findBestBRAID {braidrm}

Select Best Fitting BRAID Surface Model

Description

Fits several BRAID surface models to the given data, and selects the most parsimonious model using the Akaike information criterion.

Usage

## Default S3 method:
findBestBRAID(model, data, defaults, startparv=NULL, llims=NULL,
				ulims=NULL, itype=1, getCIs=TRUE, crossval=TRUE, ...)
## S3 method for class 'formula'
findBestBRAID(model, data, ...)

Arguments

model

a two-column array containing concentrations of Drug 1 and Drug 2 in each dose pair, or a symbolic formula (e.g. act ~ conc1+conc2) specifying which variables are to be fit

data

if model is an array, a vector of measurements of response to the concentrations of Drug 1 and Drug 2; if model is a formula, a data frame containing the columns specified in formula

defaults

two-element vector specifying the default initial and maximal effects for the response surface. These values will be used in several of the models that are tried (see Details below).

startparv

an optional parameter specifying starting parameter values for the optimization

llims

a ten-element vector of lower limits on parameters being fit. Any parameters that do not require a limit can have a value of NA. If NULL (the default), llims is calculated from the starting values in startparv (or the values calculated for startparv if startparv is not specified).

ulims

a vector of upper limits on parameters being fit. Follows same behavior as llims.

itype

an integer that specifies the type of interaction(s) that is assumed in the models. The default is 1, which assumes that the interaction parameter \kappa is varying. See details below for other possible values.

getCIs

determines if confidence intervals will be calculated for all response surface parameters being fit. Parameters are fit using a bootstrapping approach which resamples residuals and refits the new data.

crossval

if TRUE, goodness of fit is determined by randomly assigning data points to four blocks, and evaluating goodness of fit on each block by fitting the remaining three. If FALSE, all data points are fit once, and goodness of fit is determined using the residuals from that fit. It is advisable not to use cross-validation when a relatively small number of data points are available, especially on the margins (when drug A or drug B has concentration 0).

...

Not used

Details

Because experiments do not reliably capture the full range of responses that a combination can produce, estimation of the initial and maximal effect parameters for a BRAID surface can be highly unstable. This function fits at least 10 distinct BRAID surface models to the given data, and selects the model which best balances simplicity with goodness of fit. For each interaction type (see below), the following 10 models are fit:

• The initial effect parameter E_0 varies freely, and the two maximal effect parameters E_{f,A} and E_{f,B} vary freely independently of one another.

• The initial effect parameter E_0 is fixed at the default value, and the two maximal effect parameters E_{f,A} and E_{f,B} vary freely independently of one another.

• The initial effect parameter E_0 the maximal effect parameter E_{f,A} vary freely, and the maximal effect parameter E_{f,B} is fixed at the default value.

• The initial effect parameter E_0 the maximal effect parameter E_{f,B} vary freely, and the maximal effect parameter E_{f,A} is fixed at the default value.

• The initial effect parameter E_0 varies freely, and the two maximal effect parameters E_{f,A} and E_{f,B} are constrained to vary as a single parameter E_f.

• The initial effect parameter E_0 varies freely, and the two maximal effect parameters E_{f,A} and E_{f,B} are fixed at the default value.

• The initial effect parameter E_0 the two maximal effect parameter E_{f,B} are fixed at the default values, and the maximal effect parameter E_{f,A} varies freely.

• The initial effect parameter E_0 the two maximal effect parameter E_{f,A} are fixed at the default values, and the maximal effect parameter E_{f,B} varies freely.

• The initial effect parameter E_0 is fixed at the default value,, and the two maximal effect parameters E_{f,A} and E_{f,B} are constrained to vary as a single parameter E_f.

• The initial effect parameter E_0 and the two maximal effect parameters E_{f,A} and E_{f,B} are all fixed at the default values.

In all models, the potencies of the two drugs (represented by {ID}_{M,A} and {ID}_{M,B}) and the Hill slopes of both drugs (represented by n_a and n_b) vary freely. Which of the interaction parameters \kappa and \delta varies depends on the parameter itype, as follows:

• itype = 1: \kappa varies freely in all models; \delta is fixed at 1 (10 models total).

• itype = 2: \delta varies freely in all models; \kappa is fixed at 0 (10 models total).

• itype = 3: Either \kappa or \delta (but not both) vary freely in all models (20 models total).

• itype = 4: Either \kappa or \delta or both vary freely in all models (30 models total).

• itype = 5: \kappa is fixed at 0 and \delta is fixed at 1 in all models (10 models total).

Value

An object of the class 'braidrm', with elements as described in braidrm.

Author(s)

Nathaniel R. Twarog

See Also

braidrm, getBRAIDbootstrap, runBRAIDanalysis

Examples

data(es8olatmz)
## Not run: summary(findBestBRAID(cbind(es8olatmz$conc1,es8olatmz$conc2),
				es8olatmz$act,defaults=c(0,-2.7)))
## End(Not run)
## Not run: summary(findBestBRAID(act~conc1+conc2,es8olatmz,defaults=c(0,-2.7),itype=2))
summary(findBestBRAID(act~conc1+conc2,es8olatmz,defaults=c(0,-4),getCIs=FALSE))