dlmoR: An open-source R package for the dim-light melatonin onset (DLMO) hockey-stick method

The dim-light melatonin onset (DLMO) is the gold-standard marker researchers use to time a person's internal circadian clock — essentially pinpointing when the brain begins releasing melatonin at night. One widely-used way to calculate DLMO from a series of melatonin measurements is the 'hockey-stick' method, originally published by Danilenko and colleagues in 2014 and distributed only as a closed-source binary program. This paper introduces dlmoR, a free, open-source R package that re-implements the hockey-stick algorithm transparently, so any researcher can inspect, modify, and reuse the code. The authors validated dlmoR against 112 melatonin time-series datasets from two independent studies, finding excellent agreement with the original program — mean timing differences of roughly 1–1.5 minutes and circular correlations above 0.96. Beyond replication, dlmoR adds new features the original lacked: interactive visual diagnostics and bootstrapped confidence intervals that quantify estimation uncertainty. The authors also used the package's flexibility to stress-test the algorithm, deliberately perturbing sampling schedules, noise levels, and data completeness, revealing that moderate disturbances keep DLMO estimates within ±10 minutes but severe disturbances can shift estimates by more than 40 minutes or make estimation impossible. The work ultimately argues that current DLMO methods lack formal uncertainty quantification and calls for a new generation of uncertainty-aware estimation approaches.

• dlmoR showed mean timing discrepancies of −1.482 ± 21.7 min versus the reference executable on the Heinrichs & Spitschan (2025) dataset and 1.165 ± 28.5 min on the Blume et al. (2024) dataset, with paired t-tests (p > 0.05) confirming no systematic bias.
• Circular correlation coefficients between dlmoR and the original binary were 0.964 and 0.986 across the two validation datasets (n = 112 total time series), indicating high agreement.
• Sensitivity analyses showed that small timing jitter, limited data loss, or modest threshold shifts kept DLMO estimates stable within ±10 min, whereas large multi-point data deletions, pronounced sampling-schedule changes, or substantial threshold alterations delayed estimates by over 40 min or prevented estimation entirely.
• dlmoR introduces bootstrapped confidence intervals and interactive visual diagnostics — capabilities absent from the original closed-source executable — enabling quantitative uncertainty assessment for each individual DLMO estimate.
• The stress-testing analysis exposed a fundamental structural limitation in the hockey-stick algorithm: its onset-window identification and melatonin-rise modelling are highly sensitive to data quality, underscoring the need for new uncertainty-aware DLMO estimation methods.

This is a software development and validation study. The authors wrote a clean-room R implementation of the Danilenko et al. (2014) hockey-stick DLMO algorithm, verified iteratively against the original binary executable. The package was benchmarked on 112 melatonin time-series datasets drawn from two pre-existing independent studies (Heinrichs & Spitschan 2025; Blume et al. 2024). Sensitivity analyses were conducted by systematically manipulating sampling schedules, threshold levels, data completeness, and noise levels in silico to characterise algorithmic robustness.

Because this is a software validation study rather than a clinical or physiological trial, it cannot speak to the biological accuracy of DLMO estimates — only their internal consistency with one reference algorithm. The large standard deviations around the mean discrepancies (±21–28 min) highlight that individual-level agreement can vary considerably even when group-level bias is absent. The study does not compare dlmoR against other DLMO methods (e.g., fixed-threshold or variable-threshold approaches), so relative performance across algorithms remains unknown. Future work should validate dlmoR estimates against gold-standard physiological endpoints (e.g., core body temperature minimum, cortisol awakening response) and develop the uncertainty-aware estimation framework the authors identify as necessary.

dlmoR sits at the methodological infrastructure layer of circadian biology: it directly enables the rigorous measurement of melatonin-based circadian phase that underpins research throughout this corpus. It extends [§97], a population-based lighting study in older adults, by providing a validated, reproducible tool for deriving the very circadian phase markers such studies depend upon. It parallels [§44], which examines the CLOCK-BMAL1 molecular circadian machinery, in that both works interrogate the precision and reliability of circadian timing — one at the molecular level, one at the measurement level. It also directly supports work like [§33] (the TREAD time-restricted eating intervention for Alzheimer's disease), where accurate, reproducible DLMO estimation is prerequisite for evaluating whether behavioural chronotherapy has shifted circadian timing. More broadly, the uncertainty quantification gaps the authors identify are relevant to any study in this corpus that uses melatonin as a circadian endpoint, including [§108] (chronic jet-lag and renal injury in mice), where misclassification of circadian phase due to algorithmic imprecision could confound outcome attribution.

• Population Based Lighting Study on Older Adults
  This population-based lighting study in older adults relies on circadian phase markers like DLMO as primary endpoints, making the measurement accuracy and reproducibility that dlmoR addresses directly relevant to interpreting its findings.
• The CLOCK-BMAL1 complex in circadian regulation: structure, mechanisms, and therapeutic targeting
  Examines the molecular architecture of the CLOCK-BMAL1 circadian oscillator, providing the mechanistic context within which DLMO — as a downstream output measure — is interpreted; comparing highlights the gap between molecular and phenotypic circadian assessment.
• TREAD: Time Restricted Eating Intervention for Alzheimer's Disease
  A time-restricted eating intervention trial for Alzheimer's disease that must measure circadian phase change as a primary outcome; the uncertainty and algorithmic sensitivity issues documented in dlmoR are directly applicable to interpreting whether DLMO shifts in such trials are real or artefactual.
• Effects of chronic jetlag on high-fat and high-fructose diet induced renal injury in mice
  Investigates chronic jet-lag effects in an animal model, where circadian misalignment is the independent variable; methodological precision in defining circadian phase onset is essential, and the sensitivity findings from dlmoR contextualise how phase-measurement error could confound such metabolic outcomes.