somers2 {Hmisc} | R Documentation

## Somers' Dxy Rank Correlation

### 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

    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
f.harrell@vanderbilt.edu

### See Also

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

### Examples

    set.seed(1)
    predicted <- runif(200)
    dead      <- sample(0:1, 200, TRUE)
    roc.area <- somers2(predicted, dead)["C"]

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