boot.null {multtest} | R Documentation

## Non-parametric bootstrap resampling function in package ‘multtest’

### Description

Given a data set and a closure, which consists of a function for computing the test statistic and its enclosing environment, this function produces a non-parametric bootstrap estimated test statistics null distribution. The observations in the data are resampled using the ordinary non-parametric bootstrap and used to produce an estimated test statistics distribution. This distribution is then centered and scaled to produce the null distribution. This function is called by `MTP`.

### Usage

    boot.null(X, label, stat.closure, W = NULL, B = 1000, test, theta0 = 0, tau0 = 1, alternative = "two.sided", seed=NULL, cluster=1,csnull=TRUE, dispatch=0.05)

    boot.resample(X,label, p, n, stat.closure, W, B, test)

    center.scale(muboot, theta0, tau0, alternative)

### Arguments

`X` | A matrix, data.frame or ExpressionSet containing the raw data. In the case of an ExpressionSet, `exprs(X)` is the data of interest and `pData(X)` may contain outcomes and covariates of interest. For `boot.resample` `X` must be a matrix. For currently implemented tests, one hypothesis is tested for each row of the data.
`label` | A vector containing the class labels for t- and f-tests.
`stat.closure` | A closure for test statistic computation, like those produced internally by the `MTP` function. The closure consists of a function for computing the test statistic and its enclosing environment, with bindings for relevant additional arguments (such as null values, outcomes, and covariates).
`W` | A vector or matrix containing non-negative weights to be used in computing the test statistics. If a matrix, `W` must be the same dimension as `X` with one weight for each value in `X`. If a vector, `W` may contain one weight for each observation (i.e. column) of `X` or one weight for each variable (i.e. row) of `X`. In either case, the weights are duplicated appropriately. Weighted f-tests are not available. Default is 'NULL'.
`B` | The number of bootstrap iterations (i.e. how many resampled data sets) or the number of permutations (if `nulldist` is 'perm'). Can be reduced to increase the speed of computation, at a cost to precision. Default is 1000.
`test` | Character string specifying the test statistics to use. See `MTP` for a list of tests.
`theta0` | The value used to center the test statistics. For tests based on a form of t-statistics, this should be zero (default). For f-tests, this should be 1.
`tau0` | The value used to scale the test statistics. For tests based on a form of t-statistics, this should be 1 (default). For f-tests, this should be 2/(K-1), where K is the number of groups.
`alternative` | Character string indicating the alternative hypotheses, by default 'two.sided'. For one-sided tests, use 'less' or 'greater' for null hypotheses of 'greater than or equal' (i.e. alternative is 'less') and 'less than or equal', respectively.
`seed` | Integer or vector of integers to be used as argument to `set.seed` to set the seed for the random number generator for bootstrap resampling. This argument can be used to repeat exactly a test performed with a given seed. If the seed is specified via this argument, the same seed will be returned in the seed slot of the MTP object created. Else a random seed(s) will be generated, used and returned. Vector of integers used to specify seeds for each node in a cluster used to to generate a bootstrap null distribution.
`cluster` | Integer of 1 or a cluster object created through the package snow. With cluster=1, bootstrap is implemented on single node. Supplying a cluster object results in the bootstrap being implemented in parallel on the provided nodes. This option is only available for the bootstrap procedure.
`csnull` | Indicator of whether the bootstrap estimated test statistics distribution should be centered and scaled (to produce a null distirbution) or not. If csnull==FALSE, the non-null bootstrap estimated test statistics distribution is returned.
`dispatch` | The number or percentage of bootstrap iterations to dispatch at a time to each node of the cluster if a computer cluster is used. If dispatch is a percentage, `B*dispatch` must be an integer. If dispatch is an integer, then `B/dispatch` must be an integer. Default is 5 percent.
`p` | An integer of the number of variables of interest to be tested.
`n` | An integer of the total number of samples.
`muboot` | A matrix of bootstrapped test statistics

### Value

For `boot.null` and `center.scale` a matrix of dimension number of hypotheses (`nrow(X)`) by number of bootstrap iterations (`B`). This is the estimated joint test statistics null distribution. Each column is a centered and scaled resampled vector of test statistics. Each row is the bootstrap estimated marginal null distribution for a single hypothesis. This object is returned in slot `nulldist` of an object of class `MTP` when the argument `keep.nulldist` to the `MTP` function is TRUE. For `boot.resample` a matrix of bootstrap samples prior to centering and scaling.

### Note

Thank you to Duncan Temple Lang and Peter Dimitrov for suggestions about the code.

### Author(s)

Katherine S. Pollard and Sandra Taylor, with design contributions from Sandrine Dudoit and Mark J. van der Laan.

### References

M.J. van der Laan, S. Dudoit, K.S. Pollard (2004), Augmentation Procedures for Control of the Generalized Family-Wise Error Rate and Tail Probabilities for the Proportion of False Positives, Statistical Applications in Genetics and Molecular Biology, 3(1). http://www.bepress.com/sagmb/vol3/iss1/art15/

M.J. van der Laan, S. Dudoit, K.S. Pollard (2004), Multiple Testing. Part II. Step-Down Procedures for Control of the Family-Wise Error Rate, Statistical Applications in Genetics and Molecular Biology, 3(1). http://www.bepress.com/sagmb/vol3/iss1/art14/

S. Dudoit, M.J. van der Laan, K.S. Pollard (2004), Multiple Testing. Part I. Single-Step Procedures for Control of General Type I Error Rates, Statistical Applications in Genetics and Molecular Biology, 3(1). http://www.bepress.com/sagmb/vol3/iss1/art13/

Katherine S. Pollard and Mark J. van der Laan, "Resampling-based Multiple Testing: Asymptotic Control of Type I Error and Applications to Gene Expression Data" (June 24, 2003). U.C. Berkeley Division of Biostatistics Working Paper Series. Working Paper 121. http://www.bepress.com/ucbbiostat/paper121

### See Also

`MTP`, `MTP-class`, `get.Tn`, `ss.maxT`, `mt.sample.teststat`

### Examples

    #data example: ALL data set
    set.seed(99)
    data<-matrix(rnorm(90),nr=9)

    #closure
    ttest<-meanX(psi0=0,na.rm=TRUE,standardize=TRUE,alternative="two.sided",robust=FALSE)

    #test statistics
    obs<-get.Tn(X=data,stat.closure=ttest,W=NULL)

    #bootstrap null distribution (B=100 for speed)
    nulldistn<-boot.null(X=data,W=NULL,stat.closure=ttest,B=100,test="t.onesamp",theta0=0,tau0=1,alternative="two.sided",csnull=TRUE)

    #unadjusted p-values
    rawp<-apply((obs[1,]/obs[2,])<=nulldistn,1,mean)
    sum(rawp<=0.01)

[Package multtest version 1.22.0 Index]