MuSyC_si_to_hi: Convert from slope parametrization to the exponent...

In momeara/MPStats: Tools for analyzing Morphological Profiling data

Convert from slope parametrization to the exponent parametrization for drug i

Description

This can be used for setting priors and interpreting parameter estimates

Usage

MuSyC_si_to_hi(si, Ci, E0, Ei)

Arguments

si	slope of drug i at it's IC50 and doses of all other drugs are zero
Ci	the IC50 of drug i
E0	the reponse with no treatments
Ei	the reponse of inifinite drug i and no other treatments

Value

hi the exponent in the MuSyC equation for drug i

Claim: When d1=0 and d2=C2 then d(Ed)/d(d2) = s2 where s2 = h2 * (E0 + E2) / (4 * C2)

d(Ed)/d(d2) = d/d(d2) (C1^h1 * C2^h2 * E0 + C1^h1 * d2^h2 * E2) / (C1^h1 * C2^h2 + C1^h1 * d2^h2)

Cancle the C1^h1 terms: = d/d(d2) (C2^h2 * E0 + d2^h2 * E2) / (C2^h2 + d2^h2)

distribute the derivative across the terms in the numerator = E0 * C2^h2 * [d/d(d2) 1 / (C2^h2 + d2^h2)] + E2 * [d/d(d2) d2^h2 / (C2^h2 + d2^h2)]

= E0 * C2^h2 * [h2 * d2^(h2-1) / (C2^h2 + d2^h2)^2] + E2 * [C2^h2 * h2 * d2^(h2-1) / (C2^h2 + d2^h2)^2]

= (E0 + E2) * C2^h2 * h2 * d2^(h2-1)/(C2^h2 + d2^h2)^2

Evaluate at d2 = C2: = (E0 + E2) * h2 * C2^(2*h2-1) / [4*C2^(2*h2))] = h2 * (E0 + E2) / (4 * C2)

momeara/MPStats documentation built on July 19, 2022, 3:34 p.m.