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Calculate Standardized Mean Difference for Continuous Variables

Source: R/gba_utils.R
calculate_smd.Rd

Calculates the standardized mean difference (SMD) between two groups for continuous variables using either Cohen's d or Hedges' g. SMD is a key metric for assessing baseline balance in randomized controlled trials, particularly important for GBA/AMNOG dossier submissions.

Usage

calculate_smd(
  mean1,
  sd1,
  n1,
  mean2,
  sd2,
  n2,
  method = c("cohens_d", "hedges_g"),
  conf_level = 0.95
)

Arguments

mean1

Numeric. Mean of group 1 (treatment group).

sd1

Numeric. Standard deviation of group 1. Must be positive.

n1

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

mean2

Numeric. Mean of group 2 (control/reference group).

sd2

Numeric. Standard deviation of group 2. Must be positive.

n2

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

method

Character. Method for calculating SMD. One of:

  • "cohens_d" (default): Uses pooled standard deviation

  • "hedges_g": Applies small-sample bias correction to Cohen's d

conf_level

Numeric. Confidence level for CI calculation (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 ("cohens_d" or "hedges_g")

  • se: Standard error of the SMD

Details

Cohen's d is calculated as: $$d = \frac{\bar{x}_1 - \bar{x}_2}{s_{pooled}}$$

where \(s_{pooled} = \sqrt{\frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2}}\)

Hedges' g applies a correction factor for small samples: $$g = d \times \left(1 - \frac{3}{4(n_1+n_2)-9}\right)$$

The 95% confidence interval is calculated using the large-sample variance: $$Var(d) = \frac{n_1+n_2}{n_1 n_2} + \frac{d^2}{2(n_1+n_2)}$$

References

Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum Associates.

Hedges, L. V., & Olkin, I. (1985). Statistical Methods for Meta-Analysis. Academic Press.

See also

calculate_smd_binary() for binary variables, calculate_smd_from_data() for calculating directly from data

Examples

# Cohen's d for age between treatment groups
calculate_smd(
  mean1 = 55.2, sd1 = 12.3, n1 = 150,
  mean2 = 53.8, sd2 = 11.9, n2 = 148
)
#> $smd
#> [1] 0.1156738
#> 
#> $ci_lower
#> [1] -0.1115965
#> 
#> $ci_upper
#> [1] 0.342944
#> 
#> $method
#> [1] "cohens_d"
#> 
#> $se
#> [1] 0.1159563
#> 

# Hedges' g with small sample correction
calculate_smd(
  mean1 = 55.2, sd1 = 12.3, n1 = 25,
  mean2 = 53.8, sd2 = 11.9, n2 = 23,
  method = "hedges_g"
)
#> $smd
#> [1] 0.1137085
#> 
#> $ci_lower
#> [1] -0.4530328
#> 
#> $ci_upper
#> [1] 0.6804498
#> 
#> $method
#> [1] "hedges_g"
#> 
#> $se
#> [1] 0.289159
#>