Sparse sampling (pre-clinical) data
See also “NCA Object” and, for additional reading, see “References”.
Data structure: NCA for discrete data (e.g., blood concentration data) requires the following input data:
Time of each sample
Concentrations
Output: Discrete data models (Models 200-202) estimate the parameters in the following lists.
Discrete (plasma) parameters that do not require Lambda Z estimation
Discrete (plasma) parameters that are estimated when Lambda Z is estimated
Discrete (plasma) parameters that are estimated when at steady-state
Discrete (plasma) parameters that do not require Lambda Z estimation
AUCall: Area under the curve from the time of dosing to the time of the last observation. If the last concentration is positive, AUClast=AUCall. Otherwise, AUCall will not be equal to AUClast, as it includes the additional area from the last measurable (positive) concentration down to zero or negative observations.
AUClast: Area under the curve from the time of dosing to the time of the last measurable (positive) concentration (Tlast).
AUClast_D: = AUClast/Dose
AUMClast: Area under the moment curve from the time of dosing to the last measurable (positive) concentration.
C0: Initial concentration. Given only for IV Bolus dosing. It is equal to the first observed concentration value if that value occurs at the dose time. Otherwise, it is estimated by back-extrapolating (see AUC_%Back_Ext below).
Clast: Observed concentration corresponding to Tlast.
Cmax: Maximum observed concentration, occurring at time Tmax, as defined below.
Cmax_D: = Cmax/Dose
Dose: Amount of last administered dose. This is assumed to be zero if not specified.
Dosing time: (Designated as ‘Time’ in the Dosing Used results.) Time of last administered dose. It is assumed to be zero unless otherwise specified. This parameter is used mainly with steady-state data, where input times may be coded as the time elapsed since the last dose (i.e., time resets to zero at the last dose), or the elapsed time since the time of the first dose.
MRTlast: Mean residence time from the time of dosing to the time of the last measurable concentration.
For non-infusion models: = AUMClast/AUClast
For infusion models: = (AUMClast/AUClast) – (Tinf/2)
where Tinf is the length of infusion.
No_points_lambda_z: Number of points used in computing Lambda Z. If Lambda Z cannot be estimated, this is set to zero.
N_Samples: The number of observations used in the analysis. It does not include missing or non-numeric observations, observations before dosing time, or interval observations where volume is zero, or points inserted by the engine (e.g., inserted at dosing time).
Tlag: Time of observation prior to the first observation with a measurable (positive) concentration. For discrete data (plasma), Tlag is only computed when the dosing type is extravascular.
Tlast: Time of last measurable (positive) observed concentration (missing if no positive data).
Tmax: Time of maximum observed concentration. For non-steady-state data, all data points used in the analysis are considered. If the maximum observed concentration is not unique, then the first maximum is used.
Discrete (plasma) parameters that are estimated when Lambda Z is estimated
The following list includes several parameters that are extrapolated to infinity. These parameters are calculated two ways: based on the last observed concentration (indicated by “_obs” appended to the parameter name), or based on the last predicted concentration (indicated by “_pred” appended to the parameter name), where the predicted value is based on the linear regression performed to estimate Lambda Z.
AUC_%Back_Ext(_obs, _pred): Computed for IV Bolus models. Percentage of AUCINF that was due to back extrapolation to estimate C0 when the first measured concentration is not at dosing time.
AUC_%Extrap(_obs, _pred): Percentage of AUCINF(_obs, _pred) due to extrapolation from Tlast to infinity:
= 100[(AUCINF– AUClast)/AUCINF]
AUCINF(_obs, _pred): AUC from time of dosing extrapolated to infinity, based on the last observed concentration (_obs) or last predicted concentration (_pred).
= AUClast + (Clast/Lambda_z)
AUCINF_D(_obs, _pred): = AUCINF/Dose
AUMC_%Extrap(_obs, _pred): Percent of AUMCINF(_obs, _pred) that is extrapolated.
= 100[(AUMCINF – AUMClast)/AUMCINF]
AUMCINF(_obs, _pred): Area under the first moment curve (AUMC) extrapolated to infinity.
= 
Clast_pred: Predicted concentration at Tlast:
= exp(Lambda_z_intercept – Lambda_z*Tlast)
CL(_obs, _pred), CL_F(_obs, _pred)a: Total body clearance for extravascular administration.
= Dose/AUCINF
Corr_XY: Correlation between time (X) and log concentration (Y) for the points used in the estimation of Lambda Z.
HL_Lambda_z: Terminal half-life: = ln(2)/Lambda_z
Lambda_z: First-order rate constant associated with the terminal (log-linear) portion of the curve. Estimated by linear regression of time vs. log concentration.
Lambda_z_intercept: Intercept on log scale estimated via linear regression of time vs. log concentration.
Lambda_z_lower: Lower limit on time for values to be included in the calculation of Lambda Z.
Lambda_z_upper: Upper limit on time for values to be included in the calculation of Lambda Z.
MRTINF(_obs, _pred): Mean residence time (MRT) extrapolated to infinity.
For non-steady-state data:
– For non-infusion models: = AUMCINF/AUCINF
– For infusion models: = (AUMCINF/AUCINF) – (Tinf/2), where Tinf is the length of infusion.
(Note that, for extravascular dosing (oral model 200), MRTINF includes Mean Input Time as well as time in systemic circulation.)
Rsq: Goodness of fit statistic for the terminal elimination phase.
Rsq_Adjusted: Goodness of fit statistic for the terminal elimination phase, adjusted for the number of points used in the estimation of Lambda Z.
Span: = (Lambda_z_upper – Lambda_z_lower)/HL_Lambda_z
Vss(_obs, _pred): An estimate of the volume of distribution at steady-state. For non-steady-state data:
= (MRTINF)(CL)
Computed for IV Bolus and Infusion dosing only. Not computed for extravascular dosing (oral model 200), as MRTINF for oral models includes Mean Input Time as well as time in systemic circulation and therefore is not appropriate to use in calculating Vss.
Vz(_obs, _pred), Vz_F(_obs, _pred)a: Volume of distribution based on the terminal phase.
For non-steady-state data: = Dose/[Lambda_z(AUCINF)]
aFor extravascular models (model 200), the fraction of dose absorbed cannot be estimated; therefore Volume and Clearance for these models are actually Volume/F or Clearance/F where F is the fraction of dose absorbed.
Discrete (plasma) parameters that are estimated when at steady-state
AUClower_upper: (Optional) User-requested area(s) under the curve from time “lower” to “upper”.
AUC_TAU: The partial area from dosing time to dosing time plus Tau. If dosing time plus Tau is not an exact observation time due to small sampling time deviations, the AUC is computed based on an estimated concentration at dosing time plus Tau, not on an actual concentration within a small sampling time deviation from dosing time plus Tau.
AUC_TAU_D: = AUC_TAU/Dose
AUC_TAU_%Extrap: Percentage of AUC_TAU that is due to extrapolation from Tlast to dosing time plus Tau.
= 
= 
AUMC_TAU: Area under the first moment curve from dosing time to dosing time plus Tau.
Cavg: Average concentration, computed = AUC_TAU/Tau
CLss, CLss_Fa: An estimate of the total body clearance, computed for IV Bolus and Infusion dosing only.
= 
Cmax: Maximum observed concentration, occurring at time Tmax, as defined below.
Cmin: Minimum observed concentration occurring at time Tmin as defined below.
Note: Regulatory agencies differ on the definition of Cmin: some agencies define Cmin the same as Ctau is defined below. Both Cmin and Ctau are included in the output so the correct parameter for the situation can be chosen.
Ctau: Concentration at dosing time plus Tau. Observed concentration if the value exists in the input data; otherwise, the predicted concentration value. Predicted concentrations are calculated following the same rules as for computing inserting missing endpoints needed for partial areas.
Fluctuation%: = 100[(Cmax – Cmin)/Cavg], where Cmin and Cmax were obtained between dosing time and dosing time plus Tau.
Fluctuation%_Tau: = 100[(Cmax – Ctau)/Cavg]
MRTINF(_obs, _pred): Mean residence time (MRT) extrapolated to infinity. For steady-state data:
For non-infusion: 
For infusion: 
where Tinf represents infusion duration. (Note that, for oral model 200, MRTINF includes Mean Input Time as well as time in systemic circulation.)
Swing: = (Cmax – Cmin)/Cmin
Swing_Tau: = (Cmax – Ctau)/Ctau
Tau: The (assumed equal) dosing interval for steady-state data. Available in the Dosing Used results for steady-state data.
Tmax: Time of maximum observed concentration. For steady-state data, based on observations collected during the dosing interval, that is, at or after the dosing time, but no later than the dosing time plus Tau, where Tau is the dosing interval. If the maximum observed concentration is not unique, then the first maximum is used.
Tmin: Time of minimum observed concentration. For steady-state data, based on observations collected during the dosing interval (i.e., after the dosing time, but no later than dosing time plus Tau, where Tau is the dosing interval). If the minimum observed concentration is not unique, then the first minimum is used.
Vss(_obs, _pred): An estimate of the volume of distribution at steady-state. Computed for IV Bolus and infusion dosing only.
= MRTINF(CLss)
Not computed for extravascular dosing (oral model 200), as MRTINF for oral models includes Mean Input Time as well as time in systemic circulation and therefore is not appropriate to use in calculating Vss.
Vz, Vz_Fa: For steady-state data: = 
aFor extravascular models (model 200), the fraction of dose absorbed cannot be estimated; therefore Volume and Clearance for these models are actually Volume/F or Clearance/F where F is the fraction of dose absorbed.
Data structure: NCA for interval data (e.g., urine data) requires the following input data:
Starting and ending time of each collection interval
Concentrations
Volumes
From this data, models 210–212 compute the following for the analysis:
Midpoint of each collection interval=(Starting time+Ending time)/2
Excretion rate for each interval (amount eliminated per unit of time)=(Concentration*Volume)/(Ending time-Starting time)
Output: Interval data models (Models 210–212) estimate the following parameters.
The worksheet will include the Sort(s), Carry(ies), parameter names, units, and computed values. A User Defined Parameters Pivoted worksheet will include the pivoted form of the User Defined Parameters worksheet.
Interval (urine) parameters that do not depend on Lambda Z
Amount_Recovered: Cumulative amount eliminated.
= 
AURC_all: Area under the excretion rate curve from the time of dosing to the midpoint of the interval with the last rate. If the last rate is positive, AURC_last=AURC_all.
AURC_last: Area under the excretion rate curve from time of dosing to Mid_Pt_last.
AURC_last_D: = AURC_last/Dose
Dose: Amount of last administered dose. This is assumed to be zero if not specified.
Dosing time: Available as ‘Time’ in the Dosing Used results. Time of last administered dose. It is assumed to be zero unless otherwise specified. This parameter is used mainly with steady-state data, where time may be coded as the time elapsed since the first dose, or the elapsed time since the time of the first dose.
Max_Rate: Maximum observed excretion rate, at time Tmax_Rate as defined below.
Mid_Pt_last: Midpoint of collection interval associated with last measurable (positive) observed excretion rate.
No_points_lambda_z: Number of points used in the computation of Lambda Z. If Lambda Z cannot be estimated, this is set to zero.
N_Samples: Number of observations in the analysis. Does not include missing or non-numeric observations, observations before dosing time, or interval observations where volume is zero. Does not include the point at dosing time if it was not observed but was inserted by the engine.
Percent_Recovered: = 100(Amount_Recovered/Dose)
Rate_last: Last observed measurable (positive) rate at time Mid_Pt_last.
Tlag: Midpoint of the collection interval prior to the first collection interval with measurable (positive) rate. Computed for all interval data models.
Tmax_Rate: Midpoint of the collection interval associated with the maximum observed excretion rate.
If the maximum observed excretion rate is not unique, then the first maximum is used.
Vol_UR: Sum of Volumes.
Interval (urine) parameters that are estimated when Lambda Z is estimated
The following list includes some parameters that are extrapolated to infinity. These parameters are calculated two ways: based on the last observed excretion rate: Rate_last (indicated by “_obs” appended to the parameter name), or based on the last predicted excretion rate: Rate_last_pred (indicated by “_pred” appended to the parameter name), where the predicted value is based on the linear regression performed to estimate Lambda Z.
AURC_%Extrap(_obs, _pred): Percent of AURC_INF(_obs, _pred) that is extrapolated.
AURC_INF(_obs, _pred): Area under the urinary excretion rate curve extrapolated to infinity, based on the last observed excretion rate (_obs) or the last predicted rate (_pred), i.e., the excretion rate at the final midpoint estimated using the linear regression for Lambda Z. Note that AURC_INF is theoretically equal to Amount_Recovered, but will differ due to experimental error.
Corr_XY: Correlation between midpoints and log excretion rates for the points used in the estimation of Lambda Z.
HL_Lambda_z: Terminal half-life=ln(2)/Lambda Z
Lambda_z: First-order rate constant associated with the terminal (log-linear) portion of the curve. This is estimated via linear regression of midpoints vs. log excretion rates.
Lambda_z_intercept: Intercept on log scale estimated via linear regression of midpoints vs. log excretion rates.
Lambda_z_lower: Lower limit on midpoint for values to be included in Lambda Z estimation.
Lambda_z_upper: Upper limit on midpoint for values to be included in Lambda Z estimation.
Rate_last_pred: Predicted rate at Mid_Pt_last.
= 
Rsq: Goodness of fit statistic for the terminal elimination phase.
Rsq_Adjusted: Goodness of fit statistic for the terminal elimination phase, adjusted for the number of points used in the estimation of Lambda Z.
Span: = (Lambda_z_upper – Lambda_z_lower)/HL_Lambda_z