openpkflow 2.5.0

Python-first toolkit for dissolution, NCA, PK/PD simulation, and pharmacometric reporting.

OpenPKFlow

A transparent, reproducible, open-source Python toolkit for dissolution, NCA, PK/PD simulation, and pharmacometric reporting — with full theory derivations, cross-validated formulas, and regulatory-ready documentation.

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What it does

OpenPKFlow gives formulation scientists, PK/PD researchers, and CRO/CDMO teams a clean Python workflow for:

• Dissolution similarity: f1, f2, bootstrap f2, maximum deviation, MSD (Mahalanobis Statistical Distance), model fitting (Weibull, Higuchi, first-order, zero-order, Korsmeyer-Peppas), model-dependent comparison via 90% CI
• NCA: AUClast, AUCinf, Cmax, Tmax, lambda_z, half-life, CL/F, Vz/F; three AUC methods, explicit BLQ handling, %AUCextrap flag, dose-normalised parameters, CDISC PP output; sparse NCA from 3-5 samples
• Bayesian PK (v2.0.0): MAP individual PK estimation (scipy, no extra deps) + full posterior via PyMC ([bayes] extra); Bayesian 2x2 crossover BE with P(GMR in 80-125) decision quantity alongside frequentist 90% CI
• Bioequivalence: paired 2x2 TOST (80-125% FDA/EMA limits), GMR + 90% CI, intra-subject CV; research-grade replicate-design screening with CVwR and scaled-limit summaries
• Report generation: Markdown, HTML, PDF, Word
• PK simulation: 1- and 2-compartment models, oral/IV bolus/IV infusion, repeated dosing
• Population PK diagnostics: 4-panel GOF plots (OBS vs PRED, IWRES vs TIME/IPRED), simulation-based VPC with percentile bands, NONMEM-style dataset helpers
• Population PK estimation (v2.3.0): FOCE-I (scipy, zero extra deps) and SAEM (PyMC [bayes] extra) for 1- and 2-compartment oral/IV models; diagonal or full Omega block matrix; PopPKResult with .summary(), .plot() (6-panel), .report() (research-grade; FOCE-I sanity-checked against the nlme Theophylline reference)
• Theory guide: Full LaTeX formula derivations for every module -- NCA, simulation, dissolution, IVIVC, BE, pop PK, Bayesian PK -- for regulatory review support and teaching
• ML surrogate (experimental): torch MLP that approximates 1-cmt oral profiles

It does not replace expert regulatory judgement or validated commercial platforms. It makes routine analysis faster, cleaner, and more reproducible.

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Install

pip install openpkflow

For PDF and Word reports:

pip install openpkflow[reports]

For full Bayesian PK (PyMC MCMC):

pip install openpkflow[bayes]

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Quick start: dissolution similarity

from openpkflow.dissolution import f1, f2

reference = [20.0, 40.0, 60.0, 80.0, 90.0]
test      = [21.0, 39.0, 61.0, 79.0, 88.0]

print(f"f1 = {f1(reference, test):.2f}")
print(f"f2 = {f2(reference, test):.2f}")

From a CSV file

from openpkflow.dissolution import DissolutionStudy

study = DissolutionStudy.from_csv("dissolution.csv")
# or load directly from Excel (requires pip install openpkflow[reports]):
# study = DissolutionStudy.from_excel("dissolution.xlsx", sheet_name="Data")

result = study.compare(reference="reference", test="test")
result.summary()
result.report("dissolution_report.html")
result.report("dissolution_report.pdf", format="pdf")   # requires [reports]

CSV format: formulation,batch,time,percent_released

CLI

openpkflow version
openpkflow similarity --reference "20,40,60,80" --test "21,39,61,79"

---

Quick start: NCA

from openpkflow.nca import NCAStudy

study = NCAStudy.from_csv(
    "pk_data.csv",
    auc_method="linear_up_log_down",   # required: "linear", "log", or "linear_up_log_down"
    blq_method="none",                  # required: "none", "drop", "zero", "half_lloq", "lloq"
)
summary = study.analyze()
print(summary.summary())               # tabular ASCII output

# Per-subject results
result = summary.results[0]
print(f"Subject: {result.subject}")
print(f"AUClast: {result.AUClast:.2f} h*mg/L")
print(f"Cmax:    {result.Cmax:.2f} mg/L")
print(f"Tmax:    {result.Tmax:.2f} h")
print(f"t1/2:    {result.half_life:.2f} h")
print(f"CL/F:    {result.CL_F:.2f} L/h")

# Reports
result.report("nca_subject1.html")
summary.report("nca_summary.html")

NCA CSV format

subject,time,conc,dose,route
1,0.0,0.0,320.0,oral
1,0.5,4.2,320.0,oral
1,1.0,8.1,320.0,oral
1,2.0,6.8,320.0,oral
1,4.0,3.5,320.0,oral
1,8.0,1.7,320.0,oral
1,12.0,0.9,320.0,oral
1,24.0,0.2,320.0,oral

Required columns: subject, time, conc, dose, route. Dose units must match concentration × time (mg when conc is mg/L and time is h). Route values: "oral", "iv_bolus", "iv_infusion".

Oral route yields apparent clearance and volume: CL_F, Vz_F. IV routes yield absolute clearance and volume: CL, Vz.

---

Quick start: PK simulation

import numpy as np
from openpkflow.sim import simulate
from openpkflow.sim.models import OneCompartmentModel
from openpkflow.sim.dosing import DoseRegimen

model = OneCompartmentModel(route="oral", CL_F=5.0, Vz_F=50.0, ka=1.2)
regimen = DoseRegimen.from_repeated(amount=100.0, route="oral", tau=24.0, n_doses=3)
times = np.linspace(0, 72, 500)

result = simulate(model, regimen, times)
print(result.summary())
result.report("sim_report.html")
result.report("sim_report.pdf", format="pdf")   # requires [reports]

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Quick start: Bayesian individual PK (MAP)

from openpkflow.bayes import map_individual_pk, PKPrior
import math

# Noiseless 1-cmt oral data (CL_F=5, Vz_F=50, ka=1.2, dose=100)
times = [0.5, 1.0, 2.0, 4.0, 8.0, 12.0]
concs = [1.23, 1.85, 1.97, 1.61, 0.89, 0.49]

result = map_individual_pk(times, concs, dose=100.0, route="oral", subject="S01")
print(result.summary())   # MAP estimates, SEs, diagnostics, disclaimer
result.report("map_pk_report.html")

For full posterior sampling (requires pip install openpkflow[bayes]):

from openpkflow.bayes.bayes_pk import bayes_individual_pk

result = bayes_individual_pk(times, concs, dose=100.0, route="oral",
                              n_samples=1000, tune=1000, chains=2)
print(f"CL_F = {result.cl_mean:.3g}  [95% CrI: {result.cl_95ci[0]:.3g}, {result.cl_95ci[1]:.3g}]")
print(f"P(shrinkage) = {result.shrinkage_cl:.1%}")

Quick start: Bayesian bioequivalence (requires [bayes])

import pandas as pd
from openpkflow.bayes.bayes_be import bayes_be

# Long-format 2x2 crossover data
data = pd.DataFrame({
    "subject":   ["S01","S01","S02","S02","S03","S03","S04","S04"],
    "sequence":  ["RT", "RT", "TR", "TR", "RT", "RT", "TR", "TR"],
    "period":    [1,    2,    1,    2,    1,    2,    1,    2   ],
    "treatment": ["R",  "T",  "T",  "R",  "R",  "T",  "T",  "R" ],
    "value":     [98.0, 103.0, 95.0, 91.0, 107.0, 112.0, 99.0, 94.0],
})

result = bayes_be(data, metric="AUC", n_samples=2000, tune=1000, chains=2)
print(f"P(BE) = {result.p_be:.3f}")
print(f"GMR = {result.gmr_mean:.4g}  [95% CrI: {result.gmr_95ci[0]:.4g}, {result.gmr_95ci[1]:.4g}]")
print(f"Frequentist 90% CI: [{result.freq_90ci[0]:.4g}, {result.freq_90ci[1]:.4g}]")
result.report("bayes_be_report.html")

---

Quick start: bioequivalence

import pandas as pd
from openpkflow.be import BEStudy

# Wide-format DataFrame: one row per subject, reference and test PK parameter values
be_df = pd.DataFrame({
    "subject":   ["S01", "S02", "S03", "S04", "S05", "S06"],
    "sequence":  ["RT",  "RT",  "RT",  "TR",  "TR",  "TR"],
    "reference": [100.2, 98.7, 105.1, 97.3, 102.8, 99.5],
    "test":      [95.1,  94.0,  99.8, 92.9,  97.4, 94.8],
})

study = BEStudy(be_df, parameter="AUCinf")
result = study.analyze()          # default: 80-125%, alpha=0.05
print(result.summary())
result.report("be_report.html")

# NTI products: pass narrower limits
result_nti = study.analyze(be_lower=0.90, be_upper=1.1111)

From NCAStudy results (convenience)

from openpkflow.be import BEStudy

# Run NCA separately on each formulation's PK data
# reference_nca_summary = NCAStudy.from_csv("ref_pk.csv", ...).analyze()
# test_nca_summary      = NCAStudy.from_csv("test_pk.csv", ...).analyze()

study = BEStudy.from_nca_results(
    reference_nca_summary, test_nca_summary, parameter="AUCinf"
)
result = study.analyze()

Formal BE with BioEqPy

OpenPKFlow deliberately keeps openpkflow.be as a lightweight convenience layer. For regulator-facing BE analysis with long-format crossover data, ANOVA source tables, NTI, ABEL/RSABE, and validation fixtures, export a BioEqPy-ready table:

from openpkflow.be import BEStudy
from bioeqpy import analyze

study = BEStudy(be_df, parameter="AUCinf")
bioeqpy_input = study.to_bioeqpy_dataframe()
formal_results = analyze(bioeqpy_input, parameters=["AUCinf"])

CLI

openpkflow be compare be_data.csv --parameter AUCinf --report be_report.html

CSV format: subject, sequence, reference, test

---

Quick start: population PK diagnostics

import pandas as pd
from openpkflow.pop import GOFResult, simulate_vpc
from openpkflow.sim.models import OneCompartmentModel
from openpkflow.sim.dosing import DoseRegimen

# GOF: supply your own PRED/IPRED from NONMEM or nlmixr2
gof = GOFResult(
    dv=[5.2, 8.1, 6.4, 3.2],
    pred=[4.9, 7.8, 6.0, 3.0],
    ipred=[5.1, 8.0, 6.3, 3.1],
    time=[1.0, 2.0, 4.0, 8.0],
    id=["S1", "S1", "S1", "S1"],
    sigma=0.15,
    study_label="Phase 1 Study",
)
print(gof.summary())
gof.report("gof_report.html")

# Simulation-based VPC
model = OneCompartmentModel(route="oral", CL_F=5.0, Vz_F=50.0, ka=1.2)
regimen = DoseRegimen.from_repeated(amount=100.0, route="oral", tau=24.0, n_doses=1)
observed = pd.DataFrame({"TIME": [1, 2, 4, 8, 12], "DV": [5.1, 8.2, 6.5, 3.8, 2.1]})

vpc = simulate_vpc(model, regimen, observed, n_replicates=500, seed=42)
vpc.report("vpc_report.html")

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Feature comparison

Capability	OpenPKFlow	PKNCA (R)	WinNonlin	Pharmpy
Dissolution f1 / f2	:white_check_mark:	:x:	:white_check_mark:	:x:
Bootstrap f2	:white_check_mark:	:x:	:x:	:x:
Dissolution model fitting (5 models + AICc)	:white_check_mark:	:x:	:x:	:x:
MSD / max deviation / model-dependent comparison	:white_check_mark:	:x:	:white_check_mark:	:x:
NCA (AUClast, AUCinf, CL/F, lambda_z), cross-validated vs Phoenix WinNonlin	:white_check_mark:	:white_check_mark:	:white_check_mark:	:x:
C0 back-extrapolation for IV bolus (matches WinNonlin within 2%)	:white_check_mark:	:white_check_mark:	:white_check_mark:	:x:
%AUCextrap flag, dose-normalised params	:white_check_mark:	:white_check_mark:	:white_check_mark:	:x:
CDISC PP output (SDTM, PPTESTCD codes)	:white_check_mark:	:x:	:white_check_mark:	:x:
Bioequivalence convenience (paired 2x2 TOST)	:white_check_mark:	:x:	:white_check_mark:	:x:
PK simulation (1/2-cmt, oral/IV)	:white_check_mark:	:x:	:white_check_mark:	:white_check_mark:
Population PK diagnostics (GOF, VPC)	:white_check_mark:	:x:	:x:	:white_check_mark:
Multi-format reports (HTML, PDF, DOCX)	:white_check_mark:	:x:	:white_check_mark:	:x:
Open-source & free	:white_check_mark:	:white_check_mark:	:x:	:white_check_mark:
Python-native API	:white_check_mark:	:x:	:x:	:white_check_mark:
Regulatory reference validation (citations)	:white_check_mark:	:white_check_mark:	:white_check_mark:	:x:
IVIVC (Level A)	:white_check_mark: (v1.2.0)	:x:	:white_check_mark:	:x:
Multi-media dissolution	:white_check_mark: (v1.4.0)	:x:	:white_check_mark:	:x:
Sparse-sampling NCA	:white_check_mark: (v1.5.0)	:white_check_mark:	:x:	:x:
Steady-state NCA + urinary excretion	:white_check_mark: (v1.3.0)	:white_check_mark:	:white_check_mark:	:x:
MAP individual PK (scipy, no extra deps)	:white_check_mark: (v2.0.0)	:x:	:white_check_mark:	:x:
Full Bayesian PK + Bayesian BE (PyMC)	:white_check_mark: (v2.0.0)	:x:	:x:	:x:
Population PK estimation: FOCE-I + SAEM (1/2-cmt, full Omega)	:white_check_mark: (v2.3.0)*	:x:	:x:	:x:
Replicate BE screening (CVwR/scaled-limit summaries)	:white_check_mark: (v2.4.0)**	:x:	:white_check_mark:	:x:
Formal BE ANOVA / validated RSABE decision	:x:	:x:	:white_check_mark:	:x:

* Research-grade; FOCE-I typical values are sanity-checked against nlme Theophylline reference values. nlmixr2 rerun is waiting on local Rtools/C compiler support. See HANDOFF.md. ** Research-grade screening only; not a validated FDA/EMA RSABE submission engine.

Roadmap

Post-1.0.0 milestones: IVIVC Level A (done), multi-media dissolution (done), steady-state NCA (done), sparse NCA (done), Bayesian PK + BE (done v2.0.0), FOCE-I + SAEM pop PK (done v2.1.0), 2-cmt + full Omega (done v2.2.0), covariate skeleton removal + FOCE-I reference validation (v2.3.0), replicate BE screening + release credibility sprint (v2.4.0). See ROADMAP.md for the full plan.

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Current status

Module	Status
Dissolution f1 / f2	Stable
MSD / max deviation / model-dependent comparison	Stable
Bootstrap f2	Stable
Dissolution CSV loader	Stable
Dissolution model fitting (5 models, AICc)	Stable
IVIVC Level A (Wagner-Nelson, Loo-Riegelman, convolution, Levy plot, %PE)	Stable (v1.2.0)
Multi-media dissolution (f2 across pH, ethanol dose-dumping)	Stable (v1.4.0)
HTML, Markdown, PDF, Word reports	Stable
NCA (AUClast, AUCinf, lambda_z, CL/F, steady-state, urinary excretion)	Stable (v1.3.0)
Sparse NCA (model-informed 1-cmt oral from 3-5 samples)	Stable (v1.5.0)
PK simulation (1/2-comp, oral/IV bolus/IV infusion, repeated dosing)	Stable (v0.9.1)
Population PK diagnostics (GOF, VPC)	Stable (v0.6.0)
FOCE-I pop PK estimation (scipy tier, 1/2-cmt, full Omega)*	Stable (v2.3.0)
SAEM pop PK estimation ([bayes] extra, 1/2-cmt, full Omega)*	Stable (v2.3.0)
Covariate modeling	Removed (v2.3.0 breaking change)
Validation utilities (pct_bias, rmse, within_pct)	Stable (v0.9.1)
MAP individual PK (scipy, zero extra deps)	Stable (v2.0.0)
Full Bayesian PK posterior (PyMC, [bayes] extra)	Stable (v2.0.0)
Bayesian 2x2 BE with P(GMR in 80-125) (PyMC)	Stable (v2.0.0)
Bioequivalence convenience (paired TOST)	Stable (2x2 crossover TOST, GMR + 90% CI)
ML surrogate (torch MLP, EXPERIMENTAL)	Prototype (v0.9.0)
Stable public release	Done (v2.0.0)

* Research-grade; FOCE-I typical values are sanity-checked against nlme Theophylline reference values. See HANDOFF.md.

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By the numbers

Stat	Value
Lines of source code (src/)	~19,600
Lines of tests (tests/)	~15,200
Total Python files	141 (69 src + 72 tests)
Tests	900
Public functions / methods	195
Classes	34
HTML report templates	12
Bundled example datasets	4
Git commits	100+

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Validation

All formula implementations are validated against published FDA/EMA guidance examples. Each test case cites its source: paper DOI, FDA guidance ID, or R-package vignette.

NCA: four-way cross-validation against Phoenix WinNonlin: NCA results are cross-validated against Phoenix WinNonlin (Certara), PKNCA 0.12.1, and NonCompart 0.8.0 on the standard R nlme::Theoph (12-subject oral theophylline) and nlme::Indometh (6-subject IV bolus indomethacin) datasets. Key validated parameters: AUClast, AUCinf, CL/F, Vz/F, lambda_z, half-life. C0 back-extrapolation for IV bolus data (WinNonlin's approach: OLS regression on the first 2 points, linear trapezoid area added from t=0 to t_first) is implemented in c0_back_extrapolated() and verified to match WinNonlin reference values within 2% for all 6 Indometh subjects.

See VALIDATION.md for the full regulatory test traceability matrix.

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Disclaimer

This software is for research and decision-support workflows. Final regulatory interpretation should be reviewed by qualified formulation, pharmacokinetic, and regulatory experts.

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Documentation

• Theory Guide -- Full LaTeX formula derivations for every module: NCA, simulation, dissolution, IVIVC, BE, pop PK, Bayesian PK. Designed for regulatory review support and teaching.
• Migration Guide -- WinNonlin / NONMEM / R user? Quick-reference mapping for every parameter and function.
• Tutorials -- Step-by-step worked examples for all 7 modules.
• Validation Matrix -- Every test mapped to its FDA/EMA/ICH guidance section or published DOI.
• API Reference -- Full function and class reference for all 9 modules.

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Contributing

Issues and PRs welcome at https://github.com/priyamthakar/openpkflow/issues

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Citation

If you use OpenPKFlow in research, please cite:

Thakar, P. (2026). OpenPKFlow: Python-first pharmacometrics and dissolution toolkit.
https://github.com/priyamthakar/openpkflow

License

MIT · see LICENSE