Calculate the log ratio of means (ROM) using within-group change data

Computes the natural log-transformed ratio of means (log ROM) and its standard error using the delta method, based on pre-post change scores rather than post-treatment means. This is an internal helper called row-wise by calculateEffectSizes and is not intended to be used directly.

Usage

rom.change.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_change_arm1: Mean change from baseline in arm 1 (treatment).
mean_change_arm2: Mean change from baseline in arm 2 (control/comparator).
sd_change_arm1: Standard deviation of the change score in arm 1.
sd_change_arm2: Standard deviation of the change score 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 change-score means, $\ln(\bar{x}_{\Delta,1} / \bar{x}_{\Delta,2})$.
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 change-score 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 estimator is identical in form to that used in rom.m.sd, but the inputs are mean change scores and their standard deviations: $$\ln(\text{ROM}) = \ln\!\left(\frac{\bar{x}_{\Delta,1}}{\bar{x}_{\Delta,2}}\right)$$

Its sampling variance is approximated via the delta method (Hedges et al., 1999): $$v = \frac{s_{\Delta,1}^2}{n_1 \,\bar{x}_{\Delta,1}^2} + \frac{s_{\Delta,2}^2}{n_2\, \bar{x}_{\Delta,2}^2}$$

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

A positive log ROM indicates a larger mean change in arm 1 than in arm 2. The measure is undefined when either change-score mean equals zero, so such rows are returned as NA. Note that a zero mean change score is substantively meaningful (no average change from baseline) and relatively common, so this limitation should be considered when choosing between effect size metrics.

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

Lajeunesse, M. J. (2011). On the meta-analysis of response ratios for studies with correlated and multi-group designs. Ecology, 92(11), 2049–2055. doi:10.1890/11-0423.1