arXiv subjects

Michael T. Gorczyca

Publications and source records attributed to Michael T. Gorczyca.

4 recordsLinked to original sources

arXiv2026

A Note on Harmonic Underspecification in Log-Normal Trigonometric Regression

Analysis of biological rhythm data often involves performing least squares trigonometric regression, which models the oscillations of a response over time as a sum of sinusoidal components. When the response is not normally distributed, an investigator will either transform the response before applying least squares trigonometric regression or extend trigonometric regression to a generalized linear model (GLM) framework. In this note, we compare these two approaches when the number of oscillation harmonics is underspecified. We assume data are sampled under an equispaced experimental design and that a log link function would be appropriate for a GLM. We show that when the response follows a generalized gamma distribution, least squares trigonometric regression with a log-transformed response, or log-normal trigonometric regression, produces unbiased parameter estimates for the oscillation harmonics, even when the number of oscillation harmonics is underspecified. In contrast, GLMs require correct specification to produce unbiased parameter estimates. We apply both methods to cortisol level data and find that only log-normal trigonometric regression produces parameter estimates that are invariant to the number of specified oscillation harmonics. Additionally, when a sufficiently large number of oscillation harmonics is specified, both methods produce identical parameter estimates for the oscillation harmonics.

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arXiv2025

Two-Stage Trigonometric Regression for Modeling Circadian Rhythms

Gene expression levels, hormone secretion, and internal body temperature each oscillate over an approximately 24-hour cycle, or display circadian rhythms. Many circadian biology studies have investigated how these rhythms vary across cohorts, uncovering associations between atypical rhythms and diseases such as cancer, metabolic syndrome, and sleep disorders. A challenge in analyzing circadian biology data is that the oscillation peak and trough times for a phenomenon differ across individuals. If these individual-level differences are not accounted for in trigonometric regression, which is prevalent in circadian biology studies, then estimates of the population-level amplitude parameters can suffer from attenuation bias. This attenuation bias could lead to inaccurate study conclusions. To address attenuation bias, we propose a refined two-stage (RTS) method for trigonometric regression given longitudinal data obtained from each individual participating in a study. In the first stage, the parameters of individual-level models are estimated. In the second stage, transformations of these individual-level estimates are aggregated to produce population-level parameter estimates for inference. Simulation studies show that our RTS method mitigates bias in parameter estimation, obtains greater statistical power, and maintains appropriate type I error control when compared to the standard two-stage (STS) method, which ignores individual-level differences in peak and trough times. The only exception for parameter estimation and statistical power occurs when the oscillation amplitudes are weak relative to random variability in the data and the sample size is small. Illustrations with cortisol level data and heart rate data show that our RTS method obtains larger population-level amplitude parameter estimates and smaller $p$-values for multiple hypothesis tests when compared to the STS method.

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arXiv2025

LassoRNet: Accurate dim-light melatonin onset time prediction from multiple blood tissue samples

Research on chemotherapy, heart surgery, and vaccines has indicated that the risks and benefits of a treatment could vary depending on the time of day it is administered. A challenge with performing studies on timing treatment administration is that the optimal treatment time is different for each patient, as it would be based on a patient's internal clock time (ICT) rather than the 24-hour day-night cycle time. Prediction methods have been developed to determine a patient's ICT based on biomarker measurements, which can be leveraged to personalize treatment time. However, these methods face two limitations. First, these methods are designed to output predictions given biomarker measurements from a single tissue sample, when multiple tissue samples can be collected over time. Second, these methods are based on linear modelling frameworks, which would not capture the potentially complex relationships between biomarkers and a patient's ICT. To address these two limitations, this paper introduces a recurrent neural network framework, which we refer to as LassoRNet, for predicting the ICT at which a patient's biomarkers are measured as well as the underlying offset between a patient's ICT and the 24-hour day-night cycle time, or that patient's dim-light melatonin onset (DLMO) time. A novel feature of LassoRNet is a proposed variable selection scheme that minimizes the number of biomarkers needed to predict ICT. We evaluate LassoRNet on three longitudinal circadian transcriptome study data sets where DLMO time was determined for each study participant, and find that it consistently outperforms state-of-the art in both ICT and DLMO time prediction. Notably, LassoRNet obtains a median absolute error of approximately one hour in ICT prediction and 30 to 40 minutes in DLMO time prediction, where DLMO time prediction is performed using three samples collected at sequential time points.

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arXiv2024

A mixed effects cosinor modelling framework for circadian gene expression

The cosinor model is frequently used to represent the oscillatory behavior of different genes over time. When data are collected from multiple individuals, the cosinor model is estimated with recorded gene expression levels and the 24 hour day-night cycle time at which gene expression levels are observed. However, the timing of many biological processes are based on individual-specific internal timing systems that are offset relative to day-night cycle time. When these individual-specific offsets are unknown, they pose a challenge in performing statistical analyses with a cosinor model. Specifically, when each individual participating in a study has a different offset, the parameter estimates of a population cosinor model obtained with day-night cycle time are attenuated. These attenuated parameter estimates also attenuate test statistics, which inflate type II error rates in identifying genes with oscillatory behavior. To address this attenuation bias, this paper proposes a method when data are collected in a longitudinal design. This method involves first estimating individual-specific and population cosinor models for each gene, and then translating the times at which an individual's gene expression levels are recorded based on the parameter estimates of these models. Simulation studies confirm that this method mitigates bias in estimation and inference. Illustrations with data from three circadian biology studies highlight that this method produces parameter estimates and test statistics akin to those obtained when each individual's offset is known.

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