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Standardized differences between two groups

Source: R/ps-stddiff.R
ps_stddiff.Rd

Computes the standardized difference, group 1 minus group 0, for each named variable, choosing the formula by the variable's type. A port of the CCF %stddiff SAS macro (Artis 2019, from Yang 2012), and intended to reproduce its est.stddiff output.

Usage

ps_stddiff(
  data,
  treatment_col = "tavr",
  gaussian = NULL,
  nong_ord = NULL,
  binary = NULL,
  categorical = NULL,
  weight_col = NULL,
  treated_level = NULL
)

Arguments

data

A data frame.

treatment_col

Name of the group column, coded 0/1 or logical, with both groups present. Default "tavr".

gaussian, nong_ord, binary, categorical

Character vectors of column names, by type. See Details. At least one variable is required, and a variable may appear under one type only. A binary column must be coded 0/1 or logical; a categorical column may have any coding.

weight_col

Optional name of a column of positive weights, for example the inverse-probability weights from ps_weight() or the matching weight mt_wt from ps_logistic(). Weights must be finite.

treated_level

The value of treatment_col that is treated. NULL (default) requires a 0/1 or logical column and takes 1 or TRUE. Give a value, for example "transcatheter", to use a column holding any two values.

Value

An object of class c("ps_stddiff", "ps_data") with:

$data

The input data frame, unchanged.

$meta

Named list: treatment_col, weight_col, variables (a list by type), method, n_total, n_dropped.

$tables

Named list with stddiff, a data frame with one row per variable in the order given: variable, label (the column's "label" attribute, or NA), type ("gaussian", "nong_ord", "binary", "categorical" or "onelevel") and stddiff, which is NA when the pooled variance is zero.

Details

Variable types. The type decides the formula, so it is given, not inferred: an ordinal NYHA class stored as an integer would otherwise be treated as Gaussian.

  • gaussian: difference in means over sqrt((var1 + var0) / 2). The denominator averages the two variances; it does not pool them by sample size, so it differs from a Cohen's d when the groups are unequal.

  • nong_ord: the same formula on ranks of the pooled sample, ties averaged, as PROC RANK does by default. Ranks are unweighted; only their means and variances use weight_col.

  • binary and categorical are routed by the number of levels observed, as the macro routes its BINARY= and CATG= lists: one level gives 0, two use the binary formula on the proportion at the last level in sort order (1 for a 0/1 variable, the last level for a factor), and more than two use the Mahalanobis form of Yang and Dalton (2012). For that form the last level in sort order is the one dropped, and S has diagonal (t_i (1 - t_i) + c_i (1 - c_i)) / 2 and off-diagonal -(t_i t_j + c_i c_j) / 2. A categorical difference is never negative. When S is singular, as when the two groups share no levels, the difference is NA with a warning naming the variable.

Weights. Within each group, the weights are first divided by their mean in that group, so that they average 1 there. Means are then sum(w x) / sum(w) and variances sum(w (x - m)^2) / (n - 1), which is what PROC MEANS reports with a WEIGHT statement and VARDEF=DF. The result is therefore the same when every weight in a group is multiplied by one constant, so stabilised and unstabilised weights from ps_weight() give the same differences. It equals the %stddiff macro's output when the weights already average 1 in each group, and otherwise does not: the macro's Gaussian and rank differences change with the scale of the weights. Proportions, for binary and categorical, are sum(w x) / sum(w) within a group and never depended on that scale. Weights must be positive.

Missing values. Rows with a missing group are dropped. Otherwise a missing value is dropped for that variable only, and a variable with no non-missing values gets NA.

Units. The result is a proportion of a standard deviation, not a percent. The SAS output labels the column "(%)" but does not multiply by 100.

References

Yang D, Dalton JE. A unified approach to measuring the effect size between two groups using SAS. SAS Global Forum 2012, paper 335-2012.

See also

ps_match(), ps_weight()

Examples

dta <- sample_ps_data(n = 200, seed = 42)
obj <- ps_stddiff(dta, treatment_col = "tavr",
                  gaussian = c("age", "ef"), binary = c("female", "diabetes"))
obj$tables$stddiff
#>   variable label     type     stddiff
#> 1      age  <NA> gaussian -0.79935800
#> 2       ef  <NA> gaussian  0.61385077
#> 3   female  <NA>   binary  0.39993164
#> 4 diabetes  <NA>   binary -0.05555041