# Analysis

# analyzeGlucoseProfile

function results = analyzeGlucoseProfile(data)

Function that computes the glycemic outcomes of a glucose profile.

# Input

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

# Output

results: structure
A structure with fields containing the computed metrics and stats in the glucose profile, i.e.:
- variabilityMetrics: a structure with fields containing the values of the computed variability metrics (i.e., {aucGlucose, CVGA, cogi, cvGlucose, efIndex, gmi, iqrGlucose, jIndex, mageIndex, magePlusIndex, mageMinusIndex, meanGlucose, medianGlucose, rangeGlucose, sddmIndex, sdwIndex, stdGlucose,conga,modd, stdGlucoseROC}) of the glucose profile;
- riskMetrics: a structure with fields containing the values of the computed risk metrics (i.e., {adrr, bgri, hbgi, lbgi, gri}) of the glucose profile;
- dataQualityMetrics: a structure with fields containing the values of the computed data quality metrics (i.e., {missingGlucosePercentage,numberDaysOfObservation}) of the glucose profile;
- timeMetrics: a structure with fields containing the values of the computed time related metrics (i.e., {timeInHyperglycemia, timeInL1Hyperglycemia, timeInL2Hyperglycemia, timeInHypoglycemia, timeInL1Hypoglycemia, timeInL2Hypoglycemia, timeInTarget, timeInTightTarget}) of the glucose profile;
- glycemicTransformationMetrics: a structure with fields containing the values of the computed glycemic transformed metrics (i.e., {gradeScore, gradeEuScore, gradeHyperScore, gradeHypoScore, hypoIndex, hyperIndex, igc, mrIndex}) of the glucose profile;
- eventMetrics: a structure with fields containing the values of the computed event related metrics (i.e., {hypoglycemicEvents, hyperglycemicEvents, extendedHypoglycemicEvents}) of the glucose profile.

# Preconditions

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

# Reference

None

WARNING

Currently analyzeGlucoseProfile is not CI tested.

# analyzeOneArm

function results = analyzeOneArm(arm)

Function that computes the glycemic outcomes of one arm.

# Input

arm: cell array of timetable (required)
A cell array of timetables containing the glucose data of the first arm. Each timetable corresponds to a patient and contains a column Time and a column glucose containg the glucose recordings (in mg/dl).

# Output

results: structure
A structure with fields containing the computed metrics and stats in the arm, i.e.:
- variabilityMetrics: a structure with fields:
  - values: a vector containing the values of the computed variability metrics (i.e., {aucGlucose, CVGA, cogi, cvGlucose, efIndex, gmi, iqrGlucose, jIndex, mageIndex, magePlusIndex, mageMinusIndex, meanGlucose, medianGlucose, rangeGlucose, sddmIndex, sdwIndex, stdGlucose,conga,modd, stdGlucoseROC}) for each glucose profile;
  - mean: the mean of values;
  - median: the median of values;
  - std: the standard deviation of values;
  - prc5: the 5th percentile of values;
  - prc25: the 25th percentile of values;
  - prc75: the 75th percentile of values;
  - prc95: the 95th percentile of values;
- riskMetrics: a structure with fields:
  - values: a vector containing the values of the computed risk metrics (i.e., {adrr, bgri, hbgi, lbgi, gri}) for each glucose profile;
  - mean: the mean of values;
  - median: the median of values;
  - std: the standard deviation of values;
  - prc5: the 5th percentile of values;
  - prc25: the 25th percentile of values;
  - prc75: the 75th percentile of values;
  - prc95: the 95th percentile of values;
- dataQualityMetrics: a structure with fields:
  - values: a vector containing the values of the computed data quality metrics (i.e., {missingGlucosePercentage,numberDaysOfObservation}) for each glucose profile;
  - mean: the mean of values;
  - median: the median of values;
  - std: the standard deviation of values;
  - prc5: the 5th percentile of values;
  - prc25: the 25th percentile of values;
  - prc75: the 75th percentile of values;
  - prc95: the 95th percentile of values;
- timeMetrics: a structure with fields:
  - values: a vector containing the values of the computed time related metrics (i.e., {timeInHyperglycemia, timeInL1Hyperglycemia, timeInL2Hyperglycemia, timeInHypoglycemia, timeInL1Hypoglycemia, timeInL2Hypoglycemia, timeInTarget, timeInTightTarget}) for each glucose profile;
  - mean: the mean of values;
  - median: the median of values;
  - std: the standard deviation of values;
  - prc5: the 5th percentile of values;
  - prc25: the 25th percentile of values;
  - prc75: the 75th percentile of values;
  - prc95: the 95th percentile of values;
- glycemicTransformationMetrics: a structure with fields:
  - values: a vector containing the values of the computed glycemic transformed metrics (i.e., {gradeScore, gradeEuScore, gradeHyperScore, gradeHypoScore, hypoIndex, hyperIndex, igc, mrIndex}) for each glucose profile;
  - mean: the mean of values;
  - median: the median of values;
  - std: the standard deviation of values;
  - prc5: the 5th percentile of values;
  - prc25: the 25th percentile of values;
  - prc75: the 75th percentile of values;
  - prc95: the 95th percentile of values;
- eventMetrics: a structure with fields:
  - values: a vector containing the values of the computed event related metrics (i.e., {hypoglycemicEvents, hyperglycemicEvents, extendedHypoglycemicEvents}) for each glucose profile;
  - mean: the mean of values;
  - median: the median of values;
  - std: the standard deviation of values;
  - prc5: the 5th percentile of values;
  - prc25: the 25th percentile of values;
  - prc75: the 75th percentile of values;
  - prc95: the 95th percentile of values;

# Preconditions

arm must be a cell array containing timetables;
Each timetable in arm must have a column names Time and a column named glucose.
Each timetable in arm must have an homogeneous time grid.

# Reference

None

WARNING

Currently analyzeOneArm is not CI tested.

# compareTwoArms

function [results, stats] = compareTwoArms(arm1,arm2,isPaired,alpha)

Function that compares the glycemic outcomes of two arms.

# Inputs

arm1: cell array of timetable (required)
A cell array of timetables containing the glucose data of the first arm. Each timetable corresponds to a patient and contains a column Time and a column glucose containg the glucose recordings (in mg/dl);
arm2: cell array of timetable (required)
A cell array of timetables containing the glucose data of the second arm. Each timetable corresponds to a patient and contains a column Time and a column glucose containg the glucose recordings (in mg/dl);
isPaired: integer (required)
A numeric flag defining whether to run paired or unpaired analysis. Commonly paired tests are performed when data of the same patients are present in both arms, unpaired otherwise;
alpha: double (required)
A double representing the significance level to use.

# Outputs

results: structure
A structure with field arm1 and arm2, that are two structures with field containing the computed metrics in the two arms, i.e.:
- variabilityMetrics: a structure with fields:
  - values: a vector containing the values of the computed variability metrics (i.e., {aucGlucose, CVGA, cogi, cvGlucose, efIndex, gmi, iqrGlucose, jIndex, mageIndex, magePlusIndex, mageMinusIndex, meanGlucose, medianGlucose, rangeGlucose, sddmIndex, sdwIndex, stdGlucose,conga,modd, stdGlucoseROC}) for each glucose profile;
  - mean: the mean of values;
  - median: the median of values;
  - std: the standard deviation of values;
  - prc5: the 5th percentile of values;
  - prc25: the 25th percentile of values;
  - prc75: the 75th percentile of values;
  - prc95: the 95th percentile of values;
- riskMetrics: a structure with fields:
  - values: a vector containing the values of the computed risk metrics (i.e., {adrr, bgri, hbgi, lbgi, gri}) for each glucose profile;
  - mean: the mean of values;
  - median: the median of values;
  - std: the standard deviation of values;
  - prc5: the 5th percentile of values;
  - prc25: the 25th percentile of values;
  - prc75: the 75th percentile of values;
  - prc95: the 95th percentile of values;
- dataQualityMetrics: a structure with fields:
  - values: a vector containing the values of the computed data quality metrics (i.e., {missingGlucosePercentage,numberDaysOfObservation}) for each glucose profile;
  - mean: the mean of values;
  - median: the median of values;
  - std: the standard deviation of values;
  - prc5: the 5th percentile of values;
  - prc25: the 25th percentile of values;
  - prc75: the 75th percentile of values;
  - prc95: the 95th percentile of values;
- timeMetrics: a structure with fields:
  - values: a vector containing the values of the computed time related metrics (i.e., {timeInHyperglycemia, timeInL1Hyperglycemia, timeInL2Hyperglycemia, timeInHypoglycemia, timeInL1Hypoglycemia, timeInL2Hypoglycemia, timeInTarget, timeInTightTarget}) for each glucose profile;
  - mean: the mean of values;
  - median: the median of values;
  - std: the standard deviation of values;
  - prc5: the 5th percentile of values;
  - prc25: the 25th percentile of values;
  - prc75: the 75th percentile of values;
  - prc95: the 95th percentile of values;
- glycemicTransformationMetrics: a structure with fields:
  - values: a vector containing the values of the computed glycemic transformed metrics (i.e., {gradeScore, gradeEuScore, gradeHyperScore, gradeHypoScore, hypoIndex, hyperIndex, igc, mrIndex}) for each glucose profile;
  - mean: the mean of values;
  - median: the median of values;
  - std: the standard deviation of values;
  - prc5: the 5th percentile of values;
  - prc25: the 25th percentile of values;
  - prc75: the 75th percentile of values;
  - prc95: the 95th percentile of values;
- eventMetrics: a structure with fields:
  - values: a vector containing the values of the computed event related metrics (i.e., {hypoglycemicEvents, hyperglycemicEvents, extendedHypoglycemicEvents}) for each glucose profile;
  - mean: the mean of values;
  - median: the median of values;
  - std: the standard deviation of values;
  - prc5: the 5th percentile of values;
  - prc25: the 25th percentile of values;
  - prc75: the 75th percentile of values;
  - prc95: the 95th percentile of values;
stats: structure
A structure that contains for each of the considered metrics the result of the statistical test with field p (p-value value) and h null hypothesis accepted or rejcted. Statistical tests are:
- t-test if the test isPaired and the samples are both gaussian distributed (checked with the Lilliefors test);
- unpaired t-test if the test not isPaired and the samples are both gaussian distributed (checked with the Lilliefors test);
- Wilcoxon rank test if the test isPaired and at least one of the samples is not gaussian distributed (checked with the Lilliefors test);
- Mann-Whitney U-test if the test not isPaired and at least one of the samples is not gaussian distributed (checked with the Lilliefors test).

# Preconditions

arm1 must be a cell array containing timetables;
arm2 must be a cell array containing timetables;
Each timetable in arm1 and arm2 must have a column names Time and a column named glucose.
Each timetable in arm1 and arm2 must have an homogeneous time grid;
isPaired can be 0 or 1.

# Reference

Lilliefors et al., "On the Kolmogorov-Smirnov test for normality with mean and variance unknown," Mathematics, vol. 62, 1967, pp. 399–402. DOI: 10.1080/01621459.1967.10482916.

WARNING

Currently compareTwoArms is not CI tested.

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