tww {TWW} | R Documentation |
TWW Growth Model
Description
Calculates the 3-, 4-, and 5-parameter TWW Growth model estimates. For those who
use the cycle number and fluorescence intensity to analyze real-time, or quantitative polymerase
chain reaction (qPCR), this function will calculate the TWW cycle threshold (C_{TWW}
).
Usage
tww(x, y, start = list(alpha,theta,beta,delta = NULL,phi = NULL), ...)
Arguments
x |
A numeric vector that must be same length as |
y |
A numeric vector that must be same length as |
start |
A numeric list.
The supplied list of numbers are designated as starting parameters, or initial conditions,
inserted into the nls function as |
... |
Additional optional arguments passed to the nls function. |
Details
The initialized parameters are inserted as a list in start
and are passed to the nls function using the Gauss-Newton algorithm.
If you intend to use a 3-parameter model, insert values for \alpha
, \theta
, and \beta
only. If you plan to use the
4-parameter model, you must insert values for \delta
in addition to \alpha
, \theta
, and \beta
.
If you intend to use the 5-parameter model, you need to insert initial values for all five parameters. The parameters always follows the
order \alpha
, \theta
, \beta
, \delta
, and \phi
. The number of items in the list
determines your choice of model.
The 3-parameter growth model has the form
F(x)=\alpha\ e^{-ArcSinh\left(\theta e^{-\beta x}\right)}
while the 4-parameter growth model follows the equation
F(x)=\alpha\ e^{-ArcSinh\left(\theta e^{-\beta x}\right)}+\delta
and the 5-parameter growth model is given by
F(x)=\alpha\ e^{-\phi ArcSinh\left(\theta e^{-\beta x}\right)}+\delta
In each of these models, \theta
> 0. In the 5-parameter model, \phi
> 0.
C_{TWW}
is only applicable to qPCR data and should not be considered in other cases.
Value
This function is designed to calculate the parameter estimates, standard errors, and p-values
for the TWW Growth (Decay) Model as well as estimating C_{TWW}
, inflection point (poi) coordinates,
sum of squares error (SSE), Akaike information criterion (AIC), and Bayesian information criterion (BIC).
See Also
nls
to determine the nonlinear (weighted) least-squares estimates of the parameters of a nonlinear model.
Examples
#Data source: Guescini, M et al. BMC Bioinformatics (2008) Vol 9 Pg 326
fluorescence <- c(-0.094311625, -0.022077977, -0.018940959, -0.013167045,
0.007782761, 0.046403221, 0.112927418, 0.236954113,
0.479738750, 0.938835708, 1.821600610, 3.451747880,
6.381471101, 11.318606976, 18.669664284, 27.684433343,
36.269197588, 42.479513622, 46.054327283, 47.977882896,
49.141536806, 49.828324910, 50.280629676, 50.552338600,
50.731472869, 50.833299572, 50.869115345, 50.895051731,
50.904097158, 50.890804989, 50.895911798, 50.904685027,
50.899942221, 50.876866864, 50.878926417, 50.876938783,
50.857835844, 50.858580957, 50.854100495, 50.847128383,
50.844847982, 50.851447716, 50.841698121, 50.840564351,
50.826118614, 50.828983069, 50.827490974, 50.820366077,
50.823743224, 50.857581865)
cycle_number <- 1:50
#3-parameter model
tww(x = cycle_number, y = fluorescence, start = list(40,15.5,0.05))
#4-parameter model
tww(x = cycle_number, y = fluorescence, start = list(40,15.5,0.05,0),
algorithm = "port")$c_tww
#5-parameter model
summary(tww(x = cycle_number, y = fluorescence, start = list(40,15.5,0.05,0,1),
algorithm = "port",
control = nls.control(maxiter = 250)))