Tutorial: Bioequivalence Convenience Layer¶

Theory

See the Theory Guide for the TOST mathematics, non-central t power formula, and sample size derivation.

This tutorial demonstrates OpenPKFlow's paired TOST convenience layer, formal complete balanced 2x2 ANOVA workflow, and research-grade replicate screening helper. FDA partial-replicate RSABE remains non-decisional until its external-reference validation gate is complete. EMA ABEL, full-replicate RSABE, NTI decisions, and incomplete or unbalanced formal datasets are out of scope.

1. Prepare the DataFrame¶

Create a wide-format DataFrame with one row per subject:

import pandas as pd
from openpkflow.be import BEStudy

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(df, parameter="AUCinf")
result = study.analyze()
print(result.summary())

Required columns: subject, reference, test. The sequence column ("RT" / "TR") is optional for paired TOST, but required when exporting to BioEqPy.

2. Generate a report¶

result.report("be_report.html")      # HTML (default)
result.report("be_report.md")        # Markdown

3. Interpret results¶

Output	Meaning
GMR	Geometric Mean Ratio (test / reference)
90% CI	Confidence interval from TOST
Bioequivalent	True if 90% CI falls entirely within acceptance limits
Intra-subject CV%	Within-subject variability estimate

The report includes a CI bar visualization placing the 90% CI against the acceptance window.

4. NTI products (narrow acceptance limits)¶

For narrow therapeutic index drugs, pass tighter limits:

result_nti = study.analyze(be_lower=0.90, be_upper=1.1111)
print(result_nti.summary())

5. From NCA results (convenience constructor)¶

If you ran NCA separately on each formulation, feed both NCASummaryResults objects directly:

from openpkflow.be import BEStudy
from openpkflow.nca import NCAStudy

ref_nca = NCAStudy.from_csv("ref_pk.csv", auc_method="linear_up_log_down", blq_method="none")
tst_nca = NCAStudy.from_csv("tst_pk.csv", auc_method="linear_up_log_down", blq_method="none")

ref_summary = ref_nca.analyze()
tst_summary = tst_nca.analyze()

study = BEStudy.from_nca_results(ref_summary, tst_summary, parameter="AUCinf")
result = study.analyze()
print(result.summary())

Subjects are matched by ID. Only subjects present in both result sets are used.

6. Formal complete balanced 2x2 ANOVA¶

The formal ANOVA workflow requires long-format complete balanced data. It does not silently drop subjects or accept unequal TR/RT allocation.

from openpkflow.be import formal_be_anova

formal_data = pd.DataFrame({
    "subject": ["S1", "S1", "S2", "S2", "S3", "S3", "S4", "S4"],
    "sequence": ["TR", "TR", "TR", "TR", "RT", "RT", "RT", "RT"],
    "period": [1, 2, 1, 2, 1, 2, 1, 2],
    "treatment": ["T", "R", "T", "R", "R", "T", "R", "T"],
    "AUCinf": [110, 100, 120, 109, 100, 108, 90, 101],
})

formal = formal_be_anova(formal_data, parameter="AUCinf")
print(formal.summary())
formal.report("formal_be.html")

Use the Formal BE ANOVA web page or:

openpkflow be anova formal_be.csv --parameter AUCinf --report formal_be.html

7. Export to BioEqPy¶

from bioeqpy import analyze

bioeqpy_table = study.to_bioeqpy_dataframe()
formal_results = analyze(
    bioeqpy_table,
    parameters=["AUCinf"],
    report="bioeqpy_formal_be_report.html",
)

to_bioeqpy_dataframe() returns the long-format columns BioEqPy expects: subject, sequence, period, treatment, and the selected PK parameter. The export requires TR/RT sequence labels.

8. Replicate-design screening¶

Use replicate_be() for long-format partial or full replicate datasets. The minimum columns are subject, sequence, period, treatment, and the PK metric value.

import pandas as pd
from openpkflow.be import replicate_be

df = pd.DataFrame({
    "subject": ["S01", "S01", "S01", "S02", "S02", "S02"],
    "sequence": ["TRR", "TRR", "TRR", "RTR", "RTR", "RTR"],
    "period": [1, 2, 3, 1, 2, 3],
    "treatment": ["T", "R", "R", "R", "T", "R"],
    "Cmax": [105.0, 92.0, 108.0, 95.0, 101.0, 110.0],
})

result = replicate_be(df, value_col="Cmax")
print(result.summary())

The output includes conventional ABE, CVwR%, EMA-style scaled limits, and an FDA-style RSABE point-criterion screen. These scaled outputs are explicitly research-grade and must be cross-checked before regulatory use.

9. CLI¶

openpkflow be compare be_data.csv --parameter AUCinf
openpkflow be compare be_data.csv --parameter AUCinf --report be_report.html
openpkflow be anova formal_be.csv --parameter AUCinf --report formal_be.html
openpkflow be replicate replicate_be_partial.csv --parameter Cmax --report replicate.html --json replicate.json

CSV format: subject, sequence, reference, test

Statistical note¶

The TOST procedure tests two one-sided hypotheses:

H01: GMR <= lower limit (e.g., 0.80)
H02: GMR >= upper limit (e.g., 1.25)

Both are rejected at alpha=0.05 if and only if the 90% CI lies entirely within the acceptance window. This is mathematically equivalent to verifying that both one-sided t-tests pass at alpha=0.05.

Reference: Schuirmann (1987), J Pharmacokinet Biopharm 15(6):657-680. FDA guidance: Statistical Approaches to Establishing Bioequivalence (2001).