README

A pure-PHP biostatistics library implementing descriptive, bivariate and multivariate methods for survey-based epidemiological studies — including logistic regression, VIF, Box–Tidwell, GLMM, GEE, MICE and Rubin's pooling.

📖 Overview

biostat-php brings the analytic side of a cross-sectional epidemiological study to PHP. It implements, in pure PHP and without external dependencies, the same family of statistical methods normally available only in R (stats, car, lme4, geepack, mice) or SPSS.

The library was extracted from a real research instrument — a trilingual data-collection platform used to study adolescent overweight in the Wilaya of Chlef, Algeria — where it ran the 48 pre-registered hypotheses of the underlying master thesis on a low-cost shared-hosting environment that did not allow R or Python.

Every method is cross-checked against R 4.x and IBM SPSS 25; the quantitative comparison is documented in docs/validation-tables.md and exercised by the PHPUnit suite in tests/.

🚀 Installation

composer require touilelhadj/biostat-php

Requirements:

PHP ≥ 8.0
No external PHP extension beyond the defaults (mbstring, json only for the test fixtures)
No system library, no Composer dependency at runtime

⚡ Quick start

<?php
require_once __DIR__ . '/vendor/autoload.php';

use TouilElhadj\BiostatPhp\BiostatAnalysis;

$stats = new BiostatAnalysis();

// Two-by-two table: 45 exposed cases, 18 exposed non-cases,
//                   30 unexposed cases, 22 unexposed non-cases.
$chi = $stats->chi2Test2x2(45, 18, 30, 22);
echo "chi² = {$chi['chi2']}, p = {$chi['p']}\n";
//      chi² = 1.8027, p = 0.1794

$or = $stats->oddsRatio(45, 18, 30, 22);
echo "OR = {$or['or']} [{$or['ci_low']}, {$or['ci_high']}]\n";
//      OR = 1.83 [0.84, 3.98]

// Welch's t-test
$t = $stats->tTest(
    [10, 12, 11, 13, 14, 12, 11],
    [15, 17, 16, 18, 16, 17, 15]
);
echo "t = {$t['t']}, df = {$t['df']}, p = {$t['p']}\n";

// Logistic regression (one continuous covariate)
$y = [0,0,0,1,1,1,1,1,0,1,1,0,1,1,1,0,0,1,1,1];
$x = [1,1,2,2,3,3,4,4,1,2,3,4,5,5,4,2,1,3,4,5];
$lr = $stats->logisticRegression($y, $x);
echo "OR = {$lr['or']}, p = {$lr['p']}\n";

// Benjamini–Hochberg FDR adjustment
$adj = BiostatAnalysis::benjaminiHochberg([0.001, 0.01, 0.04, 0.2, 0.5]);
//   [0.005, 0.025, 0.067, 0.25, 0.5]

More examples — including GLMM and MICE — are in examples/. A complete per-method walkthrough with R-equivalent commands is in docs/usage-examples.md.

🧪 Method catalogue

Family	Methods
Descriptive	`mean`, `std`, `median`, `quantile`
2 × 2 tables	`chi2Test2x2` (with Yates), `oddsRatio` (with Haldane–Anscombe)
Means	`tTest` (Welch), `anova`
Correlation	`pearson`, `spearman`
Binomial	`binomialTest`
Logistic regression	`logisticRegression`, `logisticRegressionMulti`, `hosmerLemeshow`
Multiple testing	`benjaminiHochberg` (FDR)
Multicollinearity	`vif`
Logit linearity	`boxTidwell`
Mixed / clustered	`glmmLogistic` (PQL), `geeLogistic` (Liang–Zeger sandwich)
Missing data	`mice` (PMM + chained Gibbs), `rubinPool` (Rubin's rules)

Mathematical formulations and bibliographic references for every method are in docs/statistical-methods.md.

✅ Verification

Reference values for every method were computed independently in R 4.3.0 and IBM SPSS 25. The tolerances used in the test suite are:

Family	Tolerance
p-values	± 0.01
Odds ratios	± 0.01
Correlation coefficients	± 0.001
Regression coefficients	± 0.05
Variance components (GLMM)	± 0.05

A complete numerical comparison table — R command, R value, PHP value, |Δ| — lives in docs/validation-tables.md.

🧰 Running the tests

composer install
composer test                      # run PHPUnit
composer test:coverage             # with HTML coverage report
composer analyse                   # PHPStan level 6
composer cs                        # PSR-12 check

📁 Repository layout

biostat-php/
├── src/
│   ├── BiostatAnalysis.php       main class (≈ 1 460 LOC)
│   ├── LinearAlgebra.php         matMul / transpose / OLS  (trait)
│   ├── Distributions.php         normal / χ² / t / F CDFs  (trait)
│   └── Exceptions/
│       └── ConvergenceException.php
├── tests/                        PHPUnit tests against R reference values
├── docs/
│   ├── statistical-methods.md    formal mathematical specification
│   ├── validation-tables.md      R vs PHP numerical comparison
│   └── usage-examples.md         worked example per public method
├── examples/                     stand-alone runnable scripts
├── composer.json                 PSR-4 autoload + dev tools
├── phpunit.xml                   PHPUnit configuration
├── paper.md                      JOSS paper (≈ 1 000 words)
├── paper.bib                     BibTeX references
├── CITATION.cff                  machine-readable citation
├── LICENSE                       MIT
└── README.md

📚 Citation

If you use this library in a research publication, please cite it. A machine-readable citation file is provided in CITATION.cff.

Recommended citation

TOUIL, E. (2026). biostat-php: a pure-PHP biostatistics library for survey-based epidemiological studies. Version 1.0.0. https://github.com/Touil-Elhadj/biostat-php

BibTeX

@software{touil_biostat_php_2026,
  author       = {TOUIL, Elhadj},
  title        = {biostat-php: a pure-PHP biostatistics library for
                  survey-based epidemiological studies},
  year         = {2026},
  version      = {1.0.0},
  url          = {https://github.com/Touil-Elhadj/biostat-php}
}

🌍 Real-world use

biostat-php is the analytic engine of the chlef-touilelhadj platform, a trilingual web instrument used to enrol 1 220 adolescents (14–19 years) in the Wilaya of Chlef, Algeria, during the 2025–2026 academic year. All statistical results of the underlying master thesis were produced by this library and independently verified against R 4.x and SPSS 25.

🤝 Contributing

Contributions are welcome — see CONTRIBUTING.md for the development workflow and the statistical-contribution checklist (every new method must ship with a closed-form reference value from R or SPSS plus a PHPUnit assertion).

🛡 Security

To report a vulnerability please follow the procedure in SECURITY.md.

touilelhadj / biostat-php

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