Proportion of true null p-values

Estimates the proportion of true null p-values, i.e., those following the Uniform(0,1) distribution.

Usage

pi0est(
  p,
  lambda = seq(0.05, 0.95, 0.05),
  pi0.method = c("smoother", "bootstrap"),
  smooth.df = 3,
  smooth.log.pi0 = FALSE,
  ...
)

Arguments

p: A vector of p-values (only necessary input).
lambda: The value of the tuning parameter to estimate \(\pi_0\). Must be in [0,1). Optional, see Storey (2002).
pi0.method: Either "smoother" or "bootstrap"; the method for automatically choosing tuning parameter in the estimation of \(\pi_0\), the proportion of true null hypotheses.
smooth.df: Number of degrees-of-freedom to use when estimating \(\pi_0\) with a smoother. Optional.
smooth.log.pi0: If TRUE and pi0.method = "smoother", \(\pi_0\) will be estimated by applying a smoother to a scatterplot of \(\log(\pi_0)\) estimates against the tuning parameter \(\lambda\). Optional.
...: Arguments passed from qvalue function.

Value

Returns a list:

pi0: A numeric that is the estimated proportion of true null p-values.
pi0.lambda: A vector of the proportion of null values at the \(\lambda\) values (see vignette).
lambda: A vector of \(\lambda\) value(s) utilized in calculating pi0.lambda.
pi0.smooth: A vector of fitted values from the smoother fit to the \(\pi_0\) estimates at each lambda value (pi0.method="bootstrap" returns NULL).

Details

If no options are selected, then the method used to estimate \(\pi_0\) is the smoother method described in Storey and Tibshirani (2003). The bootstrap method is described in Storey, Taylor & Siegmund (2004). A closed form solution of the bootstrap method is used in the package and is significantly faster.

References

Storey JD. (2002) A direct approach to false discovery rates. Journal of the Royal Statistical Society, Series B, 64: 479-498.
http://onlinelibrary.wiley.com/doi/10.1111/1467-9868.00346/abstract

Storey JD and Tibshirani R. (2003) Statistical significance for genome-wide experiments. Proceedings of the National Academy of Sciences, 100: 9440-9445.

Storey JD. (2003) The positive false discovery rate: A Bayesian interpretation and the q-value. Annals of Statistics, 31: 2013-2035.
http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.aos/1074290335

Storey JD, Taylor JE, and Siegmund D. (2004) Strong control, conservative point estimation, and simultaneous conservative consistency of false discovery rates: A unified approach. Journal of the Royal Statistical Society, Series B, 66: 187-205.
http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9868.2004.00439.x/abstract

Storey JD. (2011) False discovery rates. In International Encyclopedia of Statistical Science.
http://genomine.org/papers/Storey_FDR_2011.pdf
http://www.springer.com/statistics/book/978-3-642-04897-5

Author

John D. Storey