• Q-statistic: Tests for heterogeneity.

• I² statistic: Proportion of variability due to heterogeneity (≥ 50% indicates moderate-to-high).

• Tau²: Variance of true effect sizes.

Exploring sources of heterogeneity is essential before drawing firm conclusions.

9. What is Trim and Fill in Meta Analysis Binary?

Trim and Fill is a statistical method used to detect and adjust for publication bias in meta-analyses, including those with binary outcomes. It starts by assessing asymmetry in the funnel plot, which may indicate that smaller studies with non-significant results are missing from the published literature.

The method “trims” the asymmetric studies and estimates how many studies are likely missing. It then “fills” in these hypothetical studies to create a more symmetrical funnel plot and recalculates the pooled effect size accordingly.

Although Trim and Fill does not remove publication bias, it offers a sensitivity analysis. This helps researchers evaluate whether the overall findings are robust in the presence of possible missing or unpublished studies.

10. How Subgroup Analysis Works

Subgroup analysis explores whether the treatment effect varies across different categories of studies. For binary outcomes, studies can be grouped based on categorical moderators such as:

• Type of intervention

• Geographic region

• Study quality

• Population characteristics (e.g., age group, clinical setting)

In SPSS, subgroup analysis is typically performed using a mixed-effects model. This approach estimates separate pooled effect sizes for each subgroup and compares them to assess whether the moderator variable explains heterogeneity. If between-group differences are statistically significant, it suggests that the moderator may influence the effect size.

Subgroup analysis is especially useful when heterogeneity is present and helps generate hypotheses for future research.

11. What is Publication Bias in Meta Analysis of Binary Outcome?

Publication bias occurs when studies with null or negative results remain unpublished. Common tests include:

• Egger’s Test: Assesses asymmetry in the funnel plot.

• Peters’ Test: Adjusts for binary outcome characteristics.

• Harbord Test: Similar to Egger’s but designed for odds ratios.

Each test has its assumptions; use more than one when possible.

12. What is Used for a Funnel and Forest Plot in Meta Analysis of Binary Outcome?

• Forest Plot: Summarises effect sizes and confidence intervals visually across studies.

• Funnel Plot: Detects potential publication bias based on the symmetry of effect sizes.

SPSS generates both plots automatically in binary meta-analysis using the appropriate chart options.

13. What Are the Assumptions of Meta-Analysis for Binary Outcome?

• Binary outcomes are independent.

• Effect sizes (e.g., log ORs) are normally distributed.

• Studies are sufficiently homogeneous or accounted for via random-effects.

• No serious publication or selection bias.

14. An Example for Meta Analysis for Binary Outcome

Assume a researcher collects results from 10 clinical trials testing the efficacy of a drug to prevent infection. Each study reports event counts for the treatment and control groups. The researcher converts event data into log odds ratios and performs a meta-analysis using the random-effects model.

In the following sections, we’ll explain how to perform such an analysis in SPSS. For this example, we will use SPSS v.30, but you can use Meta MACRO from the original meta-analysis utilities by Prof. David Wilson.

Step by Step: Running Meta-Analysis in SPSS Statistics

Let’s embark on a step-by-step guide on performing the meta-analysis using SPSS

In SPSS version 28 and higher, you can directly conduct meta-analysis for binary outcomes using the native interface. The procedure supports two approaches:

• Effect size available (e.g., log odds ratio and standard error already calculated)

• Effect size not available (raw 2×2 event data: number of events and total sample size for each group)

To perform binary meta-analysis in SPSS:

1. STEP: Go to Analyze → Meta Analysis → Binary Outcome.

2. STEP: Choose the appropriate input:

• If you have raw data (e.g., event counts and sample sizes), select Effect sizes not available.
• If you have already computed log odds ratios or risk ratios, select Effect sizes available.

3. STEP: In the Variables tab:

• For raw data, assign: Events and sample sizes for the treatment and control groups.
• For calculated data, assign: Effect size variable (e.g., log OR or log RR)  and Standard error or variance.

4. STEP: In the Inference tab:

• Choose between Fixed effects or Random effects.
• Select the estimator (e.g., REML, DL, Sidik-Jonkman).
• Set standard error adjustment (e.g., Knapp-Hartung).

5. STEP: Optionally, explore:

• Bias, Trim-and-Fill, Print tabs for subgroup or meta-regression analyses.
• Plots tab to produce forest and funnel plots.

6. STEP: Click OK to run the analysis.

SPSS will produce output with pooled estimates, heterogeneity statistics, and visualizations.

17. How to Interpret SPSS Output of Binary Meta Analysis

Once the analysis is complete, SPSS generates a detailed output including pooled effect estimates, confidence intervals, heterogeneity indices, and plots.

Key components to interpret:

• Pooled Effect Size: Represents the overall estimate (e.g., OR or RR). A significant effect (e.g., OR = 1.45, 95% CI [1.10, 1.92]) indicates a meaningful association across studies.

• Heterogeneity Statistics:

  • Q-test: Tests whether effect sizes are more variable than expected by chance. A significant result suggests heterogeneity.

  • I²: Describes the percentage of total variation due to heterogeneity. Interpret as:

    • 0–40%: low

    • 30–60%: moderate

    • 50–90%: substantial

    • 75–100%: considerable

  • Tau²: The estimated between-study variance. A larger τ² indicates more between-study variability.

• Forest Plot: Displays effect size and confidence intervals for each study and the pooled estimate.

• Funnel Plot (optional): Used to assess publication bias. Asymmetry may indicate bias or small-study effects.

• Moderator Analyses: If subgroup variables are included, SPSS will display pooled estimates per group, and test for differences between them.

18. How to Report Results of Meta Analysis in APA

• Study Selection Summary: Report the total number of studies identified, screened, and included in the meta-analysis. Indicate any exclusions and provide a brief narrative consistent with the PRISMA flow diagram.
• Study Characteristics: Summarize key characteristics of the included studies, such as study design, sample sizes, outcome definitions, and population types. Mention whether studies used similar methods or settings.
• Effect Size and Model: Specify the effect size metric used (e.g., odds ratio, log odds ratio). Indicate whether a fixed-effect or random-effects model was applied, and name the estimator (e.g., REML, ML, DL).
• Heterogeneity: Report heterogeneity statistics including the Q statistic with degrees of freedom and p-value. Also include I² (%) to quantify inconsistency and τ² to reflect between-study variance.
• Publication Bias: Describe whether publication bias was assessed. Mention the use of funnel plots and any statistical tests (e.g., Egger’s, Harbord, Peters). Indicate whether the trim-and-fill method was applied and if it affected the pooled estimate.
• Subgroup and Sensitivity Analyses: If applicable, describe subgroup analyses performed based on categorical moderators (e.g., region, study quality). Report sensitivity analyses used to assess robustness of results (e.g., leave-one-out analysis, exclusion of outliers).
• Pooled Results Summary: Present the pooled effect size with its 95% confidence interval and p-value. Interpret the direction, magnitude, and statistical significance of the effect in context. Optionally, include the 95% prediction interval if available.

Example of Binary Meta Analysis Results in APA Style

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PS: This guide is tailored for SPSS version 30, and for any variations, it’s recommended to refer to the software’s documentation for accurate and updated instructions.