An approximate-copula distribution for statistical modeling.

Sarah S Ji, Benjamin B Chu, Hua Zhou, Kenneth Lange

Abstract read

In one paragraph

Article in PLoS computational biology, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

0numbers the graph read from it

0cells of the map it votes in

0citing papers in PubMed

–field-weighted citation impact

1 · What the graph read from it

What it found

Each row is one number read from the abstract, on the scale the paper reported it, with its interval. Left of the dashed line favours the treatment, right favours the comparator. Under each row is the sentence it came from. New to these charts? A ten-minute tutorial.

The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.

2 · The registry

The trial behind it

Trials whose registry record cites this paper, or whose number appears in the abstract. A trial that started after this paper was published is citing it as background, not reporting it.

Neither the registry nor the abstract names a trial number. If this is a trial report, that itself is worth knowing.

3 · Its place in the literature

Who cites it

0 citing papers in PubMed.

No citing paper in PubMed yet.

4 · The record

Corrections and comments

PubMed lists nothing against this paper. Absence here is not a guarantee, only a check that was made.

5 · Who and what money

Authors and funding

4 authors.

Sarah S JiDepartment of Biostatistics, University of California, Los Angeles, Los Angeles, California, United States of America.ORCID https://orcid.org/0000-0001-7265-4861

Benjamin B ChuDepartment of Biomedical Data Science, Stanford University, Stanford, California, United States of America.ORCID https://orcid.org/0000-0001-8342-2361

Hua ZhouDepartment of Biostatistics, University of California, Los Angeles, Los Angeles, California, United States of America.

Kenneth LangeDepartment of Computational Medicine, University of California, Los Angeles, Los Angeles, California, United States of America.

Funding

No grant is acknowledged in the PubMed record.

6 · The paper itself

Abstract

Copulas, generalized estimating equations, and generalized linear mixed models promote the analysis of grouped data where non-normal responses are correlated. Unfortunately, parameter estimation remains challenging in these three frameworks. Based on prior work of Tonda, we derive a new class of probability density functions that allow explicit calculation of moments, marginal and conditional distributions, and the score and observed information needed in maximum likelihood estimation. We also illustrate how the new distribution flexibly models longitudinal data following a non-Gaussian distribution. Finally, we conduct a tri-variate genome-wide association analysis on dichotomized systolic and diastolic blood pressure and body mass index data from the UK-Biobank, showcasing the modeling potential and computational scalability of the new distributional family.

Indexed as

Models, StatisticalAlgorithmsBlood PressureBody Mass IndexComputational BiologyComputer SimulationGenome-Wide Association StudyHumansLikelihood Functions

Identifiers

PMID41824477

DOI10.1371/journal.pcbi.1013922

PMCPMC12998956

What OpenQuestion holds

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Registered trials

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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.