SKAT (version 2.2.5)

SKAT_Null_Model: 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, Model.Y=FALSE)

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.

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''.

Model.Y

indicator variable whether the model will be also used for ChrY. It should be TRUE if you want to use SKAT_ChrY function

Author

Seunggeun Lee

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.

Examples

data(SKAT.example)
Z<-SKAT.example$Z
#############################################################
#	Compute the P-value of SKAT 

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

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

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