Study Size Weighted Averaging

study-size-weighted-averaging

Summary

Combine effect sizes (fold-changes) across multiple metabolomics studies by applying log2 transformation and computing a weighted average where weights are proportional to each study's sample size (N). This produces a single pooled fold-change estimate that reflects both the magnitude of change and the statistical power of each contributing study.

When to use

You have metabolomics results from multiple independent studies (each with a fold-change, p-value, and sample size N) and need to produce a single quantitative meta-analysis fold-change estimate. Use this skill when raw data and standard deviations are unavailable but relative change (fold-change) and study sample sizes are known, as is typical in published metabolomics comparisons.

When NOT to use

• Standard deviations or confidence intervals are available for each study—use conventional meta-analysis effect-size methods instead.
• Data are already individual-level (raw metabolite abundances), not summarized study-level results.
• You are performing qualitative vote-counting analysis; use that skill independently for trend consensus without fold-change pooling.

Inputs

• amanida data structure (S4 object) containing: identifier (metabolite name), fold-change (numeric, typically > 0), study size N (integer sample count), and p-value columns from multiple studies

Outputs

• compute_amanida @stat table containing pooled fold-change estimate, trend direction (up-regulation / down-regulation / no trend), and N_total (sum of study sizes)

How to apply

First, log2-transform each study's fold-change value to symmetrize the scale (so a 2-fold increase and 2-fold decrease are equidistant from zero). Then compute a weighted average where each transformed fold-change is multiplied by its study size N and divided by the sum of all N values. The rationale is that larger studies provide more precise estimates and should contribute proportionally more to the pooled result. This weighting ensures the meta-analysis fold-change reflects the combined evidence, not an unweighted arithmetic mean. The result is stored in the @stat table of the compute_amanida output object and reports both the pooled fold-change and the direction of regulation (up/down/no trend).

Related tools

• amanida (Executes study-size-weighted fold-change averaging via compute_amanida() function; stores results in @stat table) — https://github.com/mariallr/amanida
• R (Host language for amanida package and log2 transformation operations)

Examples

amanida_result <- compute_amanida(datafile, comp.inf = F); pooled_fc <- amanida_result@stat

Evaluation signals

• Verify @stat table contains non-zero pooled fold-change values with direction labels (up/down/no trend) and N_total equals sum of input study sizes.
• Check that log2-transformed fold-changes are symmetric around zero (e.g., 2-fold up and 0.5-fold down both have absolute magnitude ~1 on log2 scale).
• Confirm volcano plot shows pooled log2(fold-change) on x-axis aligned with combined p-value significance on y-axis.
• Validate that studies with larger N values have greater influence on the pooled fold-change estimate by sensitivity analysis (removing large-N studies shifts result meaningfully).
• Ensure N_total in output matches manual sum of input study sizes across all rows.

Limitations

• Negative fold-change values are transformed to positive (1/value) before processing; true directional information may be lost if input data mix up/down regulation inconsistently.
• Fold-changes < 2 are not recommended for biological interpretation; pooled estimates below this threshold should be treated as non-significant even if statistically combined.
• Assumes fold-changes are already normalized and comparable across studies; batch effects or different quantification platforms may bias the pooled estimate.
• No uncertainty (confidence interval) is reported for the pooled fold-change; only point estimate and direction are provided.

Evidence

• [intro] log2_transformation_and_weighting: "Fold-change: logarithmic transformation for average with weighting by number of participants"
• [readme] compute_amanida_output_structure: "In this step you will obtain an S4 object with two tables: adapted meta-analysis acces by amanida_result@stat and vote-counting acces by amanida_results@vote"
• [other] stat_table_contents: "producing meta-analysis results accessible via the @stat table containing trend direction and N_total (sum of study sizes)"
• [intro] study_size_proportional_weighting: "P-value: weighted p-values combination, which is a variant of Fisher's method. A gamma distribution is used to assign non-integral weights proportional to study size to each p-value. Fold-change:"
• [readme] input_data_requirements: "Dataset to analyse must include the following columns: identifier, p-value, fold-change, study size (N) and reference"