SKAT_Null_Model {SKAT} | R Documentation

## Get parameters and residuals from the NULL model

### Description

Compute model parameters and residuals for SKAT. You also can obtain resampled residuals that can be used to compute resampling p-value or to control family-wise error rate.

### Usage

    SKAT_Null_Model(formula, data=NULL, out_type="C", n.Resampling=0
    , type.Resampling="bootstrap", Adjustment=TRUE)

    SKAT_Null_Model_ChrX(formula, SexVar, data=NULL, out_type="C", n.Resampling=0
    , type.Resampling="bootstrap", Adjustment=TRUE)

### Arguments

`formula` | an object of class “formula”: a symbolic description of the NULL model to be fitted.
`data` | an optional data frame containing the variables in the model (default=NULL). If it is NULL, the variables are taken from 'environment(formula)'
`out_type` | an indicator of the outcome type. "C" for the continuous outcome and "D" for the dichotomous outcome.
`n.Resampling` | a numeric value of the number of resampling (default=0). If you don't want resampling, please set n.Resampling=0.
`type.Resampling` | resampling methods (default="bootstrap"). see details.
`Adjustment` | If TRUE, a small sample adjustment will be applied when the sample size < 2000 and the trait is binary (default=TRUE). See details
`SexVar` | a sex variable name in “formula”.

### Details

There are 2 different methods to get resampled residuals. "bootstrap" conducts the parametric bootstrap to resample residuals under the NULL model with considering covariates. "bootstrap.fast" (only for binary traits) is a fast implementation of "bootstrap". If there is no covariate, "bootstrap" is equivalent to the permutation method.

When the trait is binary, the SKAT can produce conservative results when the sample size is small. To address this, we developed a small sample adjustment method, which adjusts asymptotic null distribution by estimating small sample moments. See also SKAT_Null_Model_MomentAdjust.

Since small sample adjustment uses random sampling to estimate the kurtosis of the test statistics, SKAT with the (kurtosis-based) small sample adjustment can yield slightly different p-values for each run. If you want to reproduce p-values, please set a seed number using set.seed function in R.

We recently developed more advanced methods to get p-values for binary traits, and the methods are implemented in SKATBinary. We recommend to use SKATBinary function instead of SKAT when your trait is binary.

### Value

This function returns an object that has model parameters and residuals of the NULL model of no association between genetic variables and outcome phenotypes. After obtaining it, please use SKAT function to conduct the association test.

### Author(s)

Seunggeun Lee

### Examples

    data(SKAT.example)
    attach(SKAT.example)

    #############################################################
    #	Compute the P-value of SKAT

    # binary trait
    obj<-SKAT_Null_Model(y.b ~ X, out_type="D")
    SKAT(Z, obj, kernel = "linear.weighted")$p.value

    #############################################################
    # 	When you have no covariate to adjust.

    # binary trait
    obj<-SKAT_Null_Model(y.b ~ 1, out_type="D")
    SKAT(Z, obj, kernel = "linear.weighted")$p.value

    #########################################################
    # Small sample adjustment
    IDX<-c(1:100,1001:1100)

    # With-adjustment
    obj<-SKAT_Null_Model(y.b[IDX] ~ X[IDX,],out_type="D")
    SKAT(Z[IDX,], obj, kernel = "linear.weighted")$p.value

    # Without-adjustment
    obj<-SKAT_Null_Model(y.b[IDX] ~ X[IDX,],out_type="D", Adjustment=FALSE)
    SKAT(Z[IDX,], obj, kernel = "linear.weighted")$p.value

    #########################################################
    # 	Use SKATBinary

    SKATBinary(Z[IDX,], obj, kernel = "linear.weighted")$p.value

[Package SKAT version 1.3.2.1 Index]