# censored.fit: Fit Null Distribution To Censored Data by Maximum Likelihood In fdrtool: Estimation of (Local) False Discovery Rates and Higher Criticism

## Description

`censored.fit` fits a null distribution to censored data.

`fndr.cutoff` finds a suitable cutoff point based on the (approximate) false non-discovery rate (FNDR).

## Usage

 ```1 2``` ```censored.fit(x, cutoff, statistic=c("normal", "correlation", "pvalue", "studentt")) fndr.cutoff(x, statistic=c("normal", "correlation", "pvalue", "studentt")) ```

## Arguments

 `x` vector of test statistics. `cutoff` truncation point (this may a single value or a vector). `statistic` type of statistic - normal, correlation, or student t.

## Details

As null model truncated normal, truncated student t or a truncated correlation density is assumed. The truncation point is specified by the cutoff parameter. All data points whose absolute value are large than the cutoff point are ignored when fitting the truncated null model via maximum likelihood. The total number of data points is only used to estimate the fraction of null values eta0.

## Value

`censored.fit` returns a matrix whose rows contain the estimated parameters and corresponding errors for each cutoff point.

`fndr.cutoff` returns a tentative cutoff point.

`fdrtool`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```# load "fdrtool" library library("fdrtool") # simulate normal data sd.true = 2.232 n = 5000 z = rnorm(n, sd=sd.true) censored.fit(z, c(2,3,5), statistic="normal") # simulate contaminated mixture of correlation distribution r = rcor0(700, kappa=10) u1 = runif(200, min=-1, max=-0.7) u2 = runif(200, min=0.7, max=1) rc = c(r, u1, u2) censored.fit(r, 0.7, statistic="correlation") censored.fit(rc, 0.7, statistic="correlation") # pvalue example data(pvalues) co = fndr.cutoff(pvalues, statistic="pvalue") co censored.fit(pvalues, cutoff=co, statistic="pvalue") ```

### Example output

```     cutoff N.cens      eta0     eta0.SE       sd      sd.SE
[1,]      2   3167 1.0000000 0.010789492 2.223472 0.17097623
[2,]      3   4105 0.9890670 0.006531240 2.185879 0.06795245
[3,]      5   4863 0.9955343 0.002363085 2.199912 0.02986764
cutoff N.cens      eta0    eta0.SE   kappa  kappa.SE
[1,]    0.7    681 0.9855847 0.00622226 10.6381 0.6081641
cutoff N.cens      eta0    eta0.SE   kappa  kappa.SE
[1,]    0.7    681 0.6271903 0.01483325 10.6381 0.6081641
cutoff
0.6767363
cutoff N.cens      eta0    eta0.SE
[1,] 0.6767363    569 0.4103924 0.01602273
```

fdrtool documentation built on Nov. 14, 2021, 1:07 a.m.