Key Features¶

NeoPKPD provides a comprehensive suite of pharmacometrics capabilities designed for research, clinical development, and regulatory submissions.

Pharmacokinetic Models¶

Compartmental Models¶

NeoPKPD supports all standard compartmental PK models with rigorous mathematical formulations:

One-CompartmentTwo-CompartmentThree-Compartment

# IV Bolus
params = OneCompIVBolusParams(CL=5.0, V=50.0)

# Oral First-Order
params = OneCompOralFirstOrderParams(Ka=1.5, CL=5.0, V=50.0)

\[\frac{dA}{dt} = -\frac{CL}{V} \cdot A\]

params = TwoCompIVBolusParams(CL=5.0, V1=20.0, Q=15.0, V2=50.0)

\[\frac{dA_1}{dt} = -k_{10} A_1 - k_{12} A_1 + k_{21} A_2\]

params = ThreeCompIVBolusParams(CL=5.0, V1=10.0, Q2=20.0, V2=30.0, Q3=5.0, V3=100.0)

Tri-exponential decline with shallow and deep peripheral compartments.

Advanced Absorption¶

Model	Description	Use Case
Transit Compartments	Chain of N compartments	Delayed/complex absorption
Lag Time	Fixed delay before absorption	Enteric-coated tablets
Zero-Order	Constant-rate absorption	Controlled-release

Nonlinear Kinetics¶

Michaelis-Menten Elimination: Saturable metabolism
TMDD Models: Target-mediated drug disposition for biologics

Pharmacodynamic Models¶

Direct Response Models¶

# Direct Emax
result = neopkpd.simulate_pkpd_direct_emax(
    cl=5.0, v=50.0,
    e0=0.0, emax=100.0, ec50=2.0,
    doses=[{"time": 0.0, "amount": 100.0}],
    t0=0.0, t1=24.0
)

# Sigmoid Emax (Hill Equation)
result = neopkpd.simulate_pkpd_sigmoid_emax(
    cl=5.0, v=50.0,
    e0=0.0, emax=100.0, ec50=2.0, gamma=2.5,
    doses=[{"time": 0.0, "amount": 100.0}],
    t0=0.0, t1=24.0
)

Indirect Response Models¶

All four indirect response types are supported:

Type	Mechanism	Drug Effect
Type I	Inhibition of Kin	Decreases response
Type II	Inhibition of Kout	Increases response
Type III	Stimulation of Kin	Increases response
Type IV	Stimulation of Kout	Decreases response

Effect Compartment (Biophase)¶

Models temporal delay between plasma and effect site concentrations:

\[\frac{dC_e}{dt} = k_{e0} \cdot (C_p - C_e)\]

Population Modeling¶

Inter-Individual Variability (IIV)¶

Log-normal distribution of parameters across subjects:

# Define omega matrix (variance of random effects)
omega = OmegaMatrix([
    0.09 0.0;   # 30% CV on CL
    0.0  0.04   # 20% CV on V
])

pop_spec = PopulationSpec(
    model_spec,
    100,           # n subjects
    omega,
    12345          # seed
)

Inter-Occasion Variability (IOV)¶

Parameter variation between dosing occasions within the same subject.

Covariate Models¶

Multiple covariate functional forms:

Type	Formula	Example
Linear	\(\theta \cdot (1 + \theta_{cov} \cdot (COV - COV_{ref}))\)	Age effect
Power	\(\theta \cdot (COV/COV_{ref})^{\theta_{cov}}\)	Weight on CL
Exponential	\(\theta \cdot e^{\theta_{cov} \cdot COV}\)	Enzyme induction
Categorical	\(\theta \cdot \theta_{cov}\) if category	Sex effect

Residual Error Models¶

Additive: \(Y = F + \epsilon\)
Proportional: \(Y = F \cdot (1 + \epsilon)\)
Combined: \(Y = F \cdot (1 + \epsilon_1) + \epsilon_2\)
Exponential: \(Y = F \cdot e^\epsilon\)

Parameter Estimation¶

FOCE-I (First-Order Conditional Estimation with Interaction)¶

The gold standard for NLME estimation:

result = estimate(
    data,
    model_spec,
    FOCEConfig(
        max_iterations=1000,
        tolerance=1e-6
    )
)

SAEM (Stochastic Approximation EM)¶

Robust estimation for complex models:

result = estimate(
    data,
    model_spec,
    SAEMConfig(
        n_iterations=500,
        n_burn_in=100,
        n_chains=3
    )
)

Laplacian Estimation¶

For sparse data or complex likelihoods.

Estimation Diagnostics¶

Convergence assessment
Parameter uncertainty (SE, RSE, CI)
Shrinkage calculation
Correlation matrices
Objective function comparison

Non-Compartmental Analysis¶

FDA/EMA-Compliant Metrics¶

Metric	Description
Cmax	Maximum concentration
Tmax	Time to maximum concentration
AUC0-t	Area under curve to last observation
AUC0-inf	Area extrapolated to infinity
t½	Terminal half-life
CL/F	Apparent clearance
Vz/F	Apparent volume
MRT	Mean residence time

Bioequivalence Analysis¶

from neopkpd.nca import bioequivalence_90ci, tost_analysis

# 90% CI for geometric mean ratio
lower, upper = bioequivalence_90ci(test_auc, reference_auc)

# TOST analysis
result = tost_analysis(
    test_auc, reference_auc,
    theta_lower=0.80, theta_upper=1.25
)

Visual Predictive Check (VPC)¶

Standard VPC¶

Comparison of observed vs simulated percentiles:

from neopkpd import viz

fig = viz.plot_vpc_detailed(
    simulated_data,
    observed_data,
    prediction_intervals=[0.05, 0.50, 0.95]
)

Prediction-Corrected VPC (pcVPC)¶

Corrects for design differences across bins.

Stratified VPC¶

Separate VPC by covariate strata (e.g., dose group, renal function).

BLQ Handling¶

Proper visualization of below-limit-of-quantification observations.

Clinical Trial Simulation¶

Study Designs¶

Design	Description
Parallel	Independent treatment groups
Crossover (2×2)	Standard two-period crossover
Williams	Three-period, three-treatment
3+3	Traditional dose escalation
mTPI/CRM	Model-based escalation
Adaptive	Interim analysis with adaptation

Power Analysis¶

from neopkpd import trial

power = trial.estimate_power_analytical(
    n_per_arm=50,
    effect_size=0.5,
    sd=1.0,
    alpha=0.05
)

sample_size = trial.estimate_sample_size(
    target_power=0.80,
    effect_size=0.5,
    sd=1.0,
    alpha=0.05
)

Virtual Population Generation¶

Generate realistic virtual subjects with specified demographics.

Visualization¶

Dual Backend Support¶

MatplotlibPlotly

from neopkpd import viz
viz.set_backend("matplotlib")

fig = viz.plot_conc_time(result)
fig.savefig("plot.png", dpi=300)

from neopkpd import viz
viz.set_backend("plotly")

fig = viz.plot_conc_time(result)
fig.write_html("plot.html")

55+ Visualization Functions¶

Category	Functions
PK Plots	`plot_conc_time`, `plot_spaghetti`, `plot_mean_ribbon`
NCA Plots	`plot_lambda_z_fit`, `plot_auc_visualization`
PKPD Plots	`plot_effect_conc`, `plot_hysteresis`
VPC Plots	`plot_vpc_detailed`, `plot_pcvpc`, `plot_stratified_vpc`
Estimation	`plot_convergence`, `plot_shrinkage`, `plot_eta_distributions`
Bootstrap	`plot_bootstrap_distributions`, `plot_bootstrap_ci`
Sensitivity	`plot_tornado`, `plot_spider`, `plot_waterfall`
Trial	`plot_power_curve`, `plot_kaplan_meier`

Model Import¶

NONMEM¶

Parse NONMEM control stream files:

./bin/neopkpd import --input run001.ctl --format nonmem --out model.json

Supported ADVAN subroutines: ADVAN1, ADVAN2, ADVAN3, ADVAN4, ADVAN11, ADVAN12

Monolix¶

Parse Monolix project files (.mlxtran).

CDISC Data¶

Import PC, EX, and DM domains in CSV or XPT format.

Reproducibility¶

Artifact System¶

Every simulation produces a JSON artifact containing:

Complete model specification
Solver settings
Input data hash
Full results with numerical precision
Semantic version fingerprint

Golden Artifact Validation¶

./bin/neopkpd validate-golden

Ensures bit-exact reproducibility across code changes.

Replay Capability¶

./bin/neopkpd replay --artifact simulation.json

Reproduce any previous simulation exactly.

Performance¶

Julia Core¶

Just-in-time compilation for near-native speed
Efficient ODE solvers (DifferentialEquations.jl)
Parallelized population simulations

Python Integration¶

Seamless Julia-Python bridge via juliacall
NumPy/Pandas integration
Lazy initialization for fast startup

Next Steps¶

Getting Started Guide - Installation and first simulation
Architecture Overview - System design details
Julia Tutorial - Complete Julia walkthrough
Python Tutorial - Complete Python walkthrough