# HLtest: Hosmer-Lemeshow test In RRate: Estimating Replication Rate for Genome-Wide Association Studies

## Description

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

## Usage

 `1` ```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 <wjiangaa@connect.ust.hk>

## 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.

`RRate` `repRateEst`, `SEest`, `repSampleSizeRR`, `repSampleSizeRR2`,
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```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\$PzalphaR2) groupNum<-10 HLresult<-HLtest(repIdx,RRresult\$RR,g=groupNum,dir='.') ```