Sigmoidal function which fits well to many stimuli-response associations observed in biology and pharmacology. In the context of PharmacoGx we are using it to model treatment-response assocations in cancer cell lines.
Arguments
- dose
numeric()A vector oflog10(dose)values (or equivalent for the stimuli being modelleled).- HS
numeric(1)Hill coefficient (n) which defines the slope of the dose-response curve at the mid-point. This parameter describes the degree of sigmoidicity of the Hill curve. HS = 1 corresponds to the rectangular hyperbola in dose-response space.- EC50
numeric(1)The dose required to produce 50% of the theoretically maximal response in the system,E_inf. Should be in the same units asdose!- E_inf
numeric(1)Theoretical maximal response (minimal viability) in the system as a proportion in the range \[0, 1\]. Note that since we are predicting viability (percent of cells alive after treatment) instead of response, this value should be low (i.e., more cell killing).- E_ninf
numeric(1)Theoretical minimum response (basal response). Defaults to 1, which should be the case for most viability experiments since we expect no cell killing to occur prior to applying a treatment.
Value
numeric() Vector of predicted viabilities for the Hill curve defined
by EC50, E_inf, E_ninf and HS for each supplied value of dose.
References
Gesztelyi, R., Zsuga, J., Kemeny-Beke, A., Varga, B., Juhasz, B., & Tosaki, A. (2012). The Hill equation and the origin of quantitative pharmacology. Archive for History of Exact Sciences, 66(4), 427–438. https://doi.org/10.1007/s00407-012-0098-5
Motulsky, H., & Christopoulos, A. (2004). Fitting models to biological data using linear and nonlinear regression: A practical guide to curve fitting. Oxford University Press. See Chapter 41.
Examples
(viability <- hillCurve(
dose=c(0.1, 0.01, 0.001),
HS=1.1,
EC50=0.01,
E_ninf=1,
E_inf=0
))
#> [1] 0.4432565 0.5000000 0.5056987