Models: Model objective functions

In philipmorrisintl/GladiaTOX: R Package for Processing High Content Screening data

Model objective functions

Description

These functions take in the dose-response data and the model parameters, and return a likelyhood value. They are intended to be optimized using constrOptim in the gtoxFit function.

Usage

gtoxObjCnst(p, resp)

gtoxObjGnls(p, lconc, resp)

gtoxObjHill(p, lconc, resp)

Arguments

p	Numeric, the parameter values. See details for more information.
resp	Numeric, the response values
lconc	Numeric, the log10 concentration values

Details

These functions produce an estimated value based on the model and given parameters for each observation. Those estimated values are then used with the observed values and a scale term to calculate the log-likelyhood.

Let t(z,\nu) be the Student's t-ditribution with \nu degrees of freedom, y_{i} be the observed response at the i^{th} observation, and \mu_{i} be the estimated response at the i^{th} observation. We calculate z_{i} as:

z_{i} = \frac{y_{i} - \mu_{i}}{e^\sigma}

where \sigma is the scale term. Then the log-likelyhood is:

\sum_{i=1}^{n} [ln(t(z_{i}, 4)) - \sigma]

Where n is the number of observations.

Value

The log-likelyhood.

Constant Model (cnst)

gtoxObjCnst calculates the likelyhood for a constant model at 0. The only parameter passed to gtoxObjCnst by p is the scale term \sigma. The constant model value \mu_{i} for the i^{th} observation is given by:

\mu_{i} = 0

Gain-Loss Model (gnls)

gtoxObjGnls calculates the likelyhood for a 5 parameter model as the product of two Hill models with the same top and both bottoms equal to 0. The parameters passed to gtoxObjGnls by p are (in order) top (\mathit{tp}), gain log AC50 (\mathit{ga}), gain hill coefficient (gw), loss log AC50 \mathit{la}, loss hill coefficient \mathit{lw}, and the scale term (\sigma). The gain-loss model value \mu_{i} for the i^{th} observation is given by:

g_{i} = \frac{1}{1 + 10^{(\mathit{ga} - x_{i})\mathit{gw}}}

l_{i} = \frac{1}{1 + 10^{(x_{i} - \mathit{la})\mathit{lw}}}

\mu_{i} = \mathit{tp}(g_{i})(l_{i})

where x_{i} is the log concentration for the i^{th} observation.

Hill Model (hill)

gtoxObjHill calculates the likelyhood for a 3 parameter Hill model with the bottom equal to 0. The parameters passed to gtoxObjHill by p are (in order) top (\mathit{tp}), log AC50 (\mathit{ga}), hill coefficient (\mathit{gw}), and the scale term (\sigma). The hill model value \mu_{i} for the i^{th} observation is given by:

\mu_{i} = \frac{tp}{1 + 10^{(\mathit{ga} - x_{i})\mathit{gw}}}

where x_{i} is the log concentration for the i^{th} observation.

Examples

## Load level 3 data for an assay endpoint ID
dat <- gtoxLoadData(lvl=3L, type="mc", fld="aeid", val=3L)

## Compute fitting log-likelyhood
gtoxObjCnst(1, dat$resp)


## Load level 3 data for an assay endpoint ID
dat <- gtoxLoadData(lvl=3L, type="mc", fld="aeid", val=2L)

## Compute fitting log-likelyhood
gtoxObjGnls(p=c(rep(0.5,5),1e-3), lconc=dat$logc, resp=dat$resp)


## Load level 3 data for an assay endpoint ID
dat <- gtoxLoadData(lvl=3L, type="mc", fld="aeid", val=3L)

## Compute fitting log-likelyhood
gtoxObjHill(c(rep(0,3), 1e-3), dat$logc, dat$resp)

philipmorrisintl/GladiaTOX documentation built on Aug. 27, 2023, 9:07 p.m.