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arxiv: 2604.02595 · v1 · submitted 2026-04-03 · 📊 stat.ME

Multi-Site Health Research Integrating Complementary Data Sources: A Scoping Review of Statistical Inference Methods for Vertically Partitioned Data

Marie-Pier Domingue , Simon L\'evesque , Anita Burgun , Jean-Fran\c{c}ois Ethier , F\'elix Camirand Lemyre This is my paper

Pith reviewed 2026-05-13 19:13 UTC · model grok-4.3

classification 📊 stat.ME
keywords vertically partitioned datastatistical inferenceprivacy-preserving analysismulti-site health datascoping reviewlinear regressionlogistic regressiondata integration
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The pith

Vertical methods for statistical inference on partitioned health data rarely achieve equivalence to centralized results with efficient communication and strong privacy protection.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This scoping review maps existing vertical methods that let separate institutions run statistical analyses on complementary data for the same people without pooling or sharing individual records. It screened thousands of papers and extracted details from 30 methods, focusing on whether results match what a single pooled database would produce, how many communication rounds between sites are needed, and whether privacy is formally guaranteed. Most methods target linear or logistic regression, yet equivalence is not always proven, communication often requires multiple exchanges, and few papers supply actual privacy assessments despite describing their work as privacy-preserving. The review concludes that the set of available techniques remains narrow and that very few methods meet all three practical requirements at the same time.

Core claim

The scope of existing approaches enabling statistical inference for vertically partitioned data is still relatively limited. Most existing methods do not concurrently achieve results equivalent to centralized analyses, high communication efficiency, and guaranteed protection of individual-level data.

What carries the argument

Systematic extraction of three properties across identified methods: comparability with pooled analysis, efficiency of communication schemes, and confidentiality safeguards.

If this is right

  • Linear and logistic regression are the most common inference tasks addressed by vertical methods.
  • Equivalence to pooled analyses is not systematically demonstrated across all proposed methods.
  • Most methods require multiple communication rounds between participating parties.
  • Only a minority of articles provide explicit privacy assessments even though nearly all describe their approach as privacy-preserving.
  • Applications of these methods to real-world vertically partitioned health data remain limited.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • New vertical methods should be designed from the start to satisfy equivalence, low communication cost, and verifiable privacy in one package.
  • Standardized reporting requirements for privacy guarantees would make it easier to compare methods across studies.
  • The scarcity of real-data applications suggests a need to test promising methods on actual multi-site health datasets to move from theory to practice.

Load-bearing premise

That the database searches and citation screening captured a representative sample of all vertical methods and that the extracted properties were reported consistently enough across papers to support the overall characterization.

What would settle it

Identification of many additional vertical methods that simultaneously deliver exact equivalence to pooled results, require only one communication round, and include formal privacy proofs would indicate the scope is broader than reported.

Figures

Figures reproduced from arXiv: 2604.02595 by Anita Burgun, F\'elix Camirand Lemyre, Jean-Fran\c{c}ois Ethier, Marie-Pier Domingue, Simon L\'evesque.

Figure 1
Figure 1. Figure 1: (a) Centralized data. (b) Horizontally partitioned data (example of two data nodes), where each pattern [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: General process in collaborative health data research with vertically partitioned data and main features [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: PRISMA flow chart for article screening process. Detailed inclusion and exclusion criteria are described [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Main communication workflows for the vertically distributed linear regression and logistic regression [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Role of privacy among included articles. [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 1
Figure 1. Figure 1: (a) Centralized data. (b) Horizontally partitioned data (example of two data [PITH_FULL_IMAGE:figures/full_fig_p023_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: Extraction template from Covidence (1 of 2) [PITH_FULL_IMAGE:figures/full_fig_p035_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Extraction template from Covidence (2 of 2) [PITH_FULL_IMAGE:figures/full_fig_p036_2.png] view at source ↗
read the original abstract

To address the multidimensional nature of health-related questions, advances in health research often require integrating information from various data sources within statistical analyses. When complementary information pertaining to the same set of individuals are distributed across different institutions, vertical methods make it possible to obtain analysis results without sharing or pooling individual-level data. To guide stakeholders toward a transparent use of vertical methods, this study aims to (1) Identify existing vertical methods enabling statistical inference; and (2) Characterize the methodological properties of these methods and the current extent of their use with health data. We conducted a scoping review using four interdisciplinary databases. We then systematically extracted the characteristics of identified vertical methods with respect to comparability with the pooled analysis, efficiency of communication schemes and confidentiality. We additionally screened studies that cited included articles to identify applications on vertically partitioned real-world health data. Among 2887 articles initially screened, 30 were included in the review. Inference for the linear and the logistic regression framework were the most frequent statistical inference tasks undertaken in proposed methods. Equivalence with the pooled analyses was not systematically addressed and most methods required multiple communications between participating parties. Almost all articles described their approach as privacy-preserving, although a minority provided privacy assessments. The scope of existing approaches enabling statistical inference for vertically partitioned data is still relatively limited. Most existing methods do not concurrently achieve results equivalent to centralized analyses, high communication efficiency, and guaranteed protection of individual-level data.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript is a scoping review that screened 2887 articles across four databases and included 30 papers on statistical inference methods for vertically partitioned data. It focuses on methods for linear and logistic regression, extracts properties related to equivalence with pooled analyses, communication efficiency, and privacy protection, and concludes that the scope of existing approaches remains limited, with most methods failing to concurrently achieve equivalence to centralized results, high communication efficiency, and guaranteed individual-level data protection.

Significance. If the property extraction is shown to be consistent and representative, the review would usefully map the landscape of vertical methods for multi-site health research and identify key gaps, particularly the frequent trade-offs among statistical fidelity, communication overhead, and privacy guarantees. This could inform both method developers and practitioners seeking to integrate complementary data sources without pooling raw records.

major comments (2)
  1. [Abstract and Results] Abstract and Results: The abstract states that equivalence 'was not systematically addressed' yet concludes that most methods do not achieve results equivalent to centralized analyses. Clarify in the methods or results how non-equivalence was determined when papers did not address it (e.g., whether absence of reporting was coded as failure), and provide the explicit coding rubric or supplementary extraction table used for the 30 included studies.
  2. [Results] Results: Only a minority of articles provided privacy assessments, yet almost all described their approach as privacy-preserving and the headline finding states that most methods lack 'guaranteed protection.' Specify the criteria applied to evaluate privacy guarantees (self-description versus formal assessment) and how this was operationalized across heterogeneous reporting standards.
minor comments (1)
  1. [Methods] Methods: Expand the description of the citation screening process and any quality or risk-of-bias considerations applied to the included methods, even if formal bias tools were not used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for these constructive comments, which identify opportunities to improve transparency in our methods and results. We provide point-by-point responses below and will revise the manuscript to include explicit documentation of our coding process.

read point-by-point responses

  1. Referee: [Abstract and Results] Abstract and Results: The abstract states that equivalence 'was not systematically addressed' yet concludes that most methods do not achieve results equivalent to centralized analyses. Clarify in the methods or results how non-equivalence was determined when papers did not address it (e.g., whether absence of reporting was coded as failure), and provide the explicit coding rubric or supplementary extraction table used for the 30 included studies.

    Authors: We thank the referee for noting this ambiguity. Equivalence was coded only when papers explicitly addressed it (via theoretical proofs of identical estimators or empirical demonstrations of numerical equivalence to pooled results). Papers that omitted any discussion of equivalence were coded strictly as 'not addressed' and were not counted as non-equivalent. The headline conclusion that most methods fail to achieve equivalence is drawn from the subset of papers that did evaluate it (where the majority fell short) together with the observation that unverified methods cannot be assumed equivalent. We will add a supplementary extraction table and a detailed coding rubric in the revised methods section that lists, for each of the 30 studies, the exact status recorded for equivalence, number of communication rounds, and privacy evaluation. revision: yes

  2. Referee: [Results] Results: Only a minority of articles provided privacy assessments, yet almost all described their approach as privacy-preserving and the headline finding states that most methods lack 'guaranteed protection.' Specify the criteria applied to evaluate privacy guarantees (self-description versus formal assessment) and how this was operationalized across heterogeneous reporting standards.

    Authors: We agree that the distinction requires explicit statement. 'Guaranteed protection' was operationalized as the presence of a formal assessment (differential privacy bounds, cryptographic security proofs, or empirical attack-resistance evaluations). Self-descriptions such as 'privacy-preserving' or 'secure' without accompanying formal analysis were recorded but did not qualify as guaranteed protection. This rule was applied uniformly by examining the methods and results sections of each paper. We will revise the methods section to state these criteria verbatim and will add illustrative examples in the results to show how heterogeneous reporting was classified. revision: yes

Circularity Check

0 steps flagged

Scoping review of vertical inference methods contains no derivations or predictions

full rationale

The paper is a descriptive scoping review that screens 2887 articles, includes 30, and extracts methodological properties (equivalence to pooled analysis, communication rounds, privacy assessments) from external literature. It performs no mathematical derivations, statistical predictions, parameter fitting, or modeling steps. No equations, ansatzes, or self-citation chains are used to justify central claims; the characterization follows directly from the screening and coding protocol applied to independent papers. The skeptic concern about heterogeneous reporting affects the strength of the synthesis but does not create circularity within the paper's own logic.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As a scoping review the paper introduces no new free parameters, axioms, or invented entities; it only summarizes properties reported in prior methodological papers.

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