noncompAUC: Calculate the AUC using the trapezoidal rule

In shirewoman2/LaurasHelpers: Miscellaneous Helper Functions for Common PK or Analytical Chemistry Tasks

Calculate the AUC using the trapezoidal rule

Description

Given a data.frame of concentration-time data, noncompAUC calculates the area under the concentration-time curve for the times included in the input data.frame using either the linear or the linear up/log down trapezoidal rule. Optionally extrapolate to infinity or back extrapolate to t0.

Usage

noncompAUC(
  DF,
  concentration = Concentration,
  time = Time,
  type = "LULD",
  extrap_inf = FALSE,
  extrap_inf_coefs = NULL,
  extrap_inf_times = c(NA, NA),
  reportTermFit = FALSE,
  reportFractExtrap = FALSE,
  extrap_t0 = FALSE,
  extrap_t0_coefs = NULL,
  extrap_t0_model = "monoexponential",
  extrap_t0_times = c(NA, NA),
  reportBackExtrapFit = FALSE,
  reportC0 = FALSE
)

Arguments

DF	Input data.frame with concentration-time data.
concentration	The name of the column containing drug concentrations
time	The name of the column containing time data
type	The type of trapezoidal rule to use. Options are "LULD" (default) for "linear up, log down" or "linear".
extrap_inf	Extrapolate the curve to infinity? TRUE or FALSE.
extrap_inf_coefs	If you've already performed a nonlinear regression to a monoexponential decay equation, noncompAUC will use that for extrapolation to infinity. Provide a data.frame of the coefficients from a nls regression. Format must be the standard output from summary(nls(...))[["coefficients"]] or the coefficients from elimFit. It doesn't matter what you name the coefficients, but this function assumes that they will be listed with the y-intercept A0 in the first row and the rate constant k in the next row. Note that this is for a monoexponential decay. If you've fit a bi- or triexponential decay model to your data, only supply the rate constant and y intercept for the terminal portion of the data.
extrap_inf_times	If extrap_inf is TRUE but you haven't supplied the coefficients from fitting a monoexponential decay to your data, specify the time range to use for fitting as c(minTime, maxTime). If this is left as c(NA, NA), the time range from tmax to tlast will be used.
reportTermFit	TRUE or FALSE for whether to report the fit for the terminal elimination calculation. If TRUE, this changes the output from a single number to a named list that includes the AUC and the terminal elimination fit (will be named "Terminal elimination fit") from nls.
reportFractExtrap	TRUE or FALSE for whether to report the fraction of the AUC extrapolated to infinity. If TRUE, this changes the output from a single number to a named list that includes the AUC and the fraction extrapolated to infinity (will be named "Fraction extrapolated to infinity").
extrap_t0	TRUE or FALSE for whether to back extrapolate the curve to 0. This is useful when the dose was administered IV and you know you're missing a significant portion of the curve from t0 to the first sampling time.
extrap_t0_coefs	If you've already performed a nonlinear regression to a monoexponential, biexponential, or triexponential decay equation, noncompAUC will use those for back extrapolation to t0. Provide a named list of: coefs the coefficients from a nls regression. Format must be the standard output from summary(nls(...))[["coefficients"]] or the coefficients from elimFit. It doesn't matter what you name the coefficients, but this function assumes that they will be listed with the y-intercept for the first term in the first row, the rate constant for the first term in the next row, the y intercept for the second term in the next row, the rate constant for the second term in the next row after that, etc. tmax The time to start fitting the elimination curve. This will be used to determine how far back in time t0 is.
extrap_t0_model	"monoexponential" or "biexponential". Only used when extrap_t0 is TRUE and you haven't supplied your own fitted coefficients. This sets which exponential decay model to fit to your data and defaults to "monoexponential".
extrap_t0_times	If extrap_t0 is TRUE, specify the time range to use for fitting the exponential decay as c(minTime, maxTime). If this is left as c(NA, NA), the full time range from tmax to tlast will be used.
reportBackExtrapFit	TRUE or FALSE for whether to report the fit for the back-extrapolation to t0 calculation. If TRUE, this changes the output from a single number to a named list that includes the AUC and the back extrapolated fit (will be named "Back-extrapolation to t0 fit") from nls.
reportC0	TRUE or FALSE for whether to report the back-extrapolated concentration at t0. If TRUE, the output becomes a named list that includes the AUC and the extrapolated C0 value (will be named "C0"). This is useful as a sanity check because the maximum concentration at t0 in, e.g., plasma should be no larger than approximately the dose / total plasma volume, which is ~3 L in a healthy, 70-kg adult.

Details

A few notes:

• If there are two consecutive time points with the same measured concentration, that results in an undefined value for the log trapezoidal rule. To deal with this, anytime the user has opted for the linear up/log down trapezoidal rule but there are also consecutive time points with the same concentration, those individual trapezoids will be calculated linearly rather than using a log function and all AUCs will be added together at the end.

• I intentionally omitted the option of using cubic splines for calculating the AUC because they can become unstable with noisy concentration-time data and are thus less desireable than the trapezoidal rule. For more details, please see https://www.certara.com/2011/04/02/calculating-auc-linear-and-log-linear/.

Value

Returns the calculated AUC as a number or, depending on the options selected, a named list of the AUC (AUC[["AUC"]]), the fraction of the curve extrapolated to infinity (AUC[["Fraction extrapolated to infinity"]]), and the back extrapolated C0 (AUC[["C0"]]).

Examples

data(ConcTime)
IV1 <- ConcTime %>% dplyr::filter(SubjectID == 101 & Drug == "A" &
                                        DoseRoute == "IV")
noncompAUC(IV1, time = TimeHr)
noncompAUC(IV1, time = TimeHr, type = "LULD")
noncompAUC(IV1, time = TimeHr, type = "linear")

# Extrapolating to infinity
noncompAUC(IV1, time = TimeHr, extrap_inf = TRUE,
           extrap_inf_times = c(0.5, NA))

# Extrapolating to infinity and reporting the fraction extrapolated
noncompAUC(IV1, time = TimeHr, extrap_inf = TRUE,
           extrap_inf_times = c(0.5, NA),
           reportFractExtrap = TRUE)

# Back extrapolating to t0
noncompAUC(IV1, time = TimeHr, extrap_t0 = TRUE,
           extrap_t0_model = "monoexponential",
           extrap_t0_times = c(0.5, NA))

# Back extrapolating to t0 and reporting extrapolated C0
noncompAUC(IV1, time = TimeHr, extrap_t0 = TRUE,
           extrap_t0_model = "monoexponential",
           extrap_t0_times = c(0.5, NA),
           reportC0 = TRUE)

# Extrapolating to infinity, reporting the fraction extrapolated to infinity,
# back extrapolating to t0, and reporting extrapolated C0
noncompAUC(IV1, time = TimeHr,
           extrap_inf = TRUE,
           extrap_inf_times = c(0.5, NA),
           reportFractExtrap = TRUE,
           extrap_t0 = TRUE,
           extrap_t0_model = "monoexponential",
           extrap_t0_times = c(0.5, NA),
           reportC0 = TRUE)


# For supplying your own coefficients to back extrapolate with:
tmax <- 0.5
# The elimination phase begins at t = 0.5 hrs here, so don't start fitting at
# t0; you'll get bad estimates.
Fit <- nls(Concentration ~ A * exp(-k * (TimeHr - tmax)),
           data = IV1 %>%  dplyr::filter(TimeHr >= tmax),
           start = list(A = max(IV1$Concentration), k = 0.01))
MyCoefs <- summary(Fit)[["coefficients"]]

# Extrapolating to infinity with supplied coefficients
noncompAUC(IV1, time = TimeHr, extrap_inf = TRUE,
           extrap_inf_times = c(0.5, NA),
           extrap_inf_coefs = MyCoefs)

# Back extapolating to t0 with supplied coefficients
noncompAUC(IV1, time = TimeHr, extrap_t0 = TRUE,
           extrap_t0_coefs = list(coefs = MyCoefs,
                                  tmax = tmax))

shirewoman2/LaurasHelpers documentation built on Oct. 22, 2023, 2:07 p.m.