Compute a Geometric Mean

The geometric mean is typically defined for strictly positive values. This function computes the geometric mean of a numeric vector, with the option to replace certain values (e.g., zeros, non-positive values, or values below a user-specified threshold) before computation.

Usage

geometric_mean(
  x,
  na.rm = FALSE,
  replace_value = NULL,
  replace = c("all", "non-positive", "zero")
)

Arguments

x

A numeric or complex vector of values.

na.rm

Logical. If FALSE (default), the presence of zero or negative values triggers a warning and returns NA. If TRUE, such values (and any NA) are removed before computing the geometric mean.

replace_value

Numeric or NULL. The value used for replacement, depending on replace (e.g., a detection limit (LOD) or quantification limit (LOQ)). If NULL, no replacement is performed. For recommendations how to use, see details.

replace

Character string indicating which values to replace:

"all"

Replaces all values less than replace_value with replace_value. This is useful if you have a global threshold (such as a limit of detection) below which any measurement is replaced.

"non-positive"

Replaces all non-positive values (x <= 0) with replace_value. This is helpful if zeros or negative values are known to be invalid or below a certain limit.

"zero"

Replaces only exact zeros (x == 0) with replace_value. Useful if negative values should be treated as missing.

Value

A single numeric value representing the geometric mean of the processed vector x, or NA if the resulting vector is empty (e.g., if na.rm = TRUE removes all positive values) or if non-positive values exist when na.rm = FALSE.

Details

Replacement Considerations: The geometric mean is only defined for strictly positive numbers (\(x > 0\)). Despite this, the geometric mean can be useful for laboratory measurements which can contain 0 or negative values. If these values are treated as NA and are removed, this results in an upward bias due to missingness. To reduce this, values below the limit of detection (LOD) or limit of quantification (LOQ) are often replaced with the chosen limit, making this limit the practical lower limit of the measurement scale. This is therefore an often recommended approach.

There are also alternatives approaches, where values are replaced by either \(\frac{LOD}{2}\) or \(\frac{LOD}{\sqrt{2}}\) (or LOQ). These approaches create a gap in the distribution of values (e.g. no values for \(\frac{LOD}{2} < x < LOD\)) and should therefore be used with caution.

If the replacement approach for values below LOD or LOQ has a material effect on the interpretation of the results, the values should be treated as statistically censored. In this case, proper statistical methods to handle (left) censored data should be used.

When replace_value is provided, the function will first perform the specified replacements, then proceed with the geometric mean calculation. If no replacements are requested but zero or negative values remain and na.rm = FALSE, an NA will be returned with a warning.

Examples

# Basic usage with no replacements:
x <- c(1, 2, 3, 4, 5)
geometric_mean(x)
#> [1] 2.605171

# Replace all values < 0.5 with 0.5 (common in LOD scenarios):
x3 <- c(0.1, 0.2, 0.4, 1, 5)
geometric_mean(x3, replace_value = 0.5, replace = "all")
#> Warning: 3 values were substituted with 0.5.
#> [1] 0.9102821

# Remove zero or negative values, since log(0) = -Inf and log(-1) = NaN
x4 <- c(-1, 0, 1, 2, 3)
geometric_mean(x4, na.rm = TRUE)
#> [1] 1.817121