Using the exact functional test

Hua Zhong and Joe Song

2018-02-20

We illustrate the exact functional test with an example. An epigenetic indicator called CpG island methylator phenotype (CIMP) is strongly associated with liver cancers. Specimens (L. Shen et al. 2002) to study CIMP were collected and divided into three groups with different CIMP status: negative (no methylated genes), intermediate (1~2 methylated genes) and positive (>2 methylated genes).

The following table gives the frequencies of observed tumor protein p53 mutations and CIMP status:

**CpG Island Methylator Phenotype (CIMP) and p53 mutation.**
p53 mutation	CIMP Negative	CIMP Intermediate	CIMP Positive
No	12	26	18
Yes	0	8	12

require(FunChisq)

## Loading required package: FunChisq

# x is a contingency table with row variable for p53 mutation and
#   column variable for CIMP
x <- matrix(c(12,26,18,0,8,12), nrow=2, ncol=3, byrow=TRUE)
x

##      [,1] [,2] [,3]
## [1,]   12   26   18
## [2,]    0    8   12

# Test the functional dependency: p53 mutation -> CIMP
fun.chisq.test(x, method="exact")

## 
##  Exact functional test
## 
## data:  x
## statistic = 5.6436, p-value = 0.04256
## sample estimates:
## non-constant function index xi.f 
##                         0.222498

References

Shen, L., N. Ahuja, Y. Shen, N. A. Habib, M. Toyota, A. Rashid, and J.-P. J. Issa. 2002. “DNA Methylation and Environmental Exposures in Human Hepatocellular Carcinoma.” Journal of the National Cancer Institute 94 (10): 755–61.