pi0.est: Estimation of the prior probability

Description

Estimates the prior probability that a gene is not differentially expressed by the natural cubic splines based method of Storey and Tibshirani (2003).

Usage

pi0.est(p, lambda = seq(0, 0.95, 0.05), ncs.value = "max",  ncs.weights = NULL)

Arguments

a numeric vector containing the p-values of the genes.

lambda

a numeric vector or value specifying the $lambda$ values used in the estimation of the prior probability.

ncs.value

a character string. Only used if lambda is a vector. Either "max" or "paper". For details, see Details.

ncs.weights

a numerical vector of the same length as lambda containing the weights used in the natural cubic spline fit. By default no weights are used.

Value

p0: the estimate of the prior probability that a gene is not differentially expressed.
spline.out: the output of smooth.spline used in this function.

Details

For each value of lambda, $pi0(lambda)$ is computed by the number of p-values p larger than $lambda$ divided by $(1-lambda)\m$, where $m$ is the length of p. If lambda is a value, $pi0(lambda)$ is the estimate for the prior probabiltity $pi0$ that a gene is not differentially expressed. If lambda is a vector, a natural cubic spline $h$ with 3 degrees of freedom is fitted through the data points $(lambda,pi0(lambda))$, where each point is weighed by ncs.weights. $pi0$ is estimated by $h(v)$, where $v=max{lambda}$ if ncs.value="max", and $v=1$ if ncs.value="paper".

References

Storey, J.D., and Tibshirani, R. (2003). Statistical Significance for Genome-wide Studies. PNAS, 100, 9440-9445.