scaleMeanVarCurveRobust {MAnorm2}

Scale a Mean-Variance Curve in a Robust Manner

Description

scaleMeanVarCurveRobust underlies other interface functions for estimating the variance ratio factor of an unadjusted mean-variance curve (or a set of unadjusted mean-variance curves) in a robust manner.

Usage

scaleMeanVarCurveRobust(
  z,
  m,
  d0,
  p_low = 0.01,
  p_up = 0.1,
  nw = gauss.quad(128, kind = "legendre")
)

Arguments

z

A list of which each element is a vector of FZ statistics corresponding to a bioCond object (see also "Details").

m

A vector of numbers of replicates in bioCond objects. Must correspond to z one by one in the same order.

d0

A positive real specifying the number of prior degrees of freedom of the mean-variance curve(s). Inf is allowed. Note that d0 could be robustly estimated by estimateD0Robust.

p_low, p_up

Lower- and upper-tail probabilities for Winsorizing the FZ statistics associated with each bioCond.

nw

A list containing nodes and weights variables for calculating the definite integral of a function f over the interval [-1, 1], which is approximated by sum(nw$weights * f(nw$nodes)). By default, a set of Gauss-Legendre nodes along with the corresponding weights calculated by gauss.quad is used.

Details

For each bioCond object with replicate samples, a vector of FZ statistics can be deduced from the unadjusted mean-variance curve associated with it. More specifically, for each genomic interval in a bioCond with replicate samples, its FZ statistic is defined to be log(t_hat / v0), where t_hat is the observed variance of signal intensities of the interval, and v0 is the interval's prior variance read from the corresponding mean-variance curve.

Theoretically, each FZ statistic follows a scaled Fisher's Z distribution plus a constant (since the mean-variance curve is not adjusted yet), and we derive a robust estimation of log variance ratio factor by Winsorizing the FZ statistics of each bioCond and matching the resulting sample mean with the theoretical expectation of the Winsorized distribution, which is calculated by using numerical integration (see also "References").

The final estimate of log variance ratio factor is a weighted mean of estimates across bioCond objects, with the weights being their respective numbers of genomic intervals that are used to calculate FZ statistics.

Finally, we get an estimate of variance ratio factor by taking an exponential.

Value

The estimated variance ratio factor for adjusting the mean-variance curve(s). Note that the function returns NA if there are not sufficient genomic intervals for estimating it.

References

Phipson, B., et al., Robust Hyperparameter Estimation Protects against Hypervariable Genes and Improves Power to Detect Differential Expression. Annals of Applied Statistics, 2016. 10(2): p. 946-963.

See Also

bioCond for creating a bioCond object; fitMeanVarCurve for fitting a mean-variance curve; varRatio for a formal description of variance ratio factor; estimateD0Robust for estimating the number of prior degrees of freedom associated with a mean-variance curve (or a set of curves) in a robust manner; estimatePriorDfRobust for an interface to robustly estimating the number of prior degrees of freedom on bioCond objects as well as robustly adjusting their mean-variance curve(s) accordingly.

estimateD0 and scaleMeanVarCurve for the ordinary (non-robust) routines for estimating number of prior degrees of freedom and variance ratio factor, respectively.

Examples

# Refer to "Examples" given in the help page for the function
# estimateD0Robust.