Calculates the first significant cycle of the exponential region (takeoff point) using externally studentized residuals as described in Tichopad et al. (2003).
Usage
takeoff(object, pval = 0.05, nsig = 3)
Arguments
object
an object of class 'pcrfit'.
pval
the p-value for the takeoff test.
nsig
the number of successive takeoff tests. See 'Details'.
Value
A list with the following components:
topthe takeoff point.
f.topthe fluorescence at top.
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:
$$\langle \hat{\varepsilon}_i \rangle = \frac{\hat{\varepsilon}_i}{\hat{\sigma}_{(i)} \sqrt{1-h_{ii}}}, \hat{\sigma}_{(i)} = \sqrt{\frac{1}{n - p - 1} \sum_{j = 1 \atop j \ne i }^n \hat{\varepsilon}_j^2}$$
with $h_{ii}$ being the $i$th 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).
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.