Cosinor

Cosinor analysis is a statistical method used to analyze rhythmic patterns in biological time-series data, especially circadian rhythms. It aims to determine whether measurements collected over time follow a regular, sinusoidal pattern and to characterize the rhythm with concise descriptors.

The standard single-harmonic cosinor model expresses the observed value y(t) as y(t) = M + A cos(ω t) + B sin(ω t), where ω = 2π/T and T is the assumed period (commonly 24 hours for circadian data). The model can also be written as y(t) = M + R cos(ω t − φ), where M is the mesor (midline around which the rhythm oscillates), R is the amplitude and φ is the acrophase (the time of peak). The derived parameters—mesor, amplitude, and acrophase—summarize the rhythm’s level, extent, and timing.

Estimation is typically performed by least squares fitting, with ω fixed for a chosen period or estimated over a predefined range. Confidence intervals and statistical tests assess whether the rhythm is significant compared to a flat line.

Applications span physiology, endocrinology, sleep research, pharmacology, and environmental biology. Cosinor analysis is used to study hormone secretion, body temperature, activity cycles, and drug effects, among other rhythmic phenomena. Data requirements include sufficient sampling across the cycle and attention to trends or missing data; the method assumes a sinusoidal shape and can be less suitable for highly non-sinusoidal or non-stationary patterns.

Extensions include multi-harmonic cosinor models and population-mean cosinor using linear mixed models. Software implementations exist in R, Python, and MATLAB, reflecting its broad use in chronobiology and related fields.