Estimation of the Local False Discovery Rate using Type II Maximum Likelihood Estimation.

Description

Suite of R functions for the estimation of the local false discovery rate (LFDR) using Type II maximum likelihood estimation (MLE).

Details

Author(s)

Code: Ye Yang, Marta Padilla, Zhenyu Yang, Zuojing Li, Corey M. Yanofsky
Documentation: Alaa Ali, Kyle Leckett, Marta Padilla
Maintainer: D. R. Bickel <dbickel@uOttawa.ca>

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.

Examples

dFUN<-dabsTd; dfx <- 4
n.alternative <- 3; n.null <- 4; true.ncp <- 7

#NOTE: arguments for dFUN are x, df, ncp. If dFUN has other arguments, 
#please adapt them. For example:
#dFUN<-function(x,df,ncp){dnorm(x=x,mean=ncp,sd=df)};attr(dFUN,'name')<-'dnorm'

#In the examples, W is the result of the absolute value of the t.test statistics 
#on the data

W<-abs(c(rt(n=n.alternative,ncp=true.ncp,df=dfx),rt(n=n.null,ncp=0,df=dfx)))
W[c(1,3,5)]<-NA

z1<-lfdr.mle(x=W,dFUN=dFUN, df=dfx)
z2<-lfdr.mle(x=W,dFUN=dFUN, df=dfx,fixed.p0=0.4,fixed.ncp=4)
z3<-lfdr.mdl(x=W,df=dfx,dFUN=dFUN)
z4<-lfdr.l1o(x=W,df=dfx,dFUN=dFUN)
z5<-lfdr.lho(x=W,df=dfx,dFUN=dFUN,fixed.ncp=5)
z6<-lfdr.lo(x=W,v=1/3,df=dfx,dFUN=dFUN)
z7<-lfdr.mdlo(x=W,v=1/3,df=dfx,dFUN=dFUN)

Density of the absolute Student t Distribution.

Description

Density of the absolute t distribution with df degrees of freedom and non-centrality parameter ncp.

Usage

dabsTd(x, df, ncp = 0, ...)

Arguments

Value

numeric of length equal to the length of x.

Author(s)

Code: David R. Bickel,
Documentation: Alaa Ali, Kyle Leckett, Marta Padilla.

See Also

Function dt from basic R.

Examples

  z1<-dabsTd(x = c(1:4), df = 3, ncp = 3)
 

Internal Functions and Methods

Description

These functions are for internal use and/or for upcoming packages or not yet documented.

Usage

MakeNames(x, nmvar = c("X", "I"), ...)
are(object, class2)
	are_null(object)
are_prob(object, ...)

assert.are(object, class2,
	 ...)
assert.is(object, class2, text = "")
est2list(x)
	get_groups(n.features, n.null, n.groups)
get_n.groups(n.features, n.null,
	 group.size)
get_null.groups(n.null, null.n.groups)
get_null.n.groups(n.null,
	 null_group.size)
get_simulated_W(n.features, true.p0, list.ncp1,
	 rFUN, df)
is_any(object, class2)
is_err(object)
is_error(object)
	is_unk(object)
is_vide(object)


lfdr.hats(stat = NULL, lfdr.fun = "lfdr.mle",
	 dFUN = dabsTd, lower.ncp = 0.001, upper.ncp = 20, lower.p0 = 0,
	 upper.p0 = 1, fixed.p0 = NULL, fixed.ncp = NULL, d0 = 0, v = 1,
	 w = 1, ...)
make_labels(n, nmvar = c("X"), n.ini = 1)


new_est.lfdrmle(LFDR.hat,
	 p0.hat, ncp.hat, stat, method = NULL, info = list())
nsize(x)
rFUN_generator(base_rFUN, ...)
sameAsX_names(x = NULL, y = NULL)
simulated_W(n.features, n.null, rFUN = rFUN_generator(rchisq), true.ncp1, df,
	 N = (n.features - n.null), sided = ifelse(identical(rFUN,
	 rFUN_generator(rchisq)), 1, 2), logic = TRUE)
vect2string(x, sep = "", ...)
	vectorized.dabsTd(ncp, ...)
ye.mle(W, df, dFUN = dabsTd, lower.ncp = 0.001,
	 upper.ncp = 20, lower.p0 = 0, upper.p0 = 1, d0 = 0, fixed.ncp = NULL,
	 fixed.p0 = NULL, ...)

Leave-one-out (L1O) and leave-half-out (LHO) method for LFDR estimation.

Description

Estimate the local false discovery rate using the leave-one-out method (L1O) or the leave-half-out method (LHO).

Usage

lfdr.l1o(x, dFUN = dabsTd, lower.ncp = 0.001, upper.ncp = 20, lower.p0 = 0,
      upper.p0 = 1, fixed.p0 = NULL, fixed.ncp = NULL, d0 = 0, ...)

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

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

Arguments

Value

A list with:

Note

- Requires fixed.p0=NULL.

- 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: Marta Padilla
Documentation: Alaa Ali, Kyle Leckett, Marta Padilla.

References

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.mle, lfdr.mdl.

Examples

dfx <- 4;n.alt <- 1;n.null <- 4;true.ncp <- 7
#numeric imput data: statistics of the data with missing values (removed internally)
#(result of a absolute t.test statistics on the data)
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.l1o(x=W,df=dfx)
z2<-lfdr.lho(x=W,df=dfx,fixed.ncp=10)
z3<-lfdr.lo(x=W,df=dfx,v=1/3,fixed.p0=0.3)

Minimum description length (MDL) method for estimation of LFDR.

Description

Estimate the local false discovery rate using the minimum description length (MDL) method.

Usage

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

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

Arguments

Value

A list with:

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: Marta Padilla
Documentation: Alaa Ali, Kyle Leckett, Marta Padilla.

References

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.mle, lfdr.l1o.

Examples

dfx <- 4;n.alt <- 1;n.null <- 4;true.ncp <- 7
#numeric imput data: statistics of the data with missing values (removed internally)
#(result of a absolute t.test statistics on the data)
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.mdl(x=W,df=dfx)
z2<-lfdr.mdl(x=W,df=dfx,fixed.ncp=10)
z3<-lfdr.mdlo(x=W,df=dfx,v=1/3,fixed.p0=0.3)

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

Value

A list with:

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)