Protocol: Fisher-Z transformed partial correlations for continuous exposures

Tier: D (cMD paper) · Type: atomic · Category: Statistical Analysis

What

The continuous-exposure counterpart to the SMD protocol: per dataset, compute the partial correlation between each feature and a continuous exposure (age, BMI) adjusting for the remaining covariates, and Fisher-Z transform it so that effects are poolable on an approximately normal scale with a closed-form standard error.

Why it matters

The age and BMI results in the paper rest on it, and it is the reason the same random-effects pooling machinery works for both binary and continuous exposures. Separating it from the SMD protocol keeps each atomic protocol to one method with one citation, which is what the standard asks for.

Source material

• waldronlab/curatedMetagenomicDataAnalyses — vignettes/Age_metaanalysis_vignette.Rmd, R/runMetaanalysis_quantitative.R, python_modules/meta_analyses.py (singleStudyEffect with REG=True), python_tools/hierarchical_metaanalysis.py
• Paper: 10.1038/s41467-025-66888-1

Scope

In: partial correlation definition and which covariates are partialled out; the Fisher-Z transform and its standard error as a function of n and the number of covariates; back-transformation for reporting; minimum sample size; handling of exposures with restricted range in a given dataset.

Out: pooling (separate protocol).

Frontmatter starting point

type: "atomic"
category: "Statistical Analysis"
citation: ""   # Fisher's z transformation — Fisher 1915 or 1921. Establish which. NOT the cMD paper.
protocols_used:
  - name: "prevalence-filtering"
  - name: "clr-transformation"      # optional: see note
tags: [partial-correlation, fisher-z, effect-size, continuous-exposure, meta-analysis]

The transformation is a swappable slot, per review feedback — this analysis must be runnable with
or without CLR. Say explicitly what the untransformed path is and what changes in the interpretation,
rather than treating CLR as mandatory preprocessing.

Acceptance criteria

• The SE formula accounts for the number of partialled covariates, not just n
• Back-transformation for reporting is specified
• Output schema matches the SMD protocol's so both feed the same pooling step

Cite the method's origin, not its users

PROTOCOL_STANDARD.md is explicit: an atomic protocol carries "strictly 1 citation... corresponding
to the primary literature where the method was originally published." Find the paper that proposed
the method. Do not cite a paper that merely applied it — including the BugSigDB and curatedMetagenomicData
papers, which are the source of the analysis these protocols were extracted from but almost never the
source of the method.

Tracing a method back to its first publication is real work, and it is part of the task, not a
formality. Three things to expect:

• Candidate DOIs in this issue are leads, not answers. Anything marked VERIFY has not been checked.
• Some methods predate modern citation practice or have no single identifiable origin. If that is
  genuinely the case, say so in the pull request rather than reaching for a convenient recent paper.
  Raise it as an issue in waldronlab/agent-protocol-standard — the standard may need a way to express
  "classical method, no primary source".
• If you cannot name one paper that proposed everything the protocol does, it is more than one
  protocol. That test has now split four protocols out of this batch: enrichment into three methods,
  filtering from transformation, LODO from random forest, and PERMANOVA from ANOSIM.

Where the lab's own paper genuinely did propose the method — the oral-to-gut score, and LODO
cross-validation in Pasolli et al. 2016 — citing it is correct. That is the exception, not the pattern.

Before you start

Read CONTRIBUTING.md and
PROTOCOL_STANDARD.md.
The format is defined in the standard repo, not this one. Protocols are prose, not code: they say what to do
and why, precisely enough that two people — or two agents, in two languages — get the same answer. The existing
independent-filtering-variance
protocol is the model to imitate for tone and level of detail.

Validate locally before opening the PR:

git clone https://github.com/waldronlab/agent-protocol-standard.git
Rscript agent-protocol-standard/scripts/validate-protocol.R protocols

Read CONTRIBUTING.md, PROTOCOL_STANDARD.md, and the independent-filtering-variance protocol first. Then compare the cited R and Python implementations and trace Fisher's primary source. Done means a validated prose protocol specifies partialling, covariate-aware SE, back-transformation, sample and range limits, optional CLR handling, and an SMD-compatible output schema.