takeoff: Calculation of the qPCR takeoff point
In qpcR: Modelling and Analysis of Real-Time PCR Data

Description Usage Arguments Details Value Author(s) References Examples

Calculates the first significant cycle of the exponential region (takeoff point) using externally studentized residuals as described in Tichopad et al. (2003).

1	takeoff(object, pval = 0.05, nsig = 3)

`object`	an object of class 'pcrfit'.
`pval`	the p-value for the takeoff test.
`nsig`	the number of successive takeoff tests. See 'Details'.

Takeoff points are calculated essentially as described in the reference below. The steps are:

1) Fitting a linear model to background cycles 1:n, starting with n = 5.
2) Calculation of the external studentized residuals using rstudent, which uses the hat matrix of the linear model and leave-one-out:

\langle \hat{\varepsilon}_i \rangle = \frac{\hat{\varepsilon}_i}{\hat{σ}_{(i)} √{1-h_{ii}}}, \hat{σ}_{(i)} = √{\frac{1}{n - p - 1} ∑_{j = 1 \atop j \ne i }^n \hat{\varepsilon}_j^2}

with h_{ii} being the ith diagonal entry in the hat matrix H = X(X^TX)^{-1}X^T.
3) Test if the last studentized residual \langle \hat{\varepsilon}_n \rangle is an outlier in terms of t-distribution:

1 - pt(\langle \hat{\varepsilon}_n \rangle, n - p) < 0.05

with n = number of residuals and p = number of parameters.
4) Test if the next nsig - 1 cycles are also outlier cycles.
5) If so, take cycle number from 3), otherwise n = n + 1 and start at 1).

A list with the following components:

`top`	the takeoff point.
`f.top`	the fluorescence at `top`.

Andrej-Nikolai Spiess

Standardized determination of real-time PCR efficiency from a single reaction set-up.
Tichopad A, Dilger M, Schwarz G & Pfaffl MW.
Nucleic Acids Research (2003), e122.

m1 <- pcrfit(reps, 1, 2, l5)
res1 <- takeoff(m1) 
plot(m1)
abline(v = res1$top, col = 2)
abline(h = res1$f.top, col = 2)

Loading required package: MASS
Loading required package: minpack.lm
Loading required package: rgl
Loading required package: robustbase
Loading required package: Matrix
Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl_init' failed, running with rgl.useNULL = TRUE 
3: .onUnload failed in unloadNamespace() for 'rgl', details:
  call: fun(...)
  error: object 'rgl_quit' not found 
[1] "pcrfit" "nls"