# somers2: Somers' Dxy Rank Correlation In Hmisc: Harrell Miscellaneous

## Description

Computes Somers' Dxy rank correlation between a variable `x` and a binary (0-1) variable `y`, and the corresponding receiver operating characteristic curve area `c`. Note that `Dxy = 2(c-0.5)`. `somers` allows for a `weights` variable, which specifies frequencies to associate with each observation.

## Usage

 `1` ```somers2(x, y, weights=NULL, normwt=FALSE, na.rm=TRUE) ```

## Arguments

 `x` typically a predictor variable. `NA`s are allowed. `y` a numeric outcome variable coded `0-1`. `NA`s are allowed. `weights` a numeric vector of observation weights (usually frequencies). Omit or specify a zero-length vector to do an unweighted analysis. `normwt` set to `TRUE` to make `weights` sum to the actual number of non-missing observations. `na.rm` set to `FALSE` to suppress checking for NAs.

## Details

The `rcorr.cens` function, which although slower than `somers2` for large sample sizes, can also be used to obtain Dxy for non-censored binary `y`, and it has the advantage of computing the standard deviation of the correlation index.

## Value

a vector with the named elements `C`, `Dxy`, `n` (number of non-missing pairs), and `Missing`. Uses the formula `C = (mean(rank(x)[y == 1]) - (n1 + 1)/2)/(n - n1)`, where `n1` is the frequency of `y=1`.

## Author(s)

Frank Harrell
Department of Biostatistics
Vanderbilt University School of Medicine
fh@fharrell.com

`rcorr.cens`, `rank`, `wtd.rank`,

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```set.seed(1) predicted <- runif(200) dead <- sample(0:1, 200, TRUE) roc.area <- somers2(predicted, dead)["C"] # Check weights x <- 1:6 y <- c(0,0,1,0,1,1) f <- c(3,2,2,3,2,1) somers2(x, y) somers2(rep(x, f), rep(y, f)) somers2(x, y, f) ```

### Example output

```Loading required package: lattice

Attaching package: 'Hmisc'

The following objects are masked from 'package:base':

format.pval, units

C       Dxy         n   Missing
0.8888889 0.7777778 6.0000000 0.0000000
C     Dxy       n Missing
0.85    0.70   13.00    0.00
C     Dxy       n Missing
0.85    0.70   13.00    0.00
```

Hmisc documentation built on Oct. 7, 2021, 9:16 a.m.