lfdr.mle {LFDR.MLE}

Type II Maximum likelihood estimate of LFDR (LFDR-MLE).

Description

Estimates the local false discovery rate by the Type II maximum likelihood estimates (MLE).

Usage

lfdr.mle(x, dFUN = dabsTd, lower.ncp = 0.001, upper.ncp = 20,lower.p0 = 0, upper.p0 = 1,
         fixed.p0 = NULL, fixed.ncp = NULL, d0 = 0, ...)

Arguments

x

Input numeric vector of statistics.

dFUN

Density function; default dabsTd (from absolute value of the Student t distribution)

lower.ncp

The lowerbound of the location parameter of dFUN (noncentrality parameter for default dFUN=dabsTd); default value is 0.001

upper.ncp

The upperbound of the location parameter of dFUN (noncentrality parameter for default dFUN=dabsTd); default value is 20

lower.p0

The lowerbound of p0 (proportion of unaffected features (null hypothesis)); default value is 0

upper.p0

The upperbound of p0 (proportion of unaffected features (null hypothesis)); default value is 1

fixed.p0

A fixed value of p0 (proportion of unaffected features (null hypothesis)); default value is NULL

fixed.ncp

A fixed value of the location parameter of dFUN (noncentrality parameter for default dFUN=dabsTd); default value is NULL

d0

the numeric value of the null hypothesis for dFUN, default value is 0.

...

Other parameters to pass to dFUN (see notes and examples).

Value

A list with:

LFDR.hat

estimates of the LFDR

p0.hat

estimate of the proportion of unaffected features p0 (true null hypothesis).

ncp.hat

estimate of the location parameter of the distribution dFUN (ncp: noncentrality parameter of dFUN=dabsTd by default).

info

method name and information about computation failure.

Note

- The probability density function (dFUN) can be set to any other distribution, adapted so that the location parameter corresponds to ncp, other parameter to df and any other can be passed to dFUN by the dots (see examples in lfdr.mle).

- If computation fails for all features, p0.hat is set to NA and so is LFDR.hat, which is a vector of NA with lengh equal to the number of features. If it fails for a given feature, only the resulting LFDR for that feature is set to NA. Error messages are not suppressed.

Author(s)

Code: Ye Yang, Marta Padilla, Zhenyu Yang, Zuojing Li, Corey M. Yanofsky
Documentation: Alaa Ali, Kyle Leckett, Marta Padilla.

References

Yang, Y., & Bickel, D. R. (2010). Minimum description length and empirical Bayes methods of identifying SNPs associated with disease. Technical Report, Ottawa Institute of Systems Biology, COBRA Preprint Series, Article 74, available at biostats.bepress.com/cobra/ps/art74.

Bickel, D. R. (2010). Minimum description length methods of medium-scale simultaneous inference. arXiv preprint arXiv:1009.5981.

Padilla, M., & Bickel, D. R. (2012). Estimators of the local false discovery rate designed for small numbers of tests. Statistical Applications in Genetics and Molecular Biology, 11(5), art. 4.

See Also

lfdr.mdl, lfdr.l1o, lfdr.lho.

Examples

#numeric imput data: statistics of the data with missing values (removed internally)
#(result of a absolute t.test statistics on the data)
dfx <- 4;n.alt <- 1;n.null <- 4;true.ncp <- 7
W<-abs(c(rt(n=n.alt,ncp=true.ncp,df=dfx),rt(n=n.null,ncp=0,df=dfx)))
W[3]<-NA

z1<-lfdr.mle(x=W,dFUN=dabsTd, df=dfx)
z2<-lfdr.mle(x=W,dFUN=dabsTd, df=dfx, fixed.p0=0.4, fixed.ncp=4)

#other dFUN -------
#NOTE: arguments for dFUN are x, df, ncp. If dFUN has other arguments, 
#please adapt them. For example:

new.df<-function(x,df,ncp,...){df(x=x,ncp=ncp,df1=df,...)}
z3<-lfdr.mle(x=W,df=dfx,dFUN=new.df,df2=5)