Description

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

Usage

Arguments

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).

Value

A list with the following components:

Author(s)

Andrej-Nikolai Spiess

References

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.

Examples