epitools (version 0.5-9)

oddsratio: Odds ratio estimation and confidence intervals

Description

Calculates odds ratio by median-unbiased estimation (mid-p), conditional maximum likelihood estimation (Fisher), unconditional maximum likelihood estimation (Wald), and small sample adjustment (small). Confidence intervals are calculated using exact methods (mid-p and Fisher), normal approximation (Wald), and normal approximation with small sample adjustment (small).

Usage

oddsratio(x, y = NULL,
          method = c("midp", "fisher", "wald", "small"),
          conf.level = 0.95,
          rev = c("neither", "rows", "columns", "both"),
          correction = FALSE,
          verbose = FALSE)
oddsratio.midp(x, y = NULL,
               conf.level = 0.95,
               rev = c("neither", "rows", "columns", "both"),
               correction = FALSE,
               verbose = FALSE,
               interval =  c(0, 1000))
oddsratio.fisher(x, y = NULL,
                 conf.level = 0.95,
                 rev = c("neither", "rows", "columns", "both"),
                 correction = FALSE,
                 verbose = FALSE)
oddsratio.wald(x, y = NULL,
               conf.level = 0.95,
               rev = c("neither", "rows", "columns", "both"),
               correction = FALSE,
               verbose = FALSE)
oddsratio.small(x, y = NULL,
                conf.level = 0.95,
                rev = c("neither", "rows", "columns", "both"),
                correction = FALSE,
                verbose = FALSE)

Arguments

x

input data can be one of the following: r x 2 table, vector of numbers from a contigency table (will be transformed into r x 2 table in row-wise order), or single factor or character vector that will be combined with y into a table.

y

single factor or character vector that will be combined with x into a table (default is NULL)

method

method for calculating odds ratio and confidence interval

conf.level

confidence level (default is 0.95)

rev

reverse order of "rows", "colums", "both", or "neither" (default)

correction

set to TRUE for Yate's continuity correction (default is FALSE)

verbose

set to TRUE to return more detailed results (default is FALSE)

interval

interval for the uniroot that finds the odds ratio median-unbiased estimate and mid-p exact confidence interval for oddsratio.midp

...

passes optional arguments to tab2by2.test for calculatng tests of independence (p values): adding correction = TRUE implements Yate's continuity correction (default is FALSE), and adding replicates = n where n is an integer specifying the number of iterations (default is 2000) of the Monte Carlo simulation method of calculating p values.

Value

x

table that was used in analysis (verbose = TRUE)

data

same table as x but with marginal totals

p.exposed

proportions exposed (verbose = TRUE)

p.outcome

proportions experienced outcome (verbose = TRUE)

measure

risk ratio and confidence interval

conf.level

confidence level used (verbose = TRUE)

p.value

p value for test of independence

replicates

number of replicates used in Monte Carlo simulation p value (verbose = TRUE)

correction

logical specifying if continuity correction was used

Details

Calculates odds ratio by median-unbiased estimation (mid-p), conditional maximum likelihood estimation (Fisher), unconditional maximum likelihood estimation (Wald), and small sample adjustment (small). Confidence intervals are calculated using exact methods (mid-p and Fisher), normal approximation (Wald), and normal approximation with small sample adjustment (small). This function expects the following table struture:

                    disease=0   disease=1
    exposed=0 (ref)    n00         n01
    exposed=1          n10         n11	
    exposed=2          n20         n21
    exposed=3          n30         n31
  

The reason for this is because each level of exposure is compared to the reference level. If you are providing a 2x2 table the following table is preferred:

                    disease=0   disease=1
    exposed=0 (ref)    n00         n01
    exposed=1          n10         n11	
  

however, for odds ratios from 2x2 tables, the following table is equivalent:

                    disease=1   disease=0
    exposed=1          n11         n10
    exposed=0          n01         n00	
  

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, Fisher's Exact, Monte Carlo simulation, and the chi-square test.

References

Kenneth J. Rothman and Sander Greenland (1998), Modern Epidemiology, Lippincott-Raven Publishers Kenneth J. Rothman (2002), Epidemiology: An Introduction, Oxford University Press Nicolas P. Jewell (2004), Statistics for Epidemiology, 1st Edition, 2004, Chapman & Hall, pp. 73-81

See Also

tab2by2.test, riskratio, rateratio, ormidp.test, epitab

Examples

##Case-control study assessing whether exposure to tap water
##is associated with cryptosporidiosis among AIDS patients

tapw <- c("Lowest", "Intermediate", "Highest")
outc <- c("Case", "Control")	
dat <- matrix(c(2, 29, 35, 64, 12, 6),3,2,byrow=TRUE)
dimnames(dat) <- list("Tap water exposure" = tapw, "Outcome" = outc)
oddsratio(dat, rev="c")
oddsratio.midp(dat, rev="c")
oddsratio.fisher(dat, rev="c")
oddsratio.wald(dat, rev="c")
oddsratio.small(dat, rev="c")