Exploration of Drug Science

From: PKPDindex: an R/CRAN package for PK/PD index analysis

Table 1. Emax model variants (m1–m8) defined in the PKPDindex() package.

Formula	Model	Estimated parameter	Fixed parameter	Includes Hill coefficient
m1	$E = E 0_{f i x} - (\frac{E m a x_{f i x} \times C}{E I 50 + C})$	EI50	E0, Emax	No
m2	$E = E 0_{f i x} - (\frac{E m a x_{f i x} \times C^{γ}}{{E I 50}^{γ} + C^{γ}})$	EI50, “γ”	E0, Emax	Yes
m3	$E = E 0_{f i x} - (\frac{E m a x \times C}{E I 50 + C})$	EI50, Emax	E0, “γ”	No
m4	$E = E 0_{f i x} - (\frac{E m a x \times C^{γ}}{{E I 50}^{γ} + C^{γ}})$	EI50, Emax, “γ”	E0	Yes
m5	$E = E 0 - (\frac{E m a x_{f i x} \times C}{E I 50 + C})$	EI50, E0	Emax, “γ”	No
m6	$E = E 0 - (\frac{E m a x_{f i x} \times C^{γ}}{{E I 50}^{γ} + C^{γ}})$	EI50, E0, “γ”	Emax	Yes
m7	$E = E 0 - (\frac{E m a x \times C}{E I 50 + C})$	EI50, E0, Emax	“γ”	No
m8	$E = E 0 - (\frac{E m a x \times C^{γ}}{{E I 50}^{γ} + C^{γ}})$	EI50, E0, Emax, “γ”	None	Yes

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Declarations

Acknowledgments

The authors would like to thank University College London (UCL) for providing access to research databases and necessary materials.

Author contributions

NA: Conceptualization, Methodology, Software, Validation, Formal analysis, Writing—original draft, Writing—review & editing. JFS: Conceptualization, Supervision, Validation, Writing—review & editing. The authors read and approved the submitted version.

Conflicts of interest

The authors declare that they have no conflicts of interest.

Ethical approval

Not applicable.

Consent to participate

Not applicable.

Consent to publication

Not applicable.

Availability of data and materials

The PKPDindex package, including the example datasets and source code used in this protocol, is publicly available through the Comprehensive R Archive Network (CRAN) at https://CRAN.R-project.org/package=PKPDindex. All data described in this manuscript are available within the package and can be accessed by users through CRAN.

Funding

NA received a scholarship funded by Princess Nourah bint Abdulrahman University. JFS was supported by a UK Medical Research Council fellowship (MR/008665/1). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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