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

This function computes a weighted n-parameters logistic regression, given x (typically compound concentrations) and y values (responses: optic densities, fluorescence, cell counts,...). See `Details`

.

1 2 |

`x` |
: a vector of numeric values, e.g. a vector of drug concentrations. |

`y` |
: a vector of numeric values, e.g. a vector of responses, typicaly provided as proportions of control. |

`useLog` |
: Logical. Should x-values be Log10-transformed. Default to |

`LPweight` |
: a coefficient to adjust the weights. |

`npars` |
: a numeric value (or |

`method` |
: a character string to specify what weight method to use. Options are |

`silent` |
: Logical. Specify whether |

The 5-parameter logistic regression is of the form:

* y = B + (T - B)/[1 + 10^(b*(xmid - x))]^s *

where `B`

and `T`

are the bottom and top asymptotes, respectively, `b`

and `xmid`

are the Hill slope and the x-coordinate at the inflexion point, respectively, and s is an asymetric coefficient. This equation is sometimes refered to as the Richards' equation [1,2].

When specifying `npars = 4`

, the `s`

parameter is forced to be `1`

, and the corresponding model is a 4-parameter logistic regression, symetrical around its inflexion point. When specifying `npars = 3 or npars = 2`

, add 2 more constraints and force `B`

and `T`

to be `0`

and `1`

, respectively.

Weight methods:

The model parameters are optimized, simultaneously, using nlm, given a sum of squared errors function, sse(Y), to minimize:

* sse(Y) = Σ [W.(Yobs - Yfit)^2 ] *

where Yobs, Yfit and W are the vectors of observed values, fitted values and weights, respectively.

In order to reduce the effect of possible outliers, the weights can be computed in different ways, specified in `nplr`

:

residual weights,

`"res"`

:*W = (1/residuals)^LPweight*where

`residuals`

and`LPweight`

are the squared error between the observed and fitted values, and a tuning parameter, respectively. Best results are generally obtained by setting*LPweight = 0.25*(default value), while setting*LPweight = 0*results in computing a non-weighted sum of squared errors.standard weights,

`"sdw"`

:*W = 1/Var(Yobs_r)*where

`Var(Yobs_r)`

is the vector of the within-replicates variances.general weights,

`"gw"`

:*W = 1/Yfit^LPweight*where

`Yfit`

are the fitted values. As for the residuals-weights method, setting*LPweight = 0*results in computing a non-weighted sum of squared errors.

The `standard weights`

and `general weights`

methods are describes in [3].

An object of class `nplr`

.

x : the x values as they are used in the model. It can be

`Log10(x)`

if`useLog`

was set to`TRUE`

.y : the y values.

useLog : logical.

npars : the best number of parameters if

`npars="all", the specified number of parameters, otherwise.`

LPweight : the weights tuning parameter.

yFit : the y fitted values.

xCurve : the x values generated to draw the curve. 200 points between the

`min`

and`max`

of x.yCurve : the fitted values used to draw the curve. the fitted values corresponding to

`xCurve`

.inflPoint : the inflexion point x and y coordinates.

goodness : the goodness-of-fit. The correlation between the fitted and the observed y values

stdErr : the mean squared error between the fitted and the observed y values

pars : the model parameters.

AUC : the area under the curve estimated using both the trapezoid method and the Simpson's rule.

The data used in the examples are samples from the NCI-60 Growth Inhibition Data: https://wiki.nci.nih.gov/display/NCIDTPdata/NCI-60+Growth+Inhibition+Data, except for multicell.tsv which are simulated data.

Frederic Commo, Brian M. Bot

1- Richards, F. J. (1959). A flexible growth function for empirical use. J Exp Bot 10, 290-300.

2- Giraldo J, Vivas NM, Vila E, Badia A. Assessing the (a)symmetry of concentration-effect curves: empirical versus mechanistic models. Pharmacol Ther. 2002 Jul;95(1):21-45.

3- Motulsky HJ, Brown RE. Detecting outliers when fitting data with nonlinear regression - a new method based on robust nonlinear regression and the false discovery rate. BMC Bioinformatics. 2006 Mar 9;7:123.

`convertToProp`

, `getEstimates`

, `plot.nplr`

, `nplrAccessors`

1 2 3 4 5 6 | ```
# Using the PC-3 data
require(nplr)
path <- system.file("extdata", "pc3.txt", package = "nplr")
pc3 <- read.delim(path)
model <- nplr(x = pc3$CONC, y = pc3$GIPROP)
plot(model)
``` |

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