# Centered Isotonic Regression: Point and Interval Estimation for Dose-Response Studies

arXiv: https://arxiv.org/abs/1701.05964 · HTML: https://mlsanity.com/paper/1701.05964/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2017.

## Built on by (most cited first, 5 of 5)

- [Benchmarking Uncertainty Quantification Methods for Large Language Models with LM-Polygraph](https://mlsanity.com/paper/2406.15627/) (2024)
- [Rethinking Early Stopping: Refine, Then Calibrate](https://mlsanity.com/paper/2501.19195/) (2025)
- [Stratification of uncertainties recalibrated by isotonic regression and its impact on calibration error statistics](https://mlsanity.com/paper/2306.05180/) (2023)
- [CalArena: A Large-Scale Post-Hoc Calibration Benchmark](https://mlsanity.com/paper/2605.30188/) (2026)
- [Shared Doubt: Zero-Shot Cross-Lingual Confidence Estimation for Language Models](https://mlsanity.com/paper/2605.31220/) (2026)

## Abstract (arXiv)

Univariate isotonic regression (IR) has been used for nonparametric estimation in dose-response and dose-finding studies. One undesirable property of IR is the prevalence of piecewise-constant stretches in its estimates, whereas the dose-response function is usually assumed to be strictly increasing. We propose a simple modification to IR, called centered isotonic regression (CIR). CIR's estimates are strictly increasing in the interior of the dose range. In the absence of monotonicity violations, CIR and IR both return the original observations. Numerical examination indicates that for sample sizes typical of dose-response studies and with realistic dose-response curves, CIR provides a substantial reduction in estimation error compared with IR when monotonicity violations occur. We also develop analytical interval estimates for IR and CIR, with good coverage behavior. An R package implements these point and interval estimates.