HLtest {RRate}

Hosmer-Lemeshow test

Description

Test whether each element of x is sampled with the probability specified by the corrsponding element in p.

Usage

HLtest(x, p, g = 10, null = "all", boot = 1000, info = T, dir = ".")

Arguments

x

A boolean vector.

p

A probability vector having the same length with x.

g

The group number used in the test.

null

a character in c('all', 'chi2','boot'). If null=='chi2', then we use (g-1) degree of freedom chi2 distribution to approximately compute p value. If null=='boot', then we use parametric bootstrap to compute p value. If null=='all', then both methods are used. This is the default option.

boot

The resampling times to compute p value. Only effective when null=='boot' or 'all'

info

Draw the null distribution of the test statistic.

dir

The directory to save the plot of the null distribution.

Details

Null Hypothesis: Each element of x is sampled with a probability which is the corresponding element of p. We group x to g groups according to p. Then we compare the success proportion with the mean value of p in each group.

Value

A list is returned:

H

The test statistic.

pval_chi2

The p value approximated by using chi2 distribution.

pval_boot

The p value computed by using parametric bootstrap.

Author(s)

Wei Jiang, Jing-Hao Xue and Weichuan Yu

Maintainer: Wei Jiang <[e-mail]>

References

Hosmer, D. W., & Lemesbow, S. (1980). Goodness of fit tests for the multiple logistic regression model. Communications in statistics-Theory and Methods, 9(10), 1043-1069.

Jiang, W., Xue, J-H, and Yu, W. What is the probability of replicating a statistically significant association in genome-wide association studies?. Submitted.

See Also

RRate repRateEst, SEest, repSampleSizeRR, repSampleSizeRR2,

Examples

alpha<-5e-6               #Significance level in the primary study
alphaR<-5e-3              #Significance level in the replication study
zalpha2<-qnorm(1-alpha/2)
zalphaR2<-qnorm(1-alphaR/2)

##Load data
data('smryStats1')        #Example of summary statistics in 1st study
n2.0<-2000                #Number of individuals in control group
n2.1<-2000                #Number of individuals in case group

SE2<-SEest(n2.0, n2.1, smryStats1$F_U, smryStats1$F_A) #SE in replication study
######  RR estimation  ######
RRresult<-repRateEst(log(smryStats1$OR),smryStats1$SE, SE2,zalpha2,zalphaR2, output=TRUE,dir='.')

#### Hosmer-Lemeshow test  ####
data('smryStats2')        #Example of summary statistics in 2nd study
sigIdx<-(smryStats1$P<alpha)
repIdx<-(sign(smryStats1$Z[sigIdx])*smryStats2$Z[sigIdx]>zalphaR2)
groupNum<-10 
HLresult<-HLtest(repIdx,RRresult$RR,g=groupNum,dir='.')