# rate2by2.test: Comparative tests of independence in rx2 rate tables In epitools: Epidemiology Tools

## Description

Tests for independence where each row of the rx2 table is compared to the exposure reference level and test of independence two-sided p values are calculated using mid-p xxact, and normal approximation.

## Usage

 ```1 2``` ```rate2by2.test(x, y = NULL, rr = 1, rev = c("neither", "rows", "columns", "both")) ```

## Arguments

 `x` input data can be one of the following: r x 2 table where first column contains disease counts and second column contains person time at risk; or a single numeric vector for counts followed by person time at risk `y` vector of person-time at risk; if provided, x must be a vector of disease counts `rr` rate ratio reference value (default is no association) `rev` reverse order of "rows", "colums", "both", or "neither" (default)

## Details

Tests for independence where each row of the rx2 table is compared to the exposure reference level and test of independence two-sided p values are calculated using mid-p xxact, and normal approximation.

This function expects the following table struture:

 ```1 2 3 4 5 6``` ``` counts person-time exposed=0 (ref) n00 t01 exposed=1 n10 t11 exposed=2 n20 t21 exposed=3 n30 t31 ```

The reason for this is because each level of exposure is compared to the reference level.

If the table you want to provide to this function is not in the preferred form, just use the `rev` option to "reverse" the rows, columns, or both. If you are providing categorical variables (factors or character vectors), the first level of the "exposure" variable is treated as the reference. However, you can set the reference of a factor using the `relevel` function.

Likewise, each row of the rx2 table is compared to the exposure reference level and test of independence two-sided p values are calculated using mid-p exact method and normal approximation.

This function can be used to construct a p value function by testing the MUE to the null hypothesis (rr=1) and alternative hypotheses (rr not equal to 1) to calculate two-side mid-p exact p values. For more detail, see Rothman.

## Value

 `x` table that was used in analysis `p.value` p value for test of independence

## Author(s)

Tomas Aragon, [email protected], http://www.phdata.science

## References

Kenneth J. Rothman and Sander Greenland (2008), Modern Epidemiology, Lippincott Williams and Wilkins Publishers

Kenneth J. Rothman (2002), Epidemiology: An Introduction, Oxford University Press

`rateratio`,
 ``` 1 2 3 4 5 6 7 8 9 10``` ```##Examples from Rothman 1998, p. 238 bc <- c(Unexposed = 15, Exposed = 41) pyears <- c(Unexposed = 19017, Exposed = 28010) dd <- matrix(c(41,15,28010,19017),2,2) dimnames(dd) <- list(Exposure=c("Yes","No"), Outcome=c("BC","PYears")) ##midp rate2by2.test(bc,pyears) rate2by2.test(dd, rev = "r") rate2by2.test(matrix(c(15, 41, 19017, 28010),2,2)) rate2by2.test(c(15, 41, 19017, 28010)) ```