NCA parameter formulas (2024)

NCA parameter formulas

Plasma or serum data
Urine data
Sparse sampling (pre-clinical) data
Drug effect data model 220
User defined parameters
References

See also “NCA”and, for additional reading, see “References”.

Plasma or serum data

Data structure: NCA for blood concentration data requires the following input data:

•Time of each sample

•Plasma or serum concentrations

Output: Models 200–202 estimate the parameters in the following lists.

Plasma parameters that do not require Lambda Z estimation

Plasma parameters that are estimated when Lambda Z is estimated

Plasma parameters that are estimated when at steady-state

Plasma parameters that do not require Lambda Z estimation

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.

N_Samples: This parameter reports the number of non-missing observations used in the analysis of the profile (time is at or after dosing time, the observation is numeric, and the volume is positive for urine models). It does not count points inserted by engine, e.g., inserted at dosing time.

Dose: Amount of last administered dose. This is assumed to be zero if not specified.

No_points_Lambda_z: Number of points used in computing Lambda Z. If Lambda Z is not estima­ble, zero.

Tlag: Time of observation prior to the first observation with a measurable (non-zero) concentration. For plasma models, Tlag is only computed when the dosing type is extravascular.

Tmax: Time of maximum observed concentration. For non-steady-state data, the entire curve is con­sidered. If the maximum observed concentration is not unique, then the first maximum is used.

Cmax: Maximum observed concentration, occurring at time Tmax, as defined above.

Cmax_D: = Cmax/Dose

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).

Tlast: Time of last measurable (positive) observed concentration.

Clast: Observed concentration corresponding to Tlast.

AUClast: Area under the curve from the time of dosing to the time of the last measurable (positive) concentration (Tlast).

AUClast_D: = AUClast/Dose

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.

AUMClast: Area under the moment curve from the time of dosing to the last measurable (positive) concentration.

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.

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.

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.

Corr_XY: Correlation between time (X) and log concentration (Y) for the points used in the estimation of 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.

HL_Lambda_z: Terminal half-life: = ln(2)/l_z

Span: = (Lambda_z_upper – Lambda_z_lower)/HL_Lambda_z

Clast_pred: Predicted concentration at Tlast:

= exp(Lambda_z_intercept– Lambda_z*Tlast)

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

AUC_%Extrap(_obs, _pred): Percentage of AUCINF(_obs, _pred) due to extrapolation from Tlast to infinity:

= 100[(AUCINF– AUClast)/AUCINF]

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.

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)]

Cl(_obs, _pred), Cl_F(_obs, _pred)^a: Total body clearance for extravascular administration.

= Dose/AUCINF

AUMCINF(_obs, _pred): Area under the first moment curve (AUMC) extrapolated to infinity, based on the last observed concentration (obs) or the last predicted concentration (pred).

=

AUMC_%Extrap(_obs, _pred): Percent of AUMCINF(_obs, _pred) that is extrapolated.

= 100[(AUMCINF – AUMClast)/AUMCINF]

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 Tinfis the length of infusion.
(Note that, for extravascular dosing (oral model 200), MRTINF includes Mean Input Time as well as time in systemic circulation.)

Vss(_obs, _pred): For non-steady-state data: An estimate of the volume of distribution at steady-state based on the last observed (obs) or last predicted (pred) concentration.

= (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.

^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.

Plasma parameters that are estimated when at steady-state

Tau: Available in the Dosing Used results worksheet for steady-state data. The (assumed equal) dos­ing interval 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.

Cmax: Maximum observed concentration, occurring at time Tmax, as defined above.

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.

Cmin: Minimum observed concentration occurring at time Tmin as defined above.

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 that users can use the correct parameter for their situation.

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, see “Partial area calculation”.

Cavg: Average concentration, computed = AUC_TAU/Tau

Swing: = (Cmax – Cmin)/Cmin

Swing_Tau: = (Cmax – Ctau)/Ctau

Fluctuation%: = 100[(Cmax – Cmin)/Cavg] where Cminand Cmax were obtained between dos­ing time and dosing time plus Tau.

Fluctuation%_Tau: = 100[(Cmax – Ctau)/Cavg]

CLss, CLss_F^a: An estimate of the total body clearance, computed for IV Bolus and Infusion dosing only.

=

MRTINF(_obs, _pred): Mean residence time (MRT) extrapolated to infinity based on AUCINF(_obs, _pred).

For non-infusion:
For infusion:
where TI represents infusion duration. (Note that, for oral model 200, MRTINF includes Mean Input Time as well as time in systemic circulation.)

Vz, Vz_F^a: =

Vss(_obs, _pred): An estimate of the volume of distribution at steady-state based on the last observed (obs) or last predicted (pred) concentration. 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.

Accumulation Index: =

AUC_TAU: The partial area from dosing time to dosing time plus Tau. See “Partial area calculation”for information on how it is computed.

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. See “Par­tial area calculation” for information on how it is computed.

AUClower_upper: (Optional) User-requested area(s) under the curve from time “lower” to “upper”.

^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.