# smd: Compute Standardized Mean Difference In smd: Compute Standardized Mean Differences

 smd R Documentation

## Compute Standardized Mean Difference

### Description

Computes the standardized mean differnce (SMD) between two groups.

 d = \sqrt{D' S^{-1} D} 

where D is a vector of differences between group 1 and 2 and S is the covariance matrix of these differences. If D is length 1, the result is multplied by sign(D).

In the case of a numeric or integer variable, this is equivalent to:

 d = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{(s^2_1 + s^2_2)/2}} 

where \bar{x}_g is the sample mean for group g and s^2_g is the sample variance.

For a logical or factor with only two levels, the equation above is \bar{x}_g = \hat{p}_g, i.e. the sample proportion and s^2_g = \hat{p}_g(1 - \hat{p}_g).

When using the SMD to evaluate the effectiveness of weighting in achieving covariate balance, it is important to isolate the change in SMD before and after weighting to the change in mean difference, so the denominator (covariance matrix) must be held constant (Stuart 2008, \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.1002/sim.3207")}). By default, the unweighted covariance matrix is used to compute SMD in both the unweighted and weighted case. If the weights are not being used to adjust for covariate imbalance (e.g. case weights), the unwgt.var argument can be set to FALSE to use the weighted covariance matrix as the denominator.

### Usage

smd(x, g, w, std.error = FALSE, na.rm = FALSE, gref = 1L, unwgt.var = TRUE)

## S4 method for signature 'character,ANY,missing'
smd(x, g, w, std.error = FALSE, na.rm = FALSE, gref = 1L, unwgt.var = TRUE)

## S4 method for signature 'character,ANY,numeric'
smd(x, g, w, std.error = FALSE, na.rm = FALSE, gref = 1L, unwgt.var = TRUE)

## S4 method for signature 'logical,ANY,missing'
smd(x, g, w, std.error = FALSE, na.rm = FALSE, gref = 1L, unwgt.var = TRUE)

## S4 method for signature 'logical,ANY,numeric'
smd(x, g, w, std.error = FALSE, na.rm = FALSE, gref = 1L, unwgt.var = TRUE)

## S4 method for signature 'matrix,ANY,missing'
smd(x, g, w, std.error = FALSE, na.rm = FALSE, gref = 1L, unwgt.var = TRUE)

## S4 method for signature 'matrix,ANY,numeric'
smd(x, g, w, std.error = FALSE, na.rm = FALSE, gref = 1L, unwgt.var = TRUE)

## S4 method for signature 'list,ANY,missing'
smd(x, g, w, std.error = FALSE, na.rm = FALSE, gref = 1L, unwgt.var = TRUE)

## S4 method for signature 'list,ANY,numeric'
smd(x, g, w, std.error = FALSE, na.rm = FALSE, gref = 1L, unwgt.var = TRUE)

## S4 method for signature 'data.frame,ANY,missing'
smd(x, g, w, std.error = FALSE, na.rm = FALSE, gref = 1L, unwgt.var = TRUE)

## S4 method for signature 'data.frame,ANY,numeric'
smd(x, g, w, std.error = FALSE, na.rm = FALSE, gref = 1L, unwgt.var = TRUE)


### Arguments

 x a vector or matrix of values g a vector of at least 2 groups to compare. This should coercable to a factor. w a vector of numeric weights (optional) std.error Logical indicator for computing standard errors using compute_smd_var. Defaults to FALSE. na.rm Remove NA values from x? Defaults to FALSE. gref an integer indicating which level of g to use as the reference group. Defaults to 1. unwgt.var Use unweighted or weighted covariance matrix. Defaults to TRUE

### Value

a data.frame containing standardized mean differences between levels of g for values of x. The data.frame contains the columns:

• term: the level being comparing to the reference level

• estimate: SMD estimates

• std.error: (if std.error = TRUE) SMD standard error estimates

### Examples

x <- rnorm(100)
g <- rep(1:2, each = 50)
smd(x, g)


smd documentation built on May 29, 2024, 3:10 a.m.