nplr {nplr}

Function to Fit n-Parameter Logistic Regressions.

Description

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.

Usage

nplr(x, y, useLog = TRUE, LPweight = 0.25, npars = "all",
        method = c("res", "sdw", "gw"), silent = FALSE)

Arguments

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 TRUE, set to FALSE if x is already in Log10.

LPweight

: a coefficient to adjust the weights. LPweight = 0 will compute a non-weighted np-logistic regression.

npars

: a numeric value (or "all") to specify the number of parameters to use in the model. If "all" the logistic model will be tested with 2 to 5 parameters, and the best option will be returned. See Details

method

: a character string to specify what weight method to use. Options are "res"(Default), "sdw", "gw". See Details

silent

: Logical. Specify whether warnings ad/or messages has to be silenced. Default to FALSE.

Details

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) = \Sigma [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].

Value

An object of class nplr.

slots

• 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.

Note

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.

Author(s)

Frederic Commo, Brian M. Bot

References

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.

See Also

convertToProp, getEstimates, plot.nplr, nplrAccessors

Examples

# 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)