Skip to contents

Calculate Standardized Mean Difference for Binary Variables

Source: R/gba_utils.R
calculate_smd_binary.Rd

Calculates the standardized mean difference (SMD) between two groups for binary or categorical variables using the arcsine transformation or logit method. This is essential for assessing baseline balance of categorical covariates in clinical trials.

Usage

calculate_smd_binary(
  p1,
  n1,
  p2,
  n2,
  method = c("arcsine", "logit", "raw"),
  conf_level = 0.95
)

Arguments

p1

Numeric. Proportion in group 1 (treatment). Must be 0 to 1.

n1

Integer. Sample size of group 1. Must be >= 2.

p2

Numeric. Proportion in group 2 (control). Must be 0 to 1.

n2

Integer. Sample size of group 2. Must be >= 2.

method

Character. Method for calculating SMD. One of:

  • "arcsine" (default): Uses arcsine square root transformation

  • "logit": Uses logit transformation (log odds)

  • "raw": Raw proportion difference standardized by pooled variance

conf_level

Numeric. Confidence level for CI (default: 0.95)

Value

A named list with components:

  • smd: The standardized mean difference

  • ci_lower: Lower bound of confidence interval

  • ci_upper: Upper bound of confidence interval

  • method: Method used

  • se: Standard error of the SMD

Details

Arcsine method (recommended for proportions): $$SMD = 2 \times (\arcsin(\sqrt{p_1}) - \arcsin(\sqrt{p_2}))$$

This transformation stabilizes variance across the range of proportions and is bounded, making it suitable for proportions near 0 or 1.

Logit method (log odds ratio): Calculates the log odds ratio and standardizes: $$SMD = \frac{\log(OR)}{\pi/\sqrt{3}}$$

where \(OR = \frac{p_1/(1-p_1)}{p_2/(1-p_2)}\)

Raw method: $$SMD = \frac{p_1 - p_2}{\sqrt{p(1-p)}}$$

where \(p = \frac{n_1 p_1 + n_2 p_2}{n_1 + n_2}\)

References

Austin, P. C. (2009). Balance diagnostics for comparing the distribution of baseline covariates between treatment groups in propensity-score matched samples. Statistics in Medicine, 28(25), 3083-3107.

See also

calculate_smd() for continuous variables, calculate_smd_from_data() for calculating directly from data

Examples

# Compare sex distribution (60% female in treatment, 55% in control)
calculate_smd_binary(p1 = 0.60, n1 = 150, p2 = 0.55, n2 = 148)
#> $smd
#> [1] 0.1011905
#> 
#> $ci_lower
#> [1] -0.1258899
#> 
#> $ci_upper
#> [1] 0.3282709
#> 
#> $method
#> [1] "arcsine"
#> 
#> $se
#> [1] 0.1158595
#> 

# Using logit transformation
calculate_smd_binary(
  p1 = 0.60, n1 = 150,
  p2 = 0.55, n2 = 148,
  method = "logit"
)
#> $smd
#> [1] 0.1129091
#> 
#> $ci_lower
#> [1] -0.1406897
#> 
#> $ci_upper
#> [1] 0.3665079
#> 
#> $method
#> [1] "logit"
#> 
#> $se
#> [1] 0.1293895
#>