Usage: ncappc (path=, obsFile=, …)
Figure 1. Schematic work-flow of ncappc.
The ncappc functionality is a flexible tool in R to,
The work-flow of ncappc is shown in Figure 1. In order to perform traditional NCA, the only mandatory argument is obsFile, which is the name of the file with the observed concentration vs. time data. Other arguments may be assigned to the desired values, if required.
In the presence of the non-empty simFile argument (NONMEM output file witht he simulated concentration vs. time data) ncappc function performs the diagnostic tests for the related PK model besides performing the traditional NCA. This function creates a directory, called “SIMDATA”, to store the estimated NCA metrics from the simulated data. If the working directory contains any directory called “SIMDATA”, this function offers the following three options to the user:
| Name | Type | Default | Description |
|---|---|---|---|
| obsFile | String | NULL | Name of the file with the observed data |
| simFile | String | NULL | Name of the NONMEM output file with the simulated data |
| grNm | String | NULL | Column name for population group |
| grp | String or numeric array | NULL | group id (e.g c(1,2)) |
| flNm | String | NULL | Column name for population group |
| flag | String or numeric array | NULL | flag id (e.g. c(1,2)) |
| doseNm | String | NULL | Column name to specify dose identifiers |
| dose | String or numeric array | NULL | Dose identifiers to be used (c(1,2)) |
| concUnit | String | NULL | Unit of concentration |
| timeUnit | String | NULL | Unit of time |
| doseUnit | String | NULL | Unit of dose amount |
| doseNormUnit | String | NULL | Normalization factor of dose amount (e.g. “kg”) |
| obsLog | String | “FALSE” | DV in Observed data in logarithmic form (“TRUE”, “FALSE”) |
| simLog | String | “FALSE” | DV in NONMEM output in logarithmic form (“TRUE”, “FALSE”) |
| psnOut | String | “FALSE” | if the observed data is an output from PsN |
| idNmObs | String | “ID” | Column name for ID in observed data |
| timeNmObs | String | “TIME” | Column name for time in observed data |
| concNmObs | String | “DV” | Column name for conc in observed data |
| idNmSim | String | “ID” | Column name for ID in simulated data |
| timeNmSim | String | “TIME” | Column name for time in simulated data |
| concNmSim | String | “DV” | Column name for conc in simulated data |
| AUCTimeRange | Numeric array of two elements | NULL | User-defined window of time used to estimate AUC |
| backExtrp | String | “FALSE” | If back-extrapolation is needed for AUC (“TRUE” or “FALSE”) |
| LambdaTimeRange | Numeric array of two elements | NULL | User-defined window of time to estimate elimination rate-constant |
| LambdaExclude | Numeric array | NULL | User-defined excluded observation time points for estimation of elimination rate-constant |
| doseAmtNm | String | NULL | Column name to specify dose amount |
| adminType | String | “extravascular” | Route of administration (iv-bolus, iv-infusion, extravascular) |
| doseType | String | “ns” | steady-state (ss) or nonsteady-state (ns) dose |
| Tau | Numeric | NULL | dosing interval for steady-state data |
| TI | Numeric | NULL | Infusion duration |
| method | String | “linear” | Method to estimate area under the curve (e.g. “linear”, “loglinear” or “mixed”) |
| blqNm | String | NULL | Name of BLQ column if used |
| blqExcl | String or numeric | “1” | Excluded BLQ value or logical condition (e.g. 1, “>=1”, c(1,“>3”)) |
| evid | String | “FALSE” | Use EVID (yes, no) |
| evidIncl | Numeric | “0” | Included EVID |
| mdv | String | “FALSE” | Use MDV (“TRUE” (includes data for MDV==0), “FALSE”) |
| filterNm | String | NULL | Column name for filter |
| filterExcl | String or numeric | NULL | Filter identifier or logical condition used for row exclusion (e.g. c(1,2, “<20", ">=100”, “!=100”) ) |
| negConcExcl | String | “FALSE” | Exclude negative values for concentration |
| param | String array | c(“AUClast”, “Cmax”) | NCA metrics that can be used to perform diagnostic tests (“AUClast”, “AUClower_upper”, “AUCINF_obs”, “AUCINF_pred”, “AUMClast”, “Cmax”, “Tmax”, “HL_Lambda_z”) |
| timeFormat | String | “number” | time format (“number”, “H:M”, “H:M:S”) |
| dateColNm | String | NULL | colunm name for date if used (“Date”, “DATE”) |
| dateFormat | String | NULL | date format (“D-M-Y”, “D/M/Y” or any other combination of D, M and Y) |
| spread | String | “npi” | measure of the spread of simulated data (“ppi” (95% parametric prediction interval) or “npi” (95% nonparametric prediction interval)) |
| tabCol | String array | c(“AUClast”, “Cmax”, “Tmax”, “AUCINF_obs”, “Vz_obs”, “Cl_obs”, “HL_Lambda_z”) | Output columns to be printed in the report in addition to ID, dose and population strata information (list of NCA metrics in a string array) |
| figFormat | String | “tiff” | Format of the produced figures (“bmp”, “jpeg”, “tiff”, “png”) |
| noPlot | String | “FALSE” | Perform only NCA calculations without any plot generation (“TRUE”, “FALSE”) |
| printOut | String | “TRUE” | Write/print output on the disk (“TRUE”, “FALSE”) |
obsFile
The name of the file containing the observed concentration vs. time data. This is a mandatory argument and the default value to this argument is NULL. The columns within the observed data file must be separated by either comma or space or tab.
simFile
The name of the file containing the NONMEM output of the concentration vs. time data simulated using the PK model to be diagnosed. The default value to this argument is NULL. In the absence of this argument ncappc function performs only the traditional NCA; otherwise, ncappc function performs the traditional NCA as well as the diagnostic tests for the related PK model
grNm and flNm
Column name for the population group or subgroups, indicating any stratification within the entire population if present. These two arguments allows two levels of stratification and ther are interchangable to signify population groups and subgroups. The default value for these arguments are NULL.
grp and flag
Identfiers for the population stratifications (group or subgroups), present in the “grNm” or “flNm” column, respectively. The default value for this argument is NULL. If the “grNm” or “flNm” arguments are non-empty, but the “grp” and “flag” arguments are left as NULL, this function will use the unique values from the “grNm” or “flNm” column as identifiers for the population strata.
doseNm
Column name to specify the dose identifier. This is a mandatory argument for the multiple-dose data. If this argument is unused, this function will assume a single-dose data. The default value for this argument is NULL.
dose
An array of strings or numerical values specifying the dose identifiers present in the column assigned by “doseNm”. If the dose identifiers are 1 and 2, the input to this argument should be c(1,2). If the “doseNm” argument is non-empty, but the “dose” argument is unused, this function will extract the unique values from the dose column and use them as the dose identifiers. The default value for this argument is NULL.
concUnit
The unit of plasma concentration values (e.g. “ng”). The default value for this argument is NULL.
timeUnit
The unit of time intervals (e.g. “hr”). The default value for this argument is NULL.
doseUnit
Unit for the dosage amount (e.g. “ng”). The default value for this argument is NULL.
doseNormUnit
Normalization factor for the dosage amount (e.g. body weight in “kg”). The default value for this argument is NULL.
obsLog and simLog
These arguments decide if the concentration values in the observed and simulated data sets are in logarithmic form. The accepted input to these arguments is either “TRUE” or “FALSE”. The default value for these arguments is “FALSE”.
psnOut
It is possible to generate the input file with the observed data using PsN. This argument lets the function know if the input data is in PsN or NONMEM output format. The possible values to this argument are “TRUE” and “FALSE”, “FALSE” being the default value.
idNmObs and idNmSim
Column name for individual ID in observed and simulated data. The default value for this argument is “ID”.
timeNmObs and timeNmSim
Column name for time in observed and simulated data. The default value for this argument is “TIME”.
concNmObs and concNmSim
Column name for plasma concentration in observed and simulated data. The default value for this argument is “DV”.
AUCTimeRange
This argument lets the user to choose a specific window of time to be used to estimate AUC. The accepted format for the input to this argument is a numeric array of two elements; c(1,24) will estimate the AUC values within 1st to 24th unit of time interval. The default value for this argument is NULL.
backExtrp
This argument lets the user to choose if the back extrapolation for the area estimatation is performed from rhe first observed data to dosing time. The default value for this argument is “FALSE”.
LambdaTimeRange
This argument lets the user to choose a specific window of time to be used to estimate the elimination rate constant (Lambda) in the elimination phase after the last observed data. The accepted format for the input to this argument is a numeric array of two elements; c(14,24) will estimate the Lambda using the data within the 14th to 24th unit of time interval. The default value for this argument is NULL.
LambdaExclude This argument lets the user exclude observation time points for the estimation of elimination rate-constant (Lambda) in the elimination phase. The accepted format for the input to this argument is a numeric array of time points; c(8,10) will exclude time points 8 and 10 while estimating the Lambda. The default value for this argument is NULL.
doseAmtNm
Column name to specify the dose amount. This argument is unused if the value of the dose amount is provided in the “doseAmt” argument. If the “doseAmt” argument is empty, the value of the dose amount is extracted from the column specified in this argument or from the “AMT” column. The default value for this argument is “AMT”.
adminType
This argument is used to specify the route of the drug administration. The allowed values for this argument are “iv-bolus”, “iv-infusion” and “extravascular”. The default route of administration is “extravascular”
doseType
This argument is used to specify either the steady-state (“ss”) or the nonsteady-state (“ns”) dosage types. The default value to this argument is “ns”.
Tau
The dosing interval for the steady-state data. This is a mandatory argument if the doseType argument is assigned to “ss”. The default value to this argument is NULL.
TI
The infusion duration for the steady-state data. If the argument is empty, TI is calculated from the “RATE” and “AMT” values. This is a mandatory argument if the doseType argument is assigned to “ss” and the input data file does not contain “RATE” and “AMT” columns. The default value to this argument is NULL.
method
The user is allowed to choose the method of area estimation (AUC, AUMC). The “linear” option uses linear trapezoidal method of area estimation; while the “loglinear” method uses log-linear trapezoidal method. The “mixed” option uses the linear approximation for the ascending part of the curve and log-linear approximation for the descending part of the curve during the area estimation. The default value for this argument is “linear”.
blqNm
Name of the BLQ data column, if the user decides to filter the input based on BLQ data. The default value for this argument is NULL, which means the BLQ column will not be used to filter.
blqExcl
The BLQ values that will be used to filter the input data. This argument will be used only if the “blqNm” argument is non-empty. This argument accepts either numeric values and/or logical conditions (e.g. 1, “>=1”, c(1,“>3”)). The default value for this argument is 1.
evid
This argument decides if the EVID column will be used to filter the input data. The accepted input to this argument is either “TRUE” or “FALSE”. The default value for this argument is “FALSE”.
evidIncl
This arguments accepts the values of the EVID data that will included for the calculations. This argument is used only if the “evid” argument is non-empty. The default value for this argument is 0.
mdv
This argument decides if the MDV column will be used to filter the input data. The accepted input to this argument is either “TRUE” or “FALSE”. The default value for this argument is “FALSE”. If chosen “TRUE”, all rows with MDV = 0 will be selected for the calculations.
filterNm
The name of the column that will be used to filter the input data. The default value for this argument is NULL.
filterExcl
This arguments accepts the values from the “filterNm” column that will used to exclude rows form the input data. This argument accepts either string/numeric values and/or logical conditions (e.g. “a”, 1, c(1,2), “<20",
">=100”, “!=100”, c(1,“>3”), or c(“a”,“3”)). This argument is used only if the “filterNm” argument is non-empty. The default value for this argument is NULL.
negConcExcl
This argument is used to exclude the data with negative concentration values. The accepted input to this argument is either “TRUE” or “FALSE”. The default value for this argument is “FALSE”.
param
This argument lists the NCA metrics that will be used to perform the diagnostic tests. Any combination of the following NCA metrics can be assigned to this argument: “AUClast”, “AUClower_upper”, “AUCINF_obs”, “AUCINF_pred”, “AUMClast”, “Cmax”, “Tmax”, “HL_Lambda_z”. The default value for this argument is c(“AUClast”,“Cmax”).
timeFormat
The data format for the time column. The accepted formats are numerical values, “H:M” or “H:M:S”. The default value for this argument is “number”, which signifies the numerical values.
dateColNm
This function allows the user to combine the information from the “DATE” column with the “TIME” column to calculate the time difference between the observations. This argument accepts the name of the date column, if used to calculate the time difference. The default value for this argument is NULL.
dateFormat
The data format for the date column. The accepted formats are “D-M-Y”, “D/M/Y” or any otehr combination of D, M and Y. The default value for this argument is NULL.
spread
This argument determines the metric that will be used to measure the spread of the simulated distribution of the NCA metrics. The spread argument accepts either “ppi” or “npi” as input. The “ppi” uses 95% parametric prediction interval, while “npi” uses the 95% nonparametric prediction interval. The default value for this argument is “npi”.
tabCol This argument selects the table columns, in addition to ID, dose and population strata, to print in the produced report. This argument accepts a list of NCA metrics in a string array. The default value of this argument is c(“AUClast”, “Cmax”, “Tmax”, “AUCINF_obs”, “Vz_obs”, “Cl_obs”, “HL_Lambda_z”).
figFormat This argument selects the format of the produced figures. Acceptable value for this argument is either bmp, jpeg, tiff or png. The default value is “tiff”.
noPlot This argument can turn on/off plot generation during NCA calculations. Acceptable value for this argument is either “TRUE” (turns off plot generation) or “FALSE” (turns on plot generation). The default value is “FALSE”.
printOut This argument lets the user decide if the ncappc generated figures and tables will be saved on the disk. Acceptable value for this argument is either “TRUE” or “FALSE”. The default value is “TRUE”.
NCA metrics are eatimated according to traditional PK calculations. The names of the various NCA metrics estimated in this package are assigned mainly following the names used in WinNonlin. This package accepts any of the three different types of drug administration, (i) iv-bolus, (ii) iv-infusion and (iii) extravascular; ncappc also can accept both non-steady state and steady-state data. The NCa metric that are estimated and reported by ncappc are listed below.
C0
C0 is the initial concentration at the dosing time. It is the observed concentration at the dosing time, if available. Otherwise it is approximated using the following rules. For iv-bolus data, log-linear back-extrapolation (see “backExtrap” argument) is performed from the first two observations to estimate C0, provided the local slope is negative. However, if the slope is >=0 or at least one of the first two concentrations is 0, the first non-zero concentration is used as C0. For other types of administration, C0 is equal to 0 for non steady-state data and for steady-state data the minimum value observed between the dosing intervals is used to estimate C0, provided the “backExtrap” argument is set to “yes”.
Cmax, Tmax and Cmax_D
Cmax and Tmax are the value and the time of maximum observed concentration, respectively. If the maximum concentration is not unique, the first maximum is used. For steady state data, The maximum value between the dosing intervals is considered. Cmax_D is the dose normalized maximum observed concentration.
Clast and Tlast
Clast and Tlast are the last measurable positive comcentration and the corresponding time, respectively.
AUClast
The area under the concentration vs. time curve from the first observed to last measurable concentration.
AUMClast
The area under the first moment of the concentration vs. time curve from the first observed to last measurable concentration.
MRTlast
Mean residence time from the first observed to last measurable concentration. For non-infusion models,
\(MRTlast = \frac{AUMClast}{AUClast}\)
For infusion models,
\(MRTlast = \frac{AUMClast}{AUClast}-\frac{TI}{2}\)
where TI is the infusion duration.
No_points_Lambda_z
No_points_Lambda_z is the number of observed data points used to determine the best fitting regression line in the elimination phase.
AUC_pBack_Ext
The percentage of AUClast that is contributed by the back extrapolation to estimate C0. The rules to to estimate C0 is given above.
AUClower_upper
The AUC under the concentration-time profile within the user-specified window of time privided as the “AUCTimeRange” argument. In case of empty “AUCTimeRange” argument, AUClower_upper is equal to the AUClast.
Rsq, Rsq_adjusted and Corr_XY
Regression coefficient of the regression line used to estimate the elimination rate constant. Rsq_adjusted is the adjusted value of Rsq given by the following relation.
\(Rsq\_adjusted = 1-\frac{(1-Rsq^2)*(n-1)}{n-2}\)
where n is the number of points in the regression line. Corr_XY is the square root of Rsq.
Lambda_z
Elimination rate constant estimated from the regression line representing the terminal phase of the concentration-time prifile. The relation between the slope of the regression line and Lambda_z is:
\(Lambda\_z = -(slope)\)
Lambda_lower and Lambda_upper
Lower and upper limit of the time values from the concentration-time profile used to estimate Lambda_z, respectively, in case the “LambdaTimeRange” is used to specify the time range.
HL_Lambda_z
Terminal half-life of the drug:
\(HL\_Lambda\_z = \frac{ln2}{\lambda_z}\)
AUCINF_obs and AUCINF_obs_D
AUC estimated from the first sampled data extrapolated to \({\infty}\). The extrapolation in the terminal phase is based on the last observed concentration (\({Clast_obs}\)). The equiation used for the estimation is given below.
\(AUCINF\_obs = AUClast+\frac{Clast\_obs}{\lambda_z}\)
AUCINF_obs_D is the dose normalized AUCINF_obs.
AUC_pExtrap_obs
Percentage of the AUCINF_obs that is contributed by the extrapolation from the last sampling time to \({\infty}\).
\(AUC\_pExtrap\_obs = \frac{AUCINF\_obs-AUClast}{AUCINF\_obs}*100\%\)
AUMCINF_obs
AUMC estimated from the first sampled data extrapolated to \({\infty}\). The extrapolation in the terminal phase is based on the last observed concentration. The equiation used for the estimation is given below.
\(AUMCINF\_obs = AUMClast+\frac{Tlast*Clast\_obs}{\lambda_z}+\frac{Clast\_obs}{\lambda_{z}^2}\)
AUMC_pExtrap_obs
Percentage of the AUMCINF_obs that is contributed by the extrapolation from the last sampling time to \({\infty}\).
\(AUMC\_pExtrap\_obs = \frac{AUMCINF\_obs-AUMClast}{AUMCINF\_obs}*100\%\)
Vz_obs
Volume of distribution estimated based on total AUC using the following equation.
\(Vz\_obs = \frac{Dose}{\lambda_z*AUCINF\_obs}\)
Cl_obs
Total body clearance.
\(Cl\_obs = \frac{Dose}{AUCINF\_obs}\)
AUCINF_pred and AUCINF_pred_D
AUC from the first sampled data extrapolated to \({\infty}\). The extrapolation in the terminal phase is based on the last predicted concentration obtained from the regression line used to estimate Lambda_z (\({Clast\_pred}\)). The equiation used for the estimation is given below.
\(AUCINF\_pred = AUClast+\frac{Clast\_pred}{\lambda_z}\)
AUCINF_pred_D is the dose normalized AUCINF_pred.
AUC_pExtrap_pred
Percentage of the AUCINF_pred that is contributed by the extrapolation from the last sampling time to \({\infty}\).
\(AUC\_pExtrap\_pred = \frac{AUCINF\_pred-AUClast}{AUCINF\_pred}*100\%\)
AUMCINF_pred
AUMC estimated from the first sampled data extrapolated to \({\infty}\). The extrapolation in the terminal phase is based on the last predicted concentration obtained from the regression line used to estimate Lambda_z (\({Clast\_pred}\)). The equiation used for the estimation is given below.
\(AUMCINF\_pred = AUMClast+\frac{Tlast*Clast\_pred}{\lambda_z}+\frac{Clast\_pred}{\lambda_{z}^2}\)
AUMC_pExtrap_pred
Percentage of the AUMCINF_pred that is contributed by the extrapolation from the last sampling time to \({\infty}\).
\(AUMC\_pExtrap\_pred = \frac{AUMCINF\_pred-AUMClast}{AUMCINF\_pred}*100\%\)
Vz_pred
Volume of distribution estimated based on total AUC using the following equation.
\(Vz\_pred = \frac{Dose}{\lambda_z*AUCINF\_pred}\)
Cl_pred
Total body clearance.
\(Cl\_pred = \frac{Dose}{AUCINF\_pred}\)
MRTINF_obs
Mean residence time from the first sampled time extrapolated to \({\infty}\) based on the last observed concentration (\({Clast\_obs}\)).
For non-infusion non steady-state data:
\(MRTINF\_obs = \frac{AUMCINF\_obs}{AUCINF\_obs}\)
For infusion non steady-state data:
\(MRTINF\_obs = \frac{AUMCINF\_obs}{AUCINF\_obs}-\frac{TI}{2}\)
where \({TI}\) is the infusion duration. For non-infusion steady-state data:
\(MRTINF\_obs = \frac{AUMCINF\_obs|_{0}^{\tau}+\tau*(AUCINF\_obs-AUC|_{0}^{\tau})}{AUCINF\_obs|_{0}^{\tau}}\)
For infusion steady-state data:
\(MRTINF\_obs = \frac{AUMCINF\_obs|_{0}^{\tau}+\tau*(AUCINF\_obs-AUC|_{0}^{\tau})}{AUCINF\_obs|_{0}^{\tau}}-\frac{TI}{2}\)
For steady-state data \({\tau}\) represents the dosing interval.
MRTINF_pred
Mean residence time from the first sampled time extrapolated to \({\infty}\) based on the last predicted concentration obtained from the regression line used to estimate Lambdaz (\({Clast\_pred}\)).
For non-infusion non steady-state data:
\(MRTINF\_pred = \frac{AUMCINF\_pred}{AUCINF\_pred}\)
For infusion non steady-state data:
\(MRTINF\_pred = \frac{AUMCINF\_pred}{AUCINF\_pred}-\frac{TI}{2}\)
where \({TI}\) is the infusion duration.
For non-infusion steady-state data:
$MRTINF_pred = \frac{AUMCINF_pred|{0}{\tau}+\tau*(AUCINF_pred-AUC|{0}{\tau})}{AUCINF_pred|{0}{\tau}}$
For infusion steady-state data:
\(MRTINF\_pred = \frac{AUMCINF\_pred|_{0}^{\tau}+\tau*(AUCINF\_pred-AUC|_{0}^{\tau})}{AUCINF\_pred|_{0}^{\tau}}-\frac{TI}{2}\)
For steady-state data \({\tau}\) represents the dosing interval.
Vss_obs and Vss_pred
An estimate of the volume of distribution at steady-state.
\(Vss\_obs = MRTINF\_obs*Cl\_obs\)
\(Vss\_pred = MRTINF\_pred*Cl\_pred\)
Tau
The dosing interval for steady-state data. This value is assumed equarion over multiple doses.
Cmin and Tmin
Cmin is the minimum concentration between 0 and Tau and Tmin is the corresponding time for steady-state data.
Cavg
The average concentration between 0 and Tau for steady-state data.
\(Cavg = \frac{AUC|_{0}^{Tau}}{Tau}\)
p_Fluctuation
Percentage of the fluctuation of the concentration between 0 and Tau for steady-state data.
\(p\_Fluctuation = \frac{Cmax-Cmin}{Cavg}*100\%\)
Accumulation_Index
\(Accumulation\_Index = \frac{1}{1-e^{-\lambda_{z}*\tau}}\)
Clss
An estimate of the total body clearance for steady-state data.
\(Clss = \frac{Dose}{AUC|_{0}^{\tau}}\)
Area Under the Curve
AUC can be estimated using either the linear trapezoidal method or the log-linear trapezoidal method. It is shown that linear approximation is a better method to estimate of the area under a curve at the positive or zero local slopes (increasing concentration or at the peak), while the log-linear approximation is the method of choice to estimate of the area under a curve at the negative local slope (decreasing concentration) assuming that the plasma concentration decline mono-exponentially in the elimination phase. There are three different options available in ncappc: “linear”, “loglinear”, and “mixed”. The user can choose any of these three methods for the estimating the area under the zero-order moment (AUClast) and first-order moment (AUMClast) curves between the first and the last sampling time. If the lower and upper limit of the time range is provided, AUC is also calculated for that specified window of time (AUClower_upper).
The “linear” option under the argument, namely “method” allows the function to employ linear trapezoidal approximation (Equations 1 and 2) to estimate the area under the zero and first order moment curves.
\(AUC|_{i}^{i+1} = \frac{C_{i+1}+C_{i}}{2}*\Delta{t}\), if \(C_{i+1} \geq C_{i}\) (Equation 1)
\(AUMC|_{i}^{i+1} = \frac{(C_{i+1}*t_{i+1})+(C_{i}*t_{i})}{2}*\Delta{t}\), if \(C_{i+1} \geq C_{i}\) (Equation 2)
The “loglinear” options employ the log-linear trapezoidal approximation (Equations 3 and 4) to estimate the area under the zero and first order moment curves.
\(AUC|_{i}^{i+1} = \frac{C_{i+1}-C_{i}}{ln(\frac{C_{i+1}}{C_{i}})}*\Delta{t}\), if \(C_{i+1} < C_{i}\) (Equation 3)
\(AUMC|_{i}^{i+1} = \frac{(C_{i+1}*t_{i+1})-(C_{i}*t_{i})}{ln(\frac{C_{i+1}}{C_{i}})}*\Delta{t}-\frac{C_{i+1}-C_{i}}{ln(\frac{C_{i+1}}{C_{i}})}*\Delta{t}^2\), if \(ßC_{i+1} < C_{i}\) (Equation 4)
The “mixed” option employs the linear trapezoidal approximation for the increasing concentration between two consecutive observations or at the peak concentration, while it uses the log-linear trapezoidal approximation at the declining concentration between two consecutive observations.
\paragraph{} where, \({C_i}\) is the plasma concentration at time \({t_i}\), \({\Delta{t}}\) is \({t_{i+1}-t_{i}}\) and \({n}\) is the number of data points. Each estimated segment of AUC and AUMC is added to obtain AUClast and AUMClast, respectively.
\subsection{Extrapolation in the elimination phase} \label{subsection} The plasma concentration of the drug in the elimination phase is assumed to follow the mono-exponential decay with the rate of elimination, Lambda_z. The extrapolation of the plasma concentration from the last sampling time to infinity is performed based on the regression line estimated from the elimination phase data. All concentration data from Cmax onwards are considered as the elimination phase data. The following steps are performed to determine the optimum regression line representing the plasma concentration in the elimination phase. First, a regression line is obtained from the last three non-zero concentrations in the elimination phase and the regression coefficient or \({R^2}\) (Rsq) and Adjusted \({R^2}\) (Rsq_adjusted) are calculated. Next, one data point at a time upto Cmax is added to the set and the corresponding Rsq and Rsq_adjusted are calculated each time. In order to extrapolate the NCA metrics from the last observed value to infinity in the terminal phase, the ncappc functionality requires the following two criteria to be satisfied.
If any individual in the data set does not satisfy the above mention criteria, the NCA metrics for that individual are not extrapolated to infinity for the elimination phase. Othrwise, the regression line yielding the highest Rsq_adjusted is used to estimate Lambda_z. If there is any other regression line that yields Rsq_adjustzed within 0.0001 of the highest Rsq_adjusted and includes larger number of data points, that regression line is used to estimate Lambda_z. Lambda_z is estimated as the negative of the slope of the selected regression line representing the elimination phase of the concentration profile (Equation 5). The number of points used to determine the Lambda_z is called No_points_Lambda_z. It is possible to specify the lower and upper limit on time for the calculation of the regression line in the elimination phase (Lambda_z_lower and Lambda_z_upper, respectively).
\(Lambda\_z = -(slope) = \frac{ln(Clast)-ln(Clast-k)}{Tlast-(Tlast-k)}\) (Equation 5)
where \({k+1}\) is the number of data points out of \({n}\) data samples that are used to calculate the regression line representing the elimination phase. Clast is the plasma concentration corresponding to the last sampled time Tlast. The elimination half-life (HL_Lambda_z) is calculated from Lambda_z using Equation 6.
\(HL\_Lambda\_z = \frac{log2}{Lambda\_z}\) (Equation 6)
The ncappc functionality produces this table to report the estimated values of the NCA metrics described in the previous section for each individual along with other stratifiers (eg. population group ID, dose ID, etc.) if specified in the input command. The extension “tsv” stands for “tab separated variable”, i.e., the columns in this table are separated by tabs. “NaN” or “NA” is produced for the NCA metrics which are irrelevant for the specified data type.
If simulated data is provided, this table also reports three additional columns for each of the eight NCA metrics that can be used for the diagnostics (AUClast, AUMClast, AUClower_upper, Tmax, Cmax, HL_Lambda_z, AUCINF_obs, AUCINF_pred). The names of the additional columns for AUClast are simAUClast, dAUClast and npdeAUClast. simAUClast for an individual represents the mean of the estimated AUClast values obtained from the set of simulated data. dAUClast for an individual represents the deviation of the mean of the simulated AUClast values from the AUClast value obtained from the observed data, scaled by the “spread” of the simulated distribution as described in the corresponding command-line argument. npdeAUClast for an individual represents the NPDE value of AUClast estimated from the simulated data with respect to the value of AUClast estimated from the observed data. Similar names are assigned to the additional columns for the other seven metrics.
This table reports a set of statistical parameters calculated for the entire population or the stratified population for the following NCA metrics estimated from the observed data: Tmax, Cmax, AUClast, AUClower_upper, AUCINF_obs, AUC_pExtrap_obs, AUCINF_pred, AUC_pExtrap_pred, AUMClast, AUMCINF_obs, AUMC_pExtrap_obs, AUMCINF_pred, AUMC_pExtrap_pred, HL_Lambda_z, Rsq, Rsq_adjusted and No_points_Lambda_z. Brief description of the twelve statistical parameters reported for each NCA metric is given below.
This table reports a set of statistical parameters calculated for the entire population or the stratified population for the mean values of the following NCA metrics estimated from the simulated data: Tmax, Cmax, AUClast, AUClower_upper, AUCINF_obs, AUC_pExtrap_obs, AUCINF_pred, AUC_pExtrap_pred, AUMClast, AUMCINF_obs, AUMC_pExtrap_obs, AUMCINF_pred, AUMC_pExtrap_pred, HL_Lambda_z, Rsq, Rsq_adjusted and No_points_Lambda_z. Brief description of the twelve statistical parameters reported for each NCA metric is given below.
This table reports the simulated concentration-time profiles for each individual obtained from a number of simulations. Currently the ncappc function accepts only NONMEM output format for the simulated data. All columns from the NONMEM output file are kept unaltered in this file and an additional column, namely “NSIM”, is printed to denote the corresponding simulation number for the concentration-time profile.
This table reports the estimated NCA metrics values for each individual obtained from the simulated concentration-time profiles. The number of the reported values for each individual for each NCA metric is equal to the number of simmulations performed. “NSIM” column denotes the simulation number. “NaN” or “NA” is produced for the NCA metrics which are irrelevant for the specified data type.
Concentration vs time profile for each individual stratified by dose or population group, if any, as obtained from the observed data. The left panels represent the raw data, while the right panels represent the semi-logarithmic form of the concentration data. Each of the thin lines represents individual data and the thicker brown line represents the smooth.
The first set of figures represent the concentration vs. time profile for each individual as obtained from the observed data. If the data indicate the presence of stratified population or multiple occasions, separate figures with appropriate subnumber will be generated. Each of the lines represents individual data. The above figure shows a typical example of the concentration-time profile. The left panels represent the raw data, while the right panels represent the semi-logarithmic form of the concentration data. Each of the lines represents individual data.
The second set of figures represent the histogram of four selected NCA metrics (AUClast, AUCINF_obs, Cmax, Tmax) estimated from the observed data. If the data indicate the presence of stratified population or multiple occasions, separate figures with appropriate subnumber will be generated. The solid and dotted blue vertical lines represent the population mean and the “spread” of the data, respectively. The “spread” is either defined by the 95% parametric prediction interval or by the 95% nonparametric prediction interval of the PK measures obtained from the simulated data. The above figure shows a typical example of this set of plots.
The third set of figures represent the histograms of the population means of the NCA metrics obtained from the sets of simulated data. The red and blue solid vertical lines represent the population mean of the corresponding NCA metric obtained from the observed data and the mean of the population means of the same NCA metric obtained from the simulated data set, respectively. The blue dashed vertical lines represent the “spread” of the simulated distribution. The “spread” is either defined by the standard deviation or by the 95% nonparametric prediction interval for the population mean of the NCA metrics obtained from the simulated data. If the data indicate the presence of stratified population or multiple occasions, separate figures with appropriate subnumber will be generated for every strata. The above figure shows a typical example of this set of plots.
The fourth set of plots represent the deviation of the mean of the NCA metrics for each individual estimated from the sets of simulated data (meanSim) from the corresponding values estimated from the observed data (Obs). The deviation is scaled by the “spread” of the simulated data as defined either by the distance between the meanSim and the 95% parametric prediction interval or by the distance between the meanSim and the 95% nonparametric prediction interval boundary of the simulated NCA metric distribution nearer to the observed value (Deviation = (Obs - meanSim)/ distance between meanSim and the 95% parametric prediction interval boundary) or (Deviation = (Obs - meanSim)/ distance between meanSim and the 95% nonparametric prediction interval boundary nearer to the Obs). The negative value of the deviation signifies over-prediction of the corresponding NCA metric, while a positive value of the deviation signifies under-prediction of the same. If the data indicate the presence of stratified population or multiple occasions, separate figures with appropriate subnumber will be generated for every strata. The above figure shows a typical example of this set of plots.
The fifth set of plots represent the distribution of the NCA metrics obtained from the simulated data for the individuals that are labelled as outliers by the ncappc. These individuals are marked as outliers because the absolute value of the scaled deviation for at least one of the NCA metrics used in the diagnosis is greater than 1. The red and blue solid vertical lines represent the observed NCA metric value and the mean of the simulated NCA metric values obtained from the observed and the simulated data for that individual, respectively. The dashed blue vertical lines represent the “spread” of the simulated distribution. If the data indicate the presence of stratified population or multiple occasions, separate figures with appropriate subnumber will be generated for every strata. The above figure shows a typical example of this set of plots.
The is sixth set of figures represent the Forest plot of the NPDE type analysis displaying the mean and standard deviation of the NPDE vaues of the NCA metrics in various population groups. The red and green dots represent the mean and the standard deviation of the NPDE, respectively while the horizontal red and green lines represent the corresponding 95% confidence intervals. The Y-axis of this plot represent different population or occasion strata, if present. The above figure shows a typical example of the forest plot.
The seventh set of plots represent NPDE values of the NCA metrics for each individual within a given population group calculated from the corresponding NCA metrics estimated from the observed and the simulated data. The negative value of the NPDE signifies over-prediction of the corresponding NCA metric, while a positive value of the NPDE signifies under-prediction of the same. If the data indicate the presence of stratified population or multiple occasions, separate figures with appropriate subnumber will be generated for every strata. The above figure shows a typical example of this set of plots.
The eighth set of plots represent the histogram of the NPDE values of the NCA metrics for all individuals within a given population group. The red solid vertical represents the mean of the ideal NPDE distribution, which is the theoretical normal distribution (mean=0, SD=1). The blue solid vertical lines represent the mean of the NPDE distribution for the corresponding population group. The dashed blue vertical lines represent the standard deviation of the distribution of the NPDE values within that population group. If the data indicate the presence of stratified population or multiple occasions, separate figures with appropriate subnumber will be generated for every strata. The above figure shows a typical example of this set of plots.