TWW Growth Model

Description

Calculates the 3-, 4-, and 5-parameter TWW (Tabatabai, Wilus, Wallace) 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

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), total sum of squares (SST), root mean square error (RMSE), Akaike information criterion (AIC), and Bayesian information criterion (BIC).

References

Tabatabai M, Wilus D, Singh K, Wallace T. The TWW Growth Model and Its Application in the Analysis of Quantitative Polymerase Chain Reaction. Bioinformatics and Biology Insights. 2024;18. doi:10.1177/11779322241290126

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)))