Exposure Metrics¶

Complete documentation for primary and secondary exposure metrics in NCA following FDA/EMA guidance.

Overview¶

Exposure metrics characterize drug exposure from concentration-time profiles without assuming a specific model structure.

Primary Exposure Metrics¶

Cmax - Maximum Concentration¶

The highest observed concentration:

using NeoPKPD

times = [0.0, 0.5, 1.0, 2.0, 4.0, 8.0, 12.0, 24.0]
conc = [0.0, 1.8, 2.5, 2.0, 1.2, 0.6, 0.3, 0.075]

# From NCA result
result = run_nca(times, conc, 100.0)
println("Cmax: $(result.cmax)")

# Direct calculation
cmax = nca_cmax(conc)

Tmax - Time of Maximum Concentration¶

Time at which Cmax occurs:

# From NCA result
println("Tmax: $(result.tmax)")

# Direct calculation
tmax = nca_tmax(times, conc)

When multiple points have the same maximum concentration, Tmax is the first occurrence.

Cmin - Minimum Concentration¶

For multiple dose/steady-state analysis:

# Multiple dose NCA
result = run_nca(times, conc, 100.0; dosing_type=:multiple, tau=24.0)
println("Cmin: $(result.cmin)")

# Direct calculation
cmin = nca_cmin(conc)

Clast and Tlast - Last Measurable Concentration¶

Last concentration above the LLOQ:

# From NCA result
println("Clast: $(result.clast)")
println("Tlast: $(result.tlast)")

# With LLOQ specification
config = NCAConfig(lloq=0.05)
result = run_nca(times, conc, 100.0; config=config)

Cavg - Average Concentration¶

Average concentration over a dosing interval (AUC0-tau/tau):

result = run_nca(times, conc, 100.0; dosing_type=:steady_state, tau=24.0)
println("Cavg: $(result.cavg)")

# Direct calculation
cavg = nca_cavg(times, conc, 24.0, NCAConfig())

AUC Calculations¶

AUC Methods¶

NeoPKPD supports three AUC calculation methods:

Method	Usage	Formula
`LinearMethod()`	Ascending phases	\((C_1 + C_2) \cdot \Delta t / 2\)
`LogLinearMethod()`	Descending phases	\((C_1 - C_2) / \ln(C_1/C_2) \cdot \Delta t\)
`LinLogMixedMethod()`	Recommended default	Linear up, log-linear down

# Linear trapezoidal
config_linear = NCAConfig(method=LinearMethod())

# Log-linear trapezoidal
config_log = NCAConfig(method=LogLinearMethod())

# Lin-Log Mixed (FDA/EMA recommended)
config_mixed = NCAConfig(method=LinLogMixedMethod())

result = run_nca(times, conc, 100.0; config=config_mixed)

AUC0-t (AUC to Last)¶

Area under the curve from time 0 to the last measurable concentration:

result = run_nca(times, conc, 100.0)
println("AUC0-t: $(result.auc_0_t)")

# Direct calculation
auc_0t = auc_0_t(times, conc, NCAConfig())

AUC0-inf (AUC to Infinity)¶

AUC extrapolated to infinity using lambda_z:

\[AUC_{0-\infty} = AUC_{0-t} + \frac{C_{last}}{\lambda_z}\]

println("AUC0-inf: $(result.auc_0_inf)")
println("Extrapolation: $(result.auc_extra_pct)%")

# Direct calculation (requires lambda_z)
lambda_z = result.lambda_z_result.lambda_z
auc_inf, extra_pct = auc_0_inf(times, conc, lambda_z, result.clast, NCAConfig())

Quality Warning: If auc_extra_pct > 20%, the AUC0-inf may be unreliable.

AUC0-tau (AUC over Dosing Interval)¶

For multiple dose or steady-state analysis:

result = run_nca(times, conc, 100.0; dosing_type=:multiple, tau=24.0)
println("AUC0-tau: $(result.auc_0_tau)")

# Direct calculation
auc_tau = auc_0_tau(times, conc, 24.0, NCAConfig())

Partial AUC¶

AUC between any two time points:

# AUC from t=0 to t=4
auc_0_4 = auc_partial(times, conc, 0.0, 4.0, NCAConfig())

# AUC from t=4 to t=12
auc_4_12 = auc_partial(times, conc, 4.0, 12.0, NCAConfig())

Useful for assessing early exposure (e.g., AUC0-4h for rapid-acting drugs).

AUMC (Area Under Moment Curve)¶

First moment curve for MRT calculation:

\[AUMC = \int_0^{t_{last}} t \cdot C(t) \, dt\]

println("AUMC0-t: $(result.aumc_0_t)")
println("AUMC0-inf: $(result.aumc_0_inf)")

# Direct calculation
aumc_0t = aumc_0_t(times, conc, NCAConfig())

Dose-Normalized Metrics¶

For dose proportionality assessment:

# Dose-normalized Cmax
cmax_dn = nca_dose_normalized_cmax(result.cmax, 100.0)

# Dose-normalized AUC
auc_dn = nca_dose_normalized_auc(result.auc_0_inf, 100.0)

# From NCA result
println("Cmax/D: $(result.cmax_dn)")
println("AUC/D: $(result.auc_dn)")

Time Above Concentration¶

Time above a specified concentration threshold:

# Time above MIC of 1.0 mg/L
t_above_mic = time_above_concentration(times, conc, 1.0)
println("Time above MIC: $t_above_mic h")

Concentration at Specific Time¶

Interpolated concentration at any time point:

# Concentration at t=3h (interpolated)
c_at_3h = nca_c_at_time(times, conc, 3.0)

# Concentration at t=6h
c_at_6h = nca_c_at_time(times, conc, 6.0)

Uses linear interpolation for ascending and log-linear for descending phases.

C0 - Initial Concentration (IV)¶

Back-Extrapolation¶

For IV bolus, estimate C0 by back-extrapolation:

# Back-extrapolation from first two points
c0 = nca_c0_backextrap(times, conc)

# From terminal phase regression
c0_reg = nca_c0_from_regression(times, conc, lambda_z, intercept)

Validation¶

validation = validate_c0_extrapolation(times, conc, c0)
println("Extrapolation valid: $(validation.is_valid)")
println("Warnings: $(validation.warnings)")

BLQ Handling¶

Below Limit of Quantification handling:

# Treat BLQ as zero
config = NCAConfig(blq_handling=BLQZero(), lloq=0.05)

# Treat BLQ as LLOQ/2
config = NCAConfig(blq_handling=BLQLLOQHalf(), lloq=0.05)

# Exclude BLQ from calculations
config = NCAConfig(blq_handling=BLQMissing(), lloq=0.05)

Example: Complete Exposure Analysis¶

using NeoPKPD

# PK data
times = [0.0, 0.25, 0.5, 1.0, 1.5, 2.0, 3.0, 4.0, 6.0, 8.0, 12.0, 24.0]
conc = [0.0, 2.5, 4.8, 5.2, 4.5, 3.8, 2.6, 1.9, 1.0, 0.55, 0.18, 0.02]
dose = 500.0  # mg

# Configure NCA
config = NCAConfig(
    method = LinLogMixedMethod(),
    lambda_z_min_points = 3,
    lambda_z_r2_threshold = 0.9,
    extrapolation_max_pct = 20.0,
    lloq = 0.01
)

# Run analysis
result = run_nca(times, conc, dose; config=config, route=:extravascular)

# Report primary exposure
println("=== Primary Exposure Metrics ===")
println("Cmax:     $(round(result.cmax, digits=2)) mg/L")
println("Tmax:     $(result.tmax) h")
println("AUC0-t:   $(round(result.auc_0_t, digits=2)) mg·h/L")
println("AUC0-inf: $(round(result.auc_0_inf, digits=2)) mg·h/L")
println("AUC extrapolated: $(round(result.auc_extra_pct, digits=1))%")

# Report PK parameters
println("\n=== PK Parameters ===")
println("t1/2:  $(round(result.t_half, digits=2)) h")
println("CL/F:  $(round(result.cl_f, digits=2)) L/h")
println("Vz/F:  $(round(result.vz_f, digits=1)) L")
println("MRT:   $(round(result.mrt, digits=2)) h")

# Quality check
println("\n=== Quality Assessment ===")
println("Lambda_z R²: $(round(result.lambda_z_result.r_squared, digits=4))")
println("Points used: $(result.lambda_z_result.n_points)")
println("Quality flags: $(result.quality_flags)")
if !isempty(result.warnings)
    println("Warnings: $(result.warnings)")
end

Formulas Summary¶

Metric	Formula
Cmax	\(\max(C)\)
AUC (linear)	\(\sum \frac{(C_i + C_{i+1})}{2} \cdot (t_{i+1} - t_i)\)
AUC (log-linear)	\(\sum \frac{(C_i - C_{i+1})}{\ln(C_i/C_{i+1})} \cdot (t_{i+1} - t_i)\)
AUC0-inf	\(AUC_{0-t} + C_{last}/\lambda_z\)
AUC%extrap	\(100 \cdot (C_{last}/\lambda_z) / AUC_{0-\infty}\)
Cavg	\(AUC_{0-\tau} / \tau\)
Cmax/D	\(C_{max} / Dose\)
AUC/D	\(AUC / Dose\)