Average Slope for Drug-Absorption Rate

A small, dependency-free Python implementation of average slope (AS) from observed concentration-time data, using all consecutive observations from t = 0 through the observed Tmax (inclusive).

Definition

For n observations up to and including Tmax, the metric is:

                 1       n-1  C[i+1] - C[i]
average slope = ----- ×   Σ   ---------------
                n - 1     i    t[i+1] - t[i]

It is the arithmetic (unweighted) mean of the individual slopes between consecutive concentration-time observations. Its units are concentration/time. With equally spaced sampling, C(0) = 0, and a unique peak, the expression telescopes to Cmax / Tmax. With unequal intervals, AS generally differs from Cmax / Tmax; do not replace the mean above with a single endpoint slope.

The definition follows:

Karalis VD. On the Interplay between Machine Learning, Population Pharmacokinetics, and Bioequivalence to Introduce Average Slope as a New Measure for Absorption Rate. Applied Sciences. 2023;13(4):2257. https://doi.org/10.3390/app13042257

Install

Python 3.9 or newer is required.

python -m pip install .

For development and tests (no third-party test runner is required):

python -m pip install -e .
python -m unittest discover -s tests -v

Python API

from average_slope import average_slope

result = average_slope(
    times=[0, 0.5, 1.5, 3, 5],
    concentrations=[0, 2, 6, 9, 7],
)

print(result.average_slope)   # 3.3333333333333335
print(result.tmax)           # 3.0
print(result.interval_slopes) # (4.0, 4.0, 2.0)

CSV command line

The bundled example contains two subjects:

average-slope examples/concentration_time.csv --group subject

Write the result to a file:

average-slope input.csv --group subject --output average_slope_results.csv

Rename columns when required:

average-slope input.csv --time TIME --concentration CONC --group ID

Input rows may be unordered; the CLI sorts observations within each group by time. The Python API itself requires already ordered observations.

Data rules and explicit choices

• Time must start at exactly 0, be non-negative, finite, and strictly increasing within a profile.
• Concentrations must be finite and non-negative.
• At least one post-dose point is required before or at the peak.
• By default, the first occurrence of a tied observed Cmax defines Tmax. Choose the last occurrence with --tmax-tie last, or reject ties with --tmax-tie error.
• Missing and BLQ values are rejected rather than silently imputed. Apply and document the preprocessing rule required by your analysis plan before using this package.
• AS is calculated independently for each profile/subject; do not average concentrations across subjects first.

This software implements a calculation and is not validated for clinical or regulatory decision-making. Users remain responsible for data review, pre-specified handling rules, validation, and compliance with applicable guidance.

Repository contents

src/average_slope/       library and CLI
tests/                   unit and CLI tests
examples/                example concentration-time CSV
CITATION.cff             citation metadata
LICENSE                  MIT license
.github/workflows/       GitHub Actions tests for Python 3.9, 3.11, and 3.13