{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Cosinor analysis with pyActigraphy\n", "This notebook illustrates how to perform a single-component Cosinor analysis on actigraphy data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The idea of a Cosinor analysis is to estimate some key parameters of the actigraphy count series by fitting these data with a (co)sine curve with a period of 24h:\n", "$$ Y(t) = M + A*cos(\\frac{2\\pi}{T}*t + \\phi)$$\n", "where M is the MESOR (Midline Statistic Of Rhythm), A is the amplitude of the oscillations, T is the period and $\\phi$ is the acrophase." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then, the fit procedure provides estimates of these parameters which can then help to characterize the 24h rest-activity rhythm of an individual." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, despite its popularity in circadian rhythm analyses, the Cosinor analysis exhibits some short-comings when dealing with non-stationary signals such as actigraphy signals. Intuitively, such model with a fixed period, amplitude and offset cannot accomodate signals with:\n", "\n", "* rest-activity cycles that do not follow a perfect 24h period;\n", "* an overall daily activity that changes on a day-by-day basis;\n", "* an overall activity trend that evolves with time." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For more informations on the topic:\n", "\n", "Leise, T. L., & Harrington, M. E. (2011). *Wavelet-Based Time Series Analysis of Circadian Rhythms*. Journal of Biological Rhythms, 26(5), 454–463. https://doi.org/10.1177/0748730411416330" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For a nice comparison of several techniques, including Cosinor and SSA (available in pyActigraphy):\n", "\n", "Fossion, R., Rivera, A. L., Toledo-Roy, J. C., Ellis, J., & Angelova, M. (2017). *Multiscale adaptive analysis of circadian rhythms and intradaily variability: Application to actigraphy time series in acute insomnia subjects*. PLOS ONE, 12(7), e0181762. https://doi.org/10.1371/journal.pone.0181762" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Import packages and input data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, load your favourite python packages:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2023-01-30T15:44:14.764960Z", "start_time": "2023-01-30T15:44:13.329882Z" } }, "outputs": [], "source": [ "import pyActigraphy" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2023-01-30T15:44:14.768091Z", "start_time": "2023-01-30T15:44:14.766267Z" } }, "outputs": [], "source": [ "import plotly.graph_objects as go" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us now define the path to the example data files contained in the pyActigraphy package:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2023-01-30T15:44:14.771567Z", "start_time": "2023-01-30T15:44:14.769574Z" } }, "outputs": [], "source": [ "import os\n", "fpath = os.path.join(os.path.dirname(pyActigraphy.__file__),'tests/data/')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cosinor analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, simply import the Cosinor module:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2023-01-30T15:44:14.774536Z", "start_time": "2023-01-30T15:44:14.772880Z" }, "cell_style": "center" }, "outputs": [], "source": [ "from pyActigraphy.analysis import Cosinor" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "... and define a Cosinor object:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2023-01-30T15:44:14.779978Z", "start_time": "2023-01-30T15:44:14.775516Z" } }, "outputs": [], "source": [ "cosinor = Cosinor()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Initial fit values" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By default, the initial values of the cosine fit functions are the following:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2023-01-30T15:44:14.784367Z", "start_time": "2023-01-30T15:44:14.781405Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Name Value Min Max Stderr Vary Expr Brute_Step\n", "Acrophase 3.142 0 6.283 None True None None\n", "Amplitude 50 0 inf None True None None\n", "Mesor 50 0 inf None True None None\n", "Period 1440 0 inf None True None None\n" ] } ], "source": [ "cosinor.fit_initial_params.pretty_print()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These parameters will be estimated from the data. However, in order to ease the fit procedure, it makes sense to start from reasonable values.\n", "For example, the initial value for the period is set to 1440, the number of minutes per day. It makes only sense for data with a 1-min sampling frequency. \n", "\n", "However, it is trivial to change these intial values. \n", "\n", "For example, let's change the initial value of the period to 2880, in case you would like to analyse data with a 30-sec sampling frequency:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2023-01-30T15:44:14.787774Z", "start_time": "2023-01-30T15:44:14.785662Z" } }, "outputs": [], "source": [ "cosinor.fit_initial_params['Period'].value = 2880" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2023-01-30T15:44:14.793100Z", "start_time": "2023-01-30T15:44:14.790567Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Name Value Min Max Stderr Vary Expr Brute_Step\n", "Acrophase 3.142 0 6.283 None True None None\n", "Amplitude 50 0 inf None True None None\n", "Mesor 50 0 inf None True None None\n", "Period 2880 0 inf None True None None\n" ] } ], "source": [ "cosinor.fit_initial_params.pretty_print()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Free and fixed fit parameters" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By default, none of the fit parameters are fixed and will be estimated from the data. However, in some cases, it might be convenient to fix the initial of a parameter and not let it vary during the fit procedure." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It might be the case of the period for instance. Let us fix it to 1440." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2023-01-30T15:44:14.799900Z", "start_time": "2023-01-30T15:44:14.797270Z" } }, "outputs": [], "source": [ "cosinor.fit_initial_params['Period'].value = 1440" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2023-01-30T15:44:14.805387Z", "start_time": "2023-01-30T15:44:14.802849Z" } }, "outputs": [], "source": [ "cosinor.fit_initial_params['Period'].vary = False" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2023-01-30T15:44:14.809074Z", "start_time": "2023-01-30T15:44:14.806424Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Name Value Min Max Stderr Vary Expr Brute_Step\n", "Acrophase 3.142 0 6.283 None True None None\n", "Amplitude 50 0 inf None True None None\n", "Mesor 50 0 inf None True None None\n", "Period 1440 0 inf None False None None\n" ] } ], "source": [ "cosinor.fit_initial_params.pretty_print()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is also possible to apply lower and upper bounds to these parameters.\n", "\n", "For more informations about these parameters, please see: https://lmfit.github.io/lmfit-py/parameters.html" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Analysis of a single subject" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Read data from an example file..." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2023-01-30T15:44:14.825753Z", "start_time": "2023-01-30T15:44:14.810270Z" } }, "outputs": [], "source": [ "raw = pyActigraphy.io.read_raw_awd(fpath+'example_01.AWD', start_time='1918-01-24 08:30:00', period=\"7D\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "... and plot it for visual inspection:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2023-01-30T15:44:14.865564Z", "start_time": "2023-01-30T15:44:14.826722Z" } }, "outputs": [], "source": [ "fig = go.Figure(go.Scatter(x=raw.data.index.astype(str),y=raw.data))" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2023-01-30T15:44:15.014459Z", "start_time": "2023-01-30T15:44:14.866848Z" } }, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "type": "scatter", "x": [ "1918-01-24 08:30:00", "1918-01-24 08:31:00", "1918-01-24 08:32:00", "1918-01-24 08:33:00", "1918-01-24 08:34:00", "1918-01-24 08:35:00", "1918-01-24 08:36:00", "1918-01-24 08:37:00", "1918-01-24 08:38:00", "1918-01-24 08:39:00", "1918-01-24 08:40:00", "1918-01-24 08:41:00", "1918-01-24 08:42:00", "1918-01-24 08:43:00", "1918-01-24 08:44:00", "1918-01-24 08:45:00", "1918-01-24 08:46:00", 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\n", " | Amplitude | \n", "Acrophase | \n", "Period | \n", "Mesor | \n", "BIC | \n", "RedChiSq | \n", "
---|---|---|---|---|---|---|
example_04 | \n", "7.345742e+01 | \n", "0.927315 | \n", "1440 | \n", "81.733231 | \n", "321025.485636 | \n", "28448.100307 | \n", "
example_05 | \n", "1.352039e+02 | \n", "5.472072 | \n", "1440 | \n", "120.821941 | \n", "225115.967014 | \n", "31930.970729 | \n", "
example_02 | \n", "5.711733e-08 | \n", "3.032968 | \n", "1440 | \n", "183.388579 | \n", "207392.482663 | \n", "77803.026821 | \n", "
example_03 | \n", "3.381232e+02 | \n", "6.240036 | \n", "1440 | \n", "346.219095 | \n", "171305.166394 | \n", "146324.160952 | \n", "
example_01 | \n", "1.577049e+02 | \n", "4.750332 | \n", "1440 | \n", "171.007640 | \n", "143499.394878 | \n", "64194.285808 | \n", "
example_01_mask | \n", "1.266343e-07 | \n", "2.986621 | \n", "1440 | \n", "127.565387 | \n", "202689.738565 | \n", "60700.671139 | \n", "