R/calculate_isi_belfiore.R

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#' Belfiore Insulin Sensitivity Index Calculation (from standard 75g OGTT)
#'
#' This function calculates the Belfiore Insulin Sensitivity Index using glucose
#' and insulin sampled during a standard 75g oral glucose tolerance test.
#' Methods described in \href{https://pubmed.ncbi.nlm.nih.gov/9562967/}{Belfiore
#' et al.}.
#'
#' Note the formula uses a population normalization factor representing a Normal
#' average value for Glucose x Insulin during the OGTT, which does not have a
#' commonly accepted standard. This function returns a value that is not
#' adjusted for any population values. 
#'
#' Standard timepoints are 0, 60, and 120 min. Note: insulin unit conversion may
#' differ differ depending on assay. Insulin (pmol/l) = insulin (uU/ml)*6
#'
#' `calculate_isi_belfiore()` accepts 3 separate vectors for time, glucose,
#' insulin.
#'
#' @inheritParams calculate_isi_matsuda
#'
#' @return Insulin Sensitivity-Gutt (mL/kg/min) as a single value
#' @export
#' @examples
#' # individual objects for each item
#' time=c(0, 30, 60, 90, 120)              # minutes
#' glucose=c(93, 129, 178, 164, 97)        # mg/dL
#' insulin=c(12.8, 30.7, 68.5, 74.1, 44.0) # uU/mL
#' calculate_isi_belfiore(time, glucose, insulin)
#'
#' # handling data stored in a dataframe
#' ogtt1 <- data.frame(time=c(0, 30, 60, 90, 120),              # minutes
#'                     glucose=c(93, 129, 178, 164, 97),        # mg/dL
#'                     insulin=c(12.8, 30.7, 68.5, 74.1, 44.0)) # uU/mL
#' calculate_isi_belfiore(ogtt1$time, ogtt1$glucose, ogtt1$insulin)
#'
#' # example from Gutch et al 2015
#' ogtt2 <- data.frame(time=c(0, 30, 60, 90, 120),              # minutes
#'                     glucose=c(100, 160, 160, 160, 140),      # mg/dL
#'                     insulin=c(5, 10, 10, 10, 5))             # uU/mL
#' calculate_isi_belfiore(ogtt2$time, ogtt2$glucose, ogtt2$insulin)
#' calculate_isi_matsuda(ogtt2$time, ogtt2$glucose, ogtt2$insulin)
#'
#' # Convert units
#' ogtt5 <- data.frame(time = c(0,0.5,1,1.5,2), # time in hours
#'                     glucose = c(5.167, 7.167, 9.889, 9.111, 5.3889), # glucose in mmol/l
#'                     insulin = c(76.8,184.2,411,444.6,264)) # insulin in pmol/l
#'
#' calculate_isi_belfiore(time =  ogtt5$time,
#'                         glucose = ogtt5$glucose,
#'                         insulin = ogtt5$insulin,
#'                         time_units = "hr", insulin_units = "pmol/l", glucose_units = "mmol/l")

calculate_isi_belfiore <- function(time, glucose, insulin, 
                                   time_units = "min", 
                                    glucose_units = "mg/dl", insulin_units = "uU/ml") {
  
  if (any(!is.numeric(time)) | any(!is.numeric(glucose)) | any(!is.numeric(insulin))) {
    rlang::warn("non-numeric values in time, glucose, or insulin")
    return(NA_real_)}

  # convert units; 
  time = convert_time_to_min(time, time_units)
  glucose = convert_glucose_to_mgdl(glucose, glucose_units)
  insulin = convert_insulin_to_uU_ml(insulin, insulin_units)
  
  ind0 = which(time==0)
  g0 = glucose[ind0]
  ins0 = insulin[ind0]

  ind60 = which(time==60)
  g60 = glucose[ind60]
  ins60 = insulin[ind60]

  ind120 = which(time==120)
  g120 = glucose[ind120]
  ins120 = insulin[ind120]
  
  g_bar = (g0/2 + g60 + g120/2)/2
  ins_bar = (ins0/2 + ins60 + ins120/2)/2
  
  # g_bar <- sfsmisc::integrate.xy(c(0,1,2), c(g0,g60,g120), use.spline = FALSE)/2
  # ins_bar <- sfsmisc::integrate.xy(c(0,1,2), c(ins0,ins60,ins120),use.spline = FALSE)/2

  isi_belfiore = 2/(g_bar*ins_bar+1)
  
    return(isi_belfiore)
}