AGATA

# Variability metrics

# meanGlucose

function meanGlucose = meanGlucose(data)

Function that computes the mean glucose concentration (ignores nan values).

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • meanGlucose: double
    Mean glucose concentration (mg/dl).

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Wikipedia on mean: https://en.wikipedia.org/wiki/Mean (Accessed: 2020-12-10).

# stdGlucose

function stdGlucose = stdGlucose(data)

Function that computes the standard deviation of the glucose concentration (ignores nan values).

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • stdGlucose: double
    Standard deviation of the glucose concentration (mg/dl).

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Wikipedia on standard deviation: https://en.wikipedia.org/wiki/Standard_deviation (Accessed: 2020-12-10).

# cvGlucose

function cvGlucose = cvGlucose(data)

Function that computes the coefficient of variation of the glucose concentration (ignores nan values).

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • cvGlucose: double
    Coefficient of variation of the glucose concentration (%).

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Wikipedia on coefficient of variation: https://en.wikipedia.org/wiki/Coefficient_of_variation (Accessed: 2020-12-10).

# medianGlucose

function medianGlucose = medianGlucose(data)

Function that computes the median glucose concentration (ignores nan values).

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • medianGlucose: double
    Median glucose concentration (mg/dl).

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Wikipedia on median: https://en.wikipedia.org/wiki/Median (Accessed: 2020-12-10).

# rangeGlucose

function rangeGlucose = rangeGlucose(data)

Function that computes the range spanned by the glucose concentration (ignores nan values).

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • rangeGlucose: double
    Range spanned by the glucose concentration (%).

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Wikipedia on range: https://en.wikipedia.org/wiki/Range_(statistics) (Accessed: 2020-12-10).

# iqrGlucose

function iqrGlucose = iqrGlucose(data)

Function that computes the interquartile range of the glucose concentration (ignores nan values).

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • iqrGlucose: double
    Interquartile range of the glucose concentration (mg/dl).

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Wikipedia on IQR: https://en.wikipedia.org/wiki/Interquartile_range (Accessed: 2020-12-10).

# jIndex

function jIndex = jIndex(data)

Function that computes the J-Index of the glucose concentration (ignores nan values).

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • jIndex: double
    J-Index of the glucose concentration (mg/dl).

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Wójcicki, "J-index. A new proposition of the assessment of current glucose control in diabetic patients", Hormone and Metabolic Reseach, 1995, vol. 27, pp. 41-42. DOI: 10.1055/s-2007-979906.

# aucGlucose

function aucGlucose = aucGlucose(data)

Function that computes the area under the curve (AUC) of glucose concentration (ignores nan values), i.e., the area between the glucose trace and zero. It assumes that the glucose value between two samples is constant.

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • aucGlucose: double
    The area under the curve of glucose concentration (mg/dl*min).

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Wikipedia on AUC: https://en.wikipedia.org/wiki/Integral (Accessed: 2020-12-10).

# aucGlucoseOverBasal

function aucGlucoseOverBasal = aucGlucoseOverBasal(data,basal)

Function that computes the area under the curve (AUC) of glucose concentration over a basal value (ignores nan values). This means that glucose values above the given basal value will sum up positive AUC, while glucose values below the given basal value will sum up in negative AUC. It assumes that the glucose value between two samples is constant.

# Inputs

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl);
  • basal: double (required)
    A double defining the basal value to use (mg/dl).

# Output

  • aucGlucoseOverBasal: double
    The area under the curve of glucose concentration (mg/dl*min) over the basal value.

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Wikipedia on AUC: https://en.wikipedia.org/wiki/Integral (Accessed: 2020-12-10).

# gmi

function gmi = gmi(data)

Function that computes the glucose management indicator (GMI) of the given data (ignores nan values). Generates a warning if the given data spans less than 12 days.

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • gmi: double
    Glucose management indicator of the given data (%).

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Bergenstal et al., "Glucose Management Indicator (GMI): A new term for estimating A1C from continuous glucose monitoring", Diabetes Care, 2018, vol. 41, pp. 2275-2280. DOI: 10.2337/dc18-1581.

# sddmIndex

function sddmIndex = sddmIndex(data)

Function that computes the standard deviation of within-day means index (SDDM) (ignores nan values).

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • sddmIndex: double
    The standard deviation of within-day means index (SDDM) index.

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Rodbard et al., "New and improved methods to characterize glycemic variability using continuous glucose monitoring", Diabetes Technology & Therapeutics, 2009, vol. 11, pp. 551-565. DOI: 10.1089/dia.2009.0015.

# sdwIndex

function sdwIndex = sdwIndex(data)

Function that computes the mean of within-day standard deviation index (SDW) (ignores nan values).

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • sdwIndex: double
    The mean of within-day standard deviation (SDW) index.

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Rodbard et al., "New and improved methods to characterize glycemic variability using continuous glucose monitoring", Diabetes Technology & Therapeutics, 2009, vol. 11, pp. 551-565. DOI: 10.1089/dia.2009.0015.

# mageIndex

function mageIndex = mageIndex(data)

Function that computes the mean amplitude of glycemic excursion (MAGE) index (ignores nan values).

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • mageIndex: double
    The mean amplitude of glycemic excursion (MAGE) index.

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Service et al., "Mean amplitude of glycemic excursions, a measure of diabetic instability", Diabetes, 1970, vol. 19, pp. 644-655. DOI: 10.2337/diab.19.9.644.

# magePlusIndex

function magePlusIndex = magePlusIndex(data)

Function that computes the mean amplitude of positive glycemic excursion (MAGE+) index (ignores nan values).

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • magePlusIndex: double
    The mean amplitude of positive glycemic excursion (MAGE+) index.

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Service et al., "Mean amplitude of glycemic excursions, a measure of diabetic instability", Diabetes, 1970, vol. 19, pp. 644-655. DOI: 10.2337/diab.19.9.644.

# mageMinusIndex

function mageMinusIndex = mageMinusIndex(data)

Function that computes the mean amplitude of negative glycemic excursion (MAGE-) index (ignores nan values).

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • mageMinusIndex: double
    The mean amplitude of negative glycemic excursion (MAGE-) index.

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Service et al., "Mean amplitude of glycemic excursions, a measure of diabetic instability", Diabetes, 1970, vol. 19, pp. 644-655. DOI: 10.2337/diab.19.9.644.

# efIndex

function efIndex = efIndex(data)

Function that computes the excursion frequency (EF) index, i.e., the number of excursion > 75 (ignores nan values).

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • efIndex: double
    The excursion frequency (EF) index.

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Service et al., "Mean amplitude of glycemic excursions, a measure of diabetic instability", Diabetes, 1970, vol. 19, pp. 644-655. DOI: 10.2337/diab.19.9.644.

# CVGA

function [profileAssessment,profileCoordinates, bestControlIndex, bestControlledCoordinates]=CVGA(glucoseProfiles)

Function that performs the control variablity grid analysis (CVGA).

# Input

  • glucoseProfiles: cell array of timetable (required)

    A cell array of timetables each with column Time and glucose containing the glucose data to analyze (in mg/dl).

# Outputs

  • profileAssessment: vector of double
    A vector of double containing, for each timetable in glucoseProfiles, the euclidian distance of each point in the CVGA space from the CVGA origin;
  • profileCoordinates: bidimensional vector of double
    A bidimensional vector containing in the first column the CVGA coordinate in the x-axis and in the second column the CVGA coordinate in the y-axis of each glucose profile;
  • bestControlIndex: integer
    An integer containing the index of the best glucose profile (i.e., the glucose profile with minimum profileAssessment value);
  • bestControlledCoordinates: bidimensional vector of double
    A bidimensional vector containing in the first column the CVGA coordinate in the x-axis and in the second column the CVGA coordinate in the y-axis of the best glucose profile (i.e., the glucose profile with minimum profileAssessment value).

# Preconditions

  • glucoseProfiles must be a cell array containing timetables;
  • Each timetable in glucoseProfiles must have a column names Time and a column named glucose.

# Reference

  • Magni et al., "Evaluating the efficacy of closed-loop glucose regulation via control-variability grid analysis", Journal of Diabetes Science and Technology, 2008, vol. 2, pp. 630-635. DOI: 10.1177/193229680800200414.

# conga

function conga = conga(data)

Function that computes the Continuous Overall Net Glycemic Action (CONGA) index.

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • conga: double
    Continuous Overall Net Glycemic Action (CONGA) index.

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • McDonnell et al., "A novel approach to continuous glucose analysis utilizing glycemic variation. Diabetes Technol Ther, 2005, vol. 7, pp. 253–263. DOI: 10.1089/dia.2005.7.253.

# modd

function modd = modd(data)

Function that computes the mean of daily difference (MODD) index.

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • modd: double
    Mean of daily difference (MODD) index.

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Molnar et al., "Day-to-day variation of continuously monitored glycaemia: a further measure of diabetic instability", Diabetologia, 1972, vol. 8, pp. 342–348. DOI: 10.1007/BF01218495.

# poincareGlucose

function poincareGlucose = poincareGlucose(data)

Function that fits an ellipse corresponding to the Poincare' plot of the (x,y) = (glucose(t-1),glucose(t)) graph. To do so, it uses the least square method. If an ellipse was not detected (but a parabola or hyperbola), then an empty structure is returned.

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • poincareGlucose: structure
    A structure with fields containing the parameter of the fitted Poincare' ellipse, i.e.:
    • a: sub axis (radius) of the X axis of the non-tilt ellipse;
    • b: sub axis (radius) of the Y axis of the non-tilt ellipse;
    • phi: sub axis (radius) of the X axis of the non-tilt ellipse;
    • X0: center at the X axis of the non-tilt ellipse;
    • Y0: center at the Y axis of the non-tilt ellipse;
    • X0_in: center at the X axis of the tilted ellipse;
    • Y0_in: center at the Y axis of the tilted ellipse;
    • long_axis: size of the long axis of the ellipse;
    • short_axis: size of the short axis of the ellipse;
    • status: status of detection of an ellipse;

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Clarke et al., "Statistical Tools to Analyze Continuous Glucose Monitor Data", Diabetes Technol Ther, 2009, vol. 11, pp. S45-S54. DOI: 10.1089=dia.2008.0138.
  • Based on fit_ellipse function by Ohad Gal. https://it.mathworks.com/matlabcentral/fileexchange/3215-fit_ellipse

# glucoseROC

function glucoseROC = glucoseROC(data)

Function that computes the glucose rate-of-change (ROC) trace. As defined in the given reference, ROC at time t is defined as the difference between the glucose at time t and t-15 minutes divided by 15 (ignores nan values). By definition, the first two samples are always nan.

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • glucoseROC: timetable
    A timetable with column Time and glucoseROC containing the glucose ROC (in mg/dl/min).

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Clarke et al., "Statistical Tools to Analyze Continuous Glucose Monitor Data", Diabetes Technol Ther, 2009, vol. 11, pp. S45-S54. DOI: 10.1089=dia.2008.0138.

# stdGlucoseROC

function stdGlucoseROC = stdGlucoseROC(data)

Function that computes the standard deviation of the glucose ROC (ignores nan values).

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • stdGlucoseROC: double
    Standard deviation of the glucose ROC.

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Clarke et al., "Statistical Tools to Analyze Continuous Glucose Monitor Data", Diabetes Technol Ther, 2009, vol. 11, pp. S45-S54. DOI: 10.1089=dia.2008.0138.

# cogi

function cogi = cogi(data)

Function that computes the Continuous Glucose Monitoring Index (COGI) (ignores nan values).

# Input

  • data: timetable (required)
    A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl).

# Output

  • cogi: double
    the COGI index.

# Preconditions

  • data must be a timetable having an homogeneous time grid;
  • data must contain a column named Time and another named glucose.

# Reference

  • Leelaranthna et al., "Evaluating glucose control with a novel composite Continuous Glucose Monitoring Index", Journal of Diabetes Science and Technology, 2019, vol. 14, pp. 277-283. DOI: 10.1177/1932296819838525.

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