This document details the calculations made in the R script
`GV measures.R`

. That script is based upon the Easy GV
spreadsheet constructed by Dr. Nathan R. Hill of Oxford University. In
many cases, Easy GV does not give results consistent with the formulas
presented in the original manuscripts. In these cases,
`GV measures.R`

gives an option to calculate either the Easy
GV version or the original manuscript option.

Throughout this document, let *X*_{t} be a
glucose reading at time *t*. Let *n* be the total number
of glucose readings. Time is assumed to be measured in minutes since the
first recording in the data set. Glucose readings can be measured in
either mg/dL or mmol/L. Note that 1 mmol of glucose is equal to 18 mg of
glucose.

All functions require a vector `x`

of glucose readings.
This vector should be numeric and should not include any blank entries.
Some functions additionally require a vector `times`

of
times. This vector should also be numeric and should not include any
blank entries. Currently, the function `read.CGM`

can take a
Dexcom output file as input and return a data.frame which includes
properly formatted `x`

and `times`

vectors.

The wrapper function `GV`

returns all of the following
metrics simultaneously.

Parameters include

`x`

, a vector of glucose readings`times`

, a vector of corresponding times`n`

, the number of hours between “partner” observations. Null value is 1.`s`

, the number of minutes of slack used when searching for partners. Null value is 1.`method`

, either “manuscript” or “easy”. Null value is “manuscript”.

For a glucose measurement *X*_{t} at time
*t*, let *D*_{t} be the difference
between *X*_{t} and the mean of all glucose
measurements made *n* hours prior to
*X*_{t}, plus or minus *s* minutes. Let
*T* be the set of times with a *D*_{t}
value and let *k* be the number of such observations. Finally,
let *D̄* = ∑*D*_{t}/*k*. Then, the
original manuscript version is

\[ CONGA\_M(n) = \\sqrt{\\frac{\\sum\_T (D\_t - \\bar{D})^2}{k - 1}} \]

Furthermore, let
*D̄*^{*} = ∑|*D*_{t}|/*k*.
Then the Easy GV version is

\[ CONGA\_{GV}(n) = \\sqrt{\\frac{\\sum\_T (X\_t - \\bar{D}^\*)^2}{k - 1}} \]

Parameters include

`x`

, a vector of glucose readings`times`

, a vector of corresponding times`k`

, length of time (in minutes) used to find partners. Null value is 60.`s`

, the number of minutes of slack used when searching for partners. Null value is 1.

For a glucose measurement *X*_{t} at time
*t*, let *D*_{t} be the difference
between *X*_{t} and the mean of all glucose
measurements made *k* minutes prior to
*X*_{t}, plus or minus *s* minutes. Let
*T* be the set of times with a *D*_{t}
value and let *k* be the number of such observations. Then

\[ LI = \\frac{1}{k} \\sum\_{t\\in T} (D\_t)^2 \]

Parameters include

`x`

, a vector of glucose readings`unit`

, either “mg” if the units are mg/dL or “mmol” if the units are mmol/L. Null value is “mg”.

Let *X̄* be the mean of all glucose values, and let
*S**D*(*X*) be the standard deviation of all glucose values. If
the units are mg/dL,

\[ J = \\frac{1}{1000}(\\bar{X} + SD(X))^2 \] and if the units are mmol/L,

\[ J = \\frac{18^2}{1000}(\\bar{X} + SD(X))^2 \]

Parameters include

`x`

, a vector of glucose readings`unit`

, either “mg” if the units are mg/dL or “mmol” if the units are mmol/L. Null value is “mg”.`method`

, one of “manuscript”, “easy”, or “corrected”. Null value is “manuscript”. “Corrected” refers to the Gaynanova paper’s recommendation.

If the units are mg/dL, let
*f*(*x*) = 1.509(ln(*x*)^{1.084} − 5.381).
If the units are mmol/L, let
*f*(*x*) = 1.509(ln(18*x*)^{1.084} − 5.381).
Let
*r l(x) = cf*(

`method`

to `corrected`

or
`manuscript`

, respectively. Then, the original manuscript
version is\[ LBGI\_M = \\frac{\\sum rl(x\_t)}{n} \]

\[ HBGI\_M = \\frac{\\sum rh(x\_t)}{n} \]

where *n* is the total number of glucose readings.

The Easy GV version is

\[ LBGI\_{GV} = \\frac{\\sum rl(x\_t)}{\\sum I(rl(x\_t) > 0)} \]

\[ HBGI\_{GV} = \\frac{\\sum rh(x\_t)}{\\sum I(rh(x\_t) > 0)} \]

Parameters include

`x`

, a vector of glucose readings`unit`

, either “mg” if the units are mg/dL or “mmol” if the units are mmol/L. Null value is “mg”.`method`

, either “manuscript” or “easy”. Null value is “manuscript”.`c1`

, the glucose value below which readings are considered hypoglycemic`c2`

, the glucose value above which readings are considered hyperglycemic

If the units are mg/dL, let

*g*(*x*) = min(425[log(log(*x*/18)) + *C*]^{2}, 50)
If the units are mmol/L, let

*g*(*x*) = min(425[log(log(*x*)) + *C*]^{2}, 50)

Where the logarithm is base ten in both cases. Let *C* = 1.6
for the manuscript calculation and let *C* = 1.5554147 for the
Easy GV calculation.

For the manuscript calculation,
*G RADE*

We also calculate the contributions of hypoglycemia, euglycemia, and hyperglycemia to the GRADE score.

\[ \\text{Hypo percentage} = \\frac{\\sum\\limits\_{x\_t < C\_1} g(x\_t)}{\\sum\\limits\_{\\text{all }x\_t} g(x\_t)} \]

\[ \\text{Eu percentage} = \\frac{\\sum\\limits\_{C\_1 < x\_t < C\_2} g(x\_t)}{\\sum\\limits\_{\\text{all }x\_t} g(x\_t)} \]

\[ \\text{Hyper percentage} = \\frac{\\sum\\limits\_{x\_t > C\_2} g(x\_t)}{\\sum\\limits\_{\\text{all }x\_t} g(x\_t)} \]

If the units are mg/dL, the default values for *C*_{1}
and *C*_{2} are 70.2 and 140.4$ If the units are mmol/L,
the defaults are 3.9 and 7.8.

Parameters include

`x`

, a vector of glucose readings`times`

, a vector of corresponding times`s`

, the number of minutes of slack used when searching for partners. Null value is 1.`method`

, either “manuscript” or “easy”. Null value is “manuscript”.

For a glucose measurement *X*_{t} at time
*t*, let *D*_{t} be the difference
between *X*_{t} and the mean of all glucose
measurements made 24 hours prior to *X*_{t},
plus or minus *s* minutes. Let *T* be the set of times
with a *D*_{t} value and let *k* be the
number of such observations.

Then, the original manuscript version is

\[ MODD\_M = \\frac{1}{k} \\sum\_T | D\_t | \]

Let
*T*^{−} = *T* \ *m ax*(

\[ MODD\_{GV} = \\frac{1}{K-1} \\sum\_{T^-} | D\_t | \]

Parameters include

`x`

, a vector of glucose readings`times`

, a vector of corresponding times

Note that the original manuscript for MAGE is not very precise and does not lead to an obvious calculation of MAGE. While Easy GV does not appear to calculate MAGE in the same way as the original manuscript, the Easy GV version of MAGE is the only one we present here.

Let
*D*_{t} = *X*_{t} − *X*_{t − 1}.
Then let *E* be the set of all *D*_{t}
whose absolute value exceeds the standard deviation of all glucose
readings from the day that *D*_{t} occurred.
Then let *E*^{+} be the set that contains the positive
*D*_{t} values in *E*, with size
#*E*^{+}. Let *E*^{−} be the set that
contains the negative *D*_{t} values in
*E*, with size #*E*^{+}. We then report separate
positive and negative MAGE values and the averaged MAGE value:

\[ MAGE\_+ = \\frac{1}{\\\#E^+} \\sum\_{E^+} D\_t \]

\[ MAGE\_- = \\frac{1}{\\\#E^-} \\sum\_{E^-} D\_t \]

*M AGE = (MAGE*

Parameters include

`x`

, a vector of glucose readings`times`

, a vector of corresponding times`unit`

, either “mg” if the units are mg/dL or “mmol” if the units are mmol/L. Null value is “mg”.`method`

, either “manuscript” or “easy”. Null value is “manuscript”.

If the units are mg/dL, let

*f*(*x*) = [1.509(ln(*x*)^{1.084} − 5.381)]

If the units are mmol/L, let

*f*(*x*) = [1.509(ln(18*x*)^{1.084} − 5.381)]
Let
*r l(x) = 10f(x)^{2}
when f(x) < 0 and
rl*(

*L R^{}d = max(rl*(

and

*H R^{}d = max(rh*(

for day *d*. Let *D* be the total number of days where
glucose levels were measured. Then, the original manuscript version
is

\[ ADRR\_M = \\frac{1}{D} \\sum\\limits\_{d=1}^D (LR^d + HR^d) \]

The Easy GV version gives high and low measures separately.

\[ ADRR\_{L} = \\frac{1}{D} \\sum\\limits\_{d=1}^D (LR^d) \]

\[ ADRR\_{H} = \\frac{1}{D} \\sum\\limits\_{d=1}^D (HR^d) \]

Parameters include

`x`

, a vector of glucose readings`unit`

, either “mg” if the units are mg/dL or “mmol” if the units are mmol/L. Null value is “mg”.`index`

, a value to be considered a ‘standard’ blood glucose value, in mg/dL. Null value is 120.`method`

, either “manuscript” or “easy”. Null value is “manuscript”.

After conversion of all glucose values to mg/dL, let \(M^\* =
(10\\text{log}\\frac{x}{\\text{index}})^3\) and let
*W* = (*m ax*(

Then, the original manuscript version is

\[ M\_M = \\frac{1}{N} \\sum\\limits\_{i=1}^N |M^\*| + W \]

The Easy GV version is

\[ M\_{GV} = \\frac{1}{N} \\sum\\limits\_{i=1}^N |M^\*|\]

Parameters include

`x`

, a vector of glucose readings`times`

, a vector of corresponding times

\[ MAG = \\frac{\\sum\\limits\_{i=1}^{N-1} | x\_{i+1} - x\_i |}{(\\text{max}(t) - \\text{min}(t))/60} \]

where *N* is the total number of glucose values.

Parameters include

`x`

, a vector of glucose readings`times`

, a vector of corresponding times`overall`

, a logical, equal to`TRUE`

you want the CV for the entire dataset, or equal to`FALSE`

if you would prefer many CV values over a moving window`interval`

, size (in hours) of the moving window to be used if`overall`

is false. Null value is 1.

*C V = SD*(

where *X* is a vector of glucose readings, potentially
restricted to a particular time window.

Parameters include

`x`

, a vector of glucose readings`times`

, a vector of corresponding times`overall`

, a logical, equal to`TRUE`

you want the SD for the entire dataset, or equal to`FALSE`

if you would prefer many SD values over a moving window`interval`

, size (in hours) of the moving window to be used if`overall`

is false. Null value is 1.

\[ SD = \\sqrt{\\frac{1}{N-1}\\sum\_{t \\in T} (x\_t - \\bar{x})^2}, \]

where *T* is a set of times (potentially restricted to a
particular window) and *N* is the size of *T*.

Parameters include

`x`

, a vector of glucose readings`times`

, a vector of corresponding times`thresh`

, a threshold above (or below) which you wish to calculate the AUC. Default is 100.`above`

, a logical indicating whether you wish to calculate area above the threshold value (`TRUE`

) or below it (`FALSE`

). Default is`TRUE`

.

If `above == T`

,

\[ AUC\_+ = \\sum\_{i=1}^{N-1} I(x\_i \\geq \\nu) I(x\_{i+1} \\geq \\nu)\\Big(min(x\_i - \\nu,x\_{i+1}-\\nu)(t\_{i+1}-t\_i) + |x\_{i+1}-x\_i|(t\_{i+1}-t\_i)/2\\Big)\]

If `above == F`

,

\[ AUC\_- = -\\sum\_{i=1}^{N-1} I(x\_i \\leq \\nu) I(x\_{i+1} \\leq \\nu)\\Big(min(x\_i - \\nu,x\_{i+1}-\\nu)(t\_{i+1}-t\_i) + |x\_{i+1}-x\_i|(t\_{i+1}-t\_i)/2\\Big)\]

where *ν* is the threshold value and *N* is the length
of the glucose vector.

For each excursion beyond this threshold value, this calculation does not include the triangular area from the threshold to the first glucose value beyond the threshold, nor from the last glucose beyond the threshold back to the threshold. Hence a single glucose value beyond the threshold is not captured by the calculation.

Parameters include

`x`

, a vector of glucose readings`low`

, the lower bound of the range`high`

, the upper bound of the range

This function gives the percentage of glucose readings that fall in a
given range (*l*, *u*).

\[ TIR = \\sum\_{i=1}^N I(l \\leq x\_i \\leq u) / N \] Battelino et al suggest five ranges: below 54 mg/dL, 55-70, 71-180, 181-250, above 250.

Parameters include

`x`

, a vector of glucose readings`unit`

, either “mg” if the units are mg/dL or “mmol” if the units are mmol/L. Null value is “mg”.

Let *x̄* be the mean of all glucose readings taken. If the
units are mg/dL, then

*G MI* = 3.31 + 0.02392

If the units are mmol/L,

12.71 + 4.70587*x̄*

Parameters include

`x`

, a vector of glucose readings`times`

, a vector of corresponding times`thresh`

, a threshold, where glucoses below the threshold are considered as part of an episode`len`

, the minimum length of an episode`gap`

, the typical gap between CGM measurements, in minutes

This function counts the number of “episodes” where glucose values
remain below a certain threshold `thresh`

for a period of at
least `len`

minutes. Then the number of episodes is divided
by the amount of days that the sensor was active. This amount is
calculated by taking the total time (the time between the first and last
measurements), subtracting any gaps in time that are longer than
`gap`

+2 minutes and then adding back `gap`

minutes
for each of the gaps subtracted away.

Parameters include

`x`

, a vector of glucose readings`times`

, a vector of corresponding times

Let
*Δ x_{}i = x_{}i − x_{}i − 1
and
Δt*

Parameters include

`x`

, a vector of glucose readings

Let
*Δ**x* _{}*i

Parameters include

`file`

, the name of the file (in CSV format) to be read-in`timezero`

, set to`"first"`

if the first glucose reading should be considered time zero and set to`"midnight"`

if midnight of the day of the first reading should be considered time zero. Default is`"first"`

.`na.rm`

, a logical that is`TRUE`

if you wish to exclude all readings that are missing glucose values or time stamps and`FALSE`

if not. Default is`TRUE`

.`skip`

, the number of lines in the data file to skip before beginning to read in data`calib.col`

, the number or name of the column containing information regarding calibration status of each glucose entry`calib.tag`

, the character value used to denote calibration rows in`calib.col`

`mult.sensors`

, a logical that is`TRUE`

if you wish to split the data set into parts corresponding to different CGM sensors and`FALSE`

if not. Default is`FALSE`

.`sensor.times`

, a vector of times (in the same format as the time data) that correspond to the beginning of a new CGM sensor. These times are used to split the data between multiple sensors if`mult.sensors`

is`TRUE`

. If`sensor.times`

is`NA`

, the data is split automatically at every gap of`sensor.gap`

or more minutes.`sensor.gaps`

, a number specifying the minimum gap (in minutes) for which we should split the data into two pieces. Default is 120.`time.col`

, the number or name of the column containing time data`gluc.col`

, the number or name of the column containing glucose data`time.sep`

, character that separates date from time in your time data`time.format`

, specify date and time formats according to the specification used in the`chron`

package. Default is`c(dates = "m/d/y", times = "h:m:s")`

.`high.ind`

, character value that identifies high glucose values in the data. Default is “High”.`high.value`

, numeric value by which to replace glucose values equal to`high.ind`

. Default is 400.`low.ind`

, character value that identifies low glucose values in the data. Default is “Low”.`low.value`

, numeric value by which to replace glucose values equal to`low.ind`

. Default is 40.

This function takes in data from a CGM and converts it into a data frame with one column of glucose readings and one column of times (in minutes). These two columns can then be used with any of the glucose variability functions.

Parameters include

`x`

, a vector of glucose readings`times`

, a vector of corresponding times`unit`

, either “mg” if the units are mg/dL or “mmol” if the units are mmol/L. Null value is “mg”.

This function returns a plot of blood glucose over time.

Parameters include

`x`

, a vector of glucose readings`times`

, a vector of corresponding times`n`

, the number of hours between “partner” observations. Null value is 1.`s`

, the number of minutes of slack used when searching for partners. Null value is 1.`unit`

, either “mg” if the units are mg/dL or “mmol” if the units are mmol/L. Null value is “mg”.

This function returns a plot of the `n`

-hour changes in
glucose values over time.

Parameters include

`x`

, a vector of glucose readings`times`

, a vector of corresponding times`unit`

, either “mg” if the units are mg/dL or “mmol” if the units are mmol/L. Null value is “mg”.

This function returns a plot of the “symmetrized” glucose values used in calculating BGI and ADRR.

Parameters include

`x`

, a vector of glucose readings`times`

, a vector of corresponding times`unit`

, either “mg” if the units are mg/dL or “mmol” if the units are mmol/L. Null value is “mg”.`m.index`

, a value to be considered a ‘standard’ blood glucose value, in mg/dL. Null value is 120.`k`

, length of time (in minutes) used to find partners. Null value is 60.`s`

, the number of minutes of slack used when searching for partners. Null value is 1.`conga.n`

, the number of hours between “partner” observations. Null value is 1.`interval`

, size (in hours) of the moving window to be used if`overall`

is false. Null value is 1.`thresh`

, a threshold above (or below) which you wish to calculate percentages. Default is 100

This is a wrapper function that outputs a table with all 14 metrics, calculated for both manuscript and Easy GV methods, if applicable.

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