R/calculate_isi_cederholm.R

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#' Cederholm Insulin Sensitivity Index Calculation (from standard 75g OGTT)
#'
#' This function calculates the Cederholm Index using glucose and insulin 
#' sampled during a standard 75g oral glucose tolerance test.
#' 
#' Standard timepoints are 0, 30, 60, 90, and 120 min.
#' Note: insulin unit conversion may differ differ depending on assay. 
#' Insulin (pmol/l) = insulin (uU/ml)*6 
#' 
#' The formula used for this calculation is described in \href{https://pubmed.ncbi.nlm.nih.gov/2261853/}{Cederholm et al.}:
#' \deqn{\frac{75000 + (Glucose_{0} - Glucose_{120}) \cdot 1.15 \cdot 180 \cdot 0.19 \cdot Weight(kg)} 
#' {120 \cdot log(Insulin_{mean}) \cdot Glucose_{mean}}
#' }
#' Where 75000 is the glucose dose (mg), 0.19 represents the Glucose space (0.19 * weight), and 1.15*180 factor 
#' to converts whole blood glucose (\eqn{mmol\cdot L^{-1}}) to plasma (\eqn{mg \cdot L^{-1}}), 
#' and 120 converts 2hours to minutes.
#' 
#' If using Plasma glucose measurements the formula used is:
#' \deqn{\frac{Glucose Dose (mg) + (Glucose_{0} - Glucose_{120}) \cdot 0.19 \cdot Weight(kg)} 
#' {120 \cdot log(Insulin_{mean}) \cdot Glucose_{mean}}
#' }
#' 
#' Therefore some of these conversion factors are not needed if using plasma 
#' glucose (eg YSI measurement) and already reporting glucose in mg/dL. 
#'  
#' @param time  a column name (unquoted) indicating time values (in minutes)
#' @param glucose a column name (unquoted) storing glucose values (in mg/dL)
#' @param insulin a column name (unquoted) storing insulin values (in uU/mL = mU/L)
#' @param weight Body weight (kg); 
#' @param D Glucose dose (default 75g standard OGTT)
#' @param glucose_method Glucose measurement method (default "plasma"; enter "wbg" if fingerstick or whole blood glucose is used)
#' @param time_units if units are not in "min", can indicate here for unit conversion (options "min" or "hr")
#' @param glucose_units if units are not in "mg/dl", can indicate here for unit conversion (options "mg/dl" or "mmol/l") 
#' @param insulin_units if units are not in "uU/ml", can indicate here for unit conversion (options "uU/ml" or "pmol/l")
#' @param weight_units Body weight units, to use for conversion if not in kg
#'
#' @return Cederholm insulin sensitivity index as a single value (\eqn{mg \cdot L^2 \cdot mmol^{-1} \cdot mU^{-1} \cdot min{-1}})
#' @export
#' @md
#' @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_cederholm(time, glucose, insulin, weight=70) # 20.1356
#' 
#' # 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_cederholm(ogtt1$time, ogtt1$glucose, ogtt1$insulin, weight=70)  # 20.1356
#' 
#' 
#' 
#' # Convert units
#' ogtt5 <- data.frame(time = c(0,0.5,1,1.5,2), # time in hours
#'                     glucose = c(5.167, 7.167, 9.889, 9.111, 5.3889), # glucose in mmol/l
#'                     insulin = c(76.8,184.2,411,444.6,264)) # insulin in pmol/l
#' 
#' calculate_isi_cederholm(time =  ogtt5$time,
#'                         glucose = ogtt5$glucose,
#'                         insulin = ogtt5$insulin,
#'                         weight=154, weight_units="lbs",
#'                         time_units = "hr", insulin_units = "pmol/l", glucose_units = "mmol/l")
#'                         
#' dat <- data.frame( # data from Gutt. Diab Res Clin Pract. 2000 
#'   stringsAsFactors = TRUE,
#' cat = c("obese","obese","normal",
#'         "normal","NGT","NGT","IGT","IGT","DM2","DM2"),
#'         time = c(0L, 120L, 0L, 120L, 0L, 120L, 0L, 120L, 0L, 120L),
#'         glucose = c(106.9,145.8,18,65,88.3,
#'                     103.3,102.3,151.7,20.1,347.5),
#'                     insulin = c(19.9,96.1,87,106.7,16.2,
#'                                 73.2,25.3,140.6,30.9,57.9))
#' library(tidyverse)
#' dat |> 
#'   group_by(cat) |> 
#'     summarise(isi_ceder = calculate_isi_cederholm(time, glucose, insulin, weight=70))

calculate_isi_cederholm <- function(time, glucose, insulin, weight, D=75,
                                    glucose_method="plasma",
                                    time_units = "min", 
                            glucose_units = "mg/dl", insulin_units = "uU/ml",
                            weight_units = "kg") {
  
  if (any(is.na(time)) | any(is.na(glucose)) | any(is.na(insulin))) {
    rlang::warn("Check for missing values in time, glucose, and insulin")
    return(NA_real_)}
  
  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_)}
  
  if (!all(order(time) == seq_along(time))) {
    rlang::warn("Time values must be ordered from 0 to end") # check proper time order
    return(NA_real_)}
  
  # convert units; 
  time = convert_time_to_min(time, time_units)
  glucose_mg_L = switch(glucose_method,
    plasma = convert_glucose_to_mgdl(glucose, glucose_units)*10,
    wbg    = convert_glucose_to_mgdl(glucose, glucose_units)*1.15*10,
    stop("invalid glucose_method; use either plasma or wbg (whole blood glucose)"))
  glucose_mM = switch(glucose_method,
                        plasma = convert_glucose_to_mM(glucose, glucose_units),
                        wbg    = convert_glucose_to_mM(glucose, glucose_units)*1.15,
                        stop("invalid glucose_method; use either plasma or wbg (whole blood glucose)"))
  insulin = convert_insulin_to_uU_ml(insulin, insulin_units) # same as mU/L
  weight_kg = convert_weight_to_kg(weight, weight_units)
  
  ind0 = which(time==0)
  g0 = glucose_mg_L[ind0]
  # ins0 = insulin[ind0]

  ind120 = which(time==120)
  g120 = glucose_mg_L[ind120]
  # ins120 = insulin[ind120]
  time_max = max(time)
  
  M = (D*1000 + (g0 - g120) * 0.19 * weight_kg)/120 # mg glucose/min
  # note: mean glucose uses mmol/L for MCR calculation
  g_bar <- sfsmisc::integrate.xy(time, glucose_mM, use.spline = FALSE)/time_max # mmol/L
  MCR = M/g_bar # mg*L per min per mmol Glucose
  
  ins_bar <- sfsmisc::integrate.xy(time, insulin,use.spline = FALSE)/time_max # mU/L
  SI = MCR/log(ins_bar)
  # return(data.frame(M, MCR, SI))
  # return( (D*1000 + (g0 - g120) * 0.19 * weight_kg) / (120*log(ins_bar) * g_bar))
  return(SI)
}