# Error metrics

# rmse

function rmse = rmse(data,dataHat)

Function that computes the root mean squared error (RMSE) between two glucose traces (ignores nan values).

# Inputs

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

# Output

rmse: double
The computed root mean squared error (mg/dl).

# Preconditions

data and dataHat must be a timetable having an homogeneous time grid;
data and dataHat must contain a column named Time and another named glucose;
data and dataHat must start from the same timestamp;
data and dataHat must end with the same timestamp;
data and dataHat must have the same length.

# Reference

Wikipedia on RMSE: https://en.wikipedia.org/wiki/Root-mean-square_deviation. (Accessed: 2020-12-10)

# cod

function cod = cod(data,dataHat)

Function that computes the coefficient of determination (COD) between two glucose traces (ignores nan values).

# Inputs

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

# Output

cod: double
The computed coefficient of determination (%).

# Preconditions

data and dataHat must be a timetable having an homogeneous time grid;
data and dataHat must contain a column named Time and another named glucose;
data and dataHat must start from the same timestamp;
data and dataHat must end with the same timestamp;
data and dataHat must have the same length.

# Reference

Wright, "Correlation and causation", Journal of Agricultural Research, vol. 20, 1921, pp. 557–585.

# mard

function mard = mard(data,dataHat)

Function that computes the mean absolute relative difference (MARD) between two glucose traces (ignores nan values).

# Inputs

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

# Output

mard: double
The mean absolute relative difference (MARD) (%).

# Preconditions

data and dataHat must be a timetable having an homogeneous time grid;
data and dataHat must contain a column named Time and another named glucose;
data and dataHat must start from the same timestamp;
data and dataHat must end with the same timestamp;
data and dataHat must have the same length.

# Reference

Gini, "Measurement of Inequality and Incomes", The Economic Journal, vol. 31, 1921, pp. 124–126. DOI:10.2307/2223319.

# clarke

function results = clarke(data,dataHat)

Function that performs Clarke Error Grid Analysis (CEGA) (ignores nan values).

# Inputs

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

# Output

results: structure
A structure containing the results of the CEGA with fields:
- A: the percentage of time spent in Zone A (%);
- B: the percentage of time spent in Zone B (%);
- C: the percentage of time spent in Zone C (%);
- D: the percentage of time spent in Zone D (%);
- E: the percentage of time spent in Zone E (%).

# Preconditions

data and dataHat must be a timetable having an homogeneous time grid;
data and dataHat must contain a column named Time and another named glucose;
data and dataHat must start from the same timestamp;
data and dataHat must end with the same timestamp;
data and dataHat must have the same length.

# Reference

Clarke et al., "Evaluating clinical accuracy of systems for self-monitoring of blood glucose", Diabetes Care, 1987, vol. 10, pp. 622–628. DOI: 10.2337/diacare.10.5.622.

# timeDelay

function timeDelay = timeDelay(data,dataHat)

Function that computes the time delay between two glucose traces (ignores nan values). The time delay is computed as the time shift necessary to maximize the correlation between the two traces.

# Inputs

data: timetable (required)
A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl);
dataHat: timetable (required)
A timetable with columns Time and glucose containing the inferred glucose data (mg/dl) to comapre with data;

# Output

timeDelay: double
The computed time delay (min).

# Preconditions

data and dataHat must be a timetable having an homogeneous time grid;
data and dataHat must contain a column named Time and another named glucose;
data and dataHat must start from the same timestamp;
data and dataHat must end with the same timestamp;
data and dataHat must have the same length.

# Reference

Wikipedia on time delay using correlation. https://en.wikipedia.org/wiki/Cross-correlation#Time_delay_analysis (Accessed: 2020-12-10).

# gRMSE

function gRMSE = gRMSE(data,dataHat)

Function that computes the glucose root mean squared erro (gRMSE) between two glucose traces (ignores nan values).

# Inputs

data: timetable (required)
A timetable with columns Time and glucose containing the glucose data to analyze (mg/dl);
dataHat: timetable (required)
A timetable with columns Time and glucose containing the inferred glucose data (mg/dl) to comapre with data;

# Output

gRMSE: double
The computed glucose root mean squared error (mg/dl).

# Preconditions

data and dataHat must be a timetable having an homogeneous time grid;
data and dataHat must contain a column named Time and another named glucose;
data and dataHat must start from the same timestamp;
data and dataHat must end with the same timestamp;
data and dataHat must have the same length.

# Reference

Del Favero et al., "A glucose-specific metric to assess predictors and identify models", IEEE Transactions on Biomedical Engineering, 2012, vol. 59, pp. 1281-1290. DOI: 10.1109/TBME.2012.2185234.

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