findBestBRAID: Select Best Fitting BRAID Surface Model
In braidrm: Fitting Dose Response with the BRAID Combined Action Model

Description Usage Arguments Details Value Author(s) See Also Examples

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

## 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, ...)

`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

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 E0 varies freely, and the two maximal effect parameters EfA and EfB vary freely independently of one another.
The initial effect parameter E0 is fixed at the default value, and the two maximal effect parameters EfA and EfB vary freely independently of one another.
The initial effect parameter E0 the maximal effect parameter EfA vary freely, and the maximal effect parameter EfB is fixed at the default value.
The initial effect parameter E0 the maximal effect parameter EfB vary freely, and the maximal effect parameter EfA is fixed at the default value.
The initial effect parameter E0 varies freely, and the two maximal effect parameters EfA and EfB are constrained to vary as a single parameter Ef.
The initial effect parameter E0 varies freely, and the two maximal effect parameters EfA and EfB are fixed at the default value.
The initial effect parameter E0 the two maximal effect parameter EfB are fixed at the default values, and the maximal effect parameter EfA varies freely.
The initial effect parameter E0 the two maximal effect parameter EfA are fixed at the default values, and the maximal effect parameter EfB varies freely.
The initial effect parameter E0 is fixed at the default value,, and the two maximal effect parameters EfA and EfB are constrained to vary as a single parameter Ef.
The initial effect parameter E0 and the two maximal effect parameters EfA and EfB are all fixed at the default values.

In all models, the potencies of the two drugs (represented by IDMA and IDMB) and the Hill slopes of both drugs (represented by na and nb) vary freely. Which of the interaction parameters κ and δ varies depends on the parameter itype, as follows:

itype = 1: κ varies freely in all models; δ is fixed at 1 (10 models total).
itype = 2: δ varies freely in all models; κ is fixed at 0 (10 models total).
itype = 3: Either κ or δ (but not both) vary freely in all models (20 models total).
itype = 4: Either κ or δ or both vary freely in all models (30 models total).
itype = 5: κ is fixed at 0 and δ is fixed at 1 in all models (10 models total).

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

Nathaniel R. Twarog

braidrm, getBRAIDbootstrap, runBRAIDanalysis

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))