Efficient frequentist fractional polynomials for skewed dose-response and survival data: a variance-reducing alternative to OLS-FP

Serhii Zabolotnii

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arXiv · 2605.16846

Efficient frequentist fractional polynomials for skewed dose-response and survival data: a variance-reducing alternative to OLS-FP

Serhii Zabolotnii

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Abstract

Fractional polynomials (FP) are a standard tool for modelling nonlinear dose-response and covariate effects, implemented in the widely used mfp package. The conventional FP fit estimates its coefficients by ordinary least squares (OLS-FP), which is statistically inefficient when the regression errors are skewed or heavy-tailed, a common situation for survival times, concentrations and biomarkers. We present a drop-in replacement that keeps the identical FP model and design but estimates the coefficients with a moment-based score tuned to the residual skewness and kurtosis, giving a closed-form efficiency factor g2 = 1 - gamma3^2/(2+gamma4) relative to OLS-FP. Across skewed error laws the method reduces slope-coefficient variance by 10-20% for mildly skewed errors and up to roughly 60% for heavy-tailed log-normal errors, at realistic sample sizes, while keeping confidence-interval coverage close to nominal, and it reverts exactly to OLS-FP under symmetry, so it is never harmful when no gain is available. On the German Breast Cancer Study Group cohort it narrows the tumour-size confidence interval by 26% (bootstrap variance ratio 0.53 against the predicted 0.56), and a primary-biliary-cirrhosis cohort reproduces the gain. The estimator is closed-form, runs in milliseconds, and is released as a reproducible R package (pmm_fp in EstemPMM) with a one-command replication bundle; its core variance identity is machine-checked in Lean 4.

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Serhii Zabolotnii. 2026-05-16. Efficient frequentist fractional polynomials for skewed dose-response and survival data: a variance-reducing alternative to OLS-FP. https://arxiv.org/abs/2605.16846

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