Calculate the log ratio of means (ROM) using means and standard deviations

Computes the natural log-transformed ratio of means (log ROM, also called the log response ratio) and its standard error using the delta method. This is an internal helper called row-wise by calculateEffectSizes and is not intended to be used directly.

Usage

rom.m.sd(x, ...)

Arguments

x

A data.frame in which each row represents one trial arm comparison. Must contain the columns listed under ....

...

The following columns are required and consumed from x:

mean_arm1: Mean of the outcome in arm 1 (treatment).
mean_arm2: Mean of the outcome in arm 2 (control/comparator).
sd_arm1: Standard deviation of the outcome in arm 1.
sd_arm2: Standard deviation of the outcome in arm 2.
n_arm1: Sample size of arm 1. Must be > 0.
n_arm2: Sample size of arm 2. Must be > 0.

Additional columns in x are silently ignored.

Value

A data.frame with the same number of rows as x and two numeric columns:

es: Log ratio of means, $\ln(\bar{x}_1 / \bar{x}_2)$.
se: Standard error of es, derived via the delta method.

Rows are set to NA for both columns when any required input is NA, when either mean equals zero (log ROM is undefined), when either sample size is non-positive, or when the computed variance is non-finite or not strictly positive.

Details

The log ROM effect size is defined as: $$\ln(\text{ROM}) = \ln\!\left(\frac{\bar{x}_1}{\bar{x}_2}\right)$$

Its sampling variance is approximated via the delta method (Hedges et al., 1999): $$v = \frac{s_1^2}{n_1 \bar{x}_1^2} + \frac{s_2^2}{n_2 \bar{x}_2^2}$$

The standard error returned in se is $\sqrt{v}$.

A positive log ROM indicates that arm 1 has a higher mean than arm 2. The measure is undefined when either group mean equals zero, which is why such rows are returned as NA.

References

Hedges, L. V., Gurevitch, J., & Curtis, P. S. (1999). The meta-analysis of response ratios in experimental ecology. Ecology, 80(4), 1150–1156. doi:10.1890/0012-9658(1999)080[1150:TMAORR]2.0.CO;2