Spectral change or Jensen gap? Log-ratio baseline correction for time-frequency M/EEG is negatively biased

Time-frequency M/EEG analysis generally involves baseline correction to measure spectral changes following events of interest. The decibel or "log-ratio" baseline correction method divides spectral power in a target time window by average baseline power and log-transforms this ratio. This approach has several desirable properties and is ubiquitously available in popular software tools. However, we show that due to the concavity of the logarithm function, it follows from Jensen's inequality that log-ratio baseline correction is negatively biased, falsely indicating a decrease in spectral power when none exists.

We propose an unbiased alternative to log-ratio correction in which mean log-transformed baseline power is subtracted from log-transformed power in a target time window. This "mean-log-ratio" approach preserves the advantages of log-ratio correction without bias is easily implemented.

Using real and simulated data, we find that log-ratio baseline correction can cause true increases in spectral power to be incorrectly measured as decreases. This downward bias is evident across software implementations of this correction method.

Whereas downward bias was evident for log-ratio baseline correction, simple mean-subtraction correction (in which mean baseline power is subtracted) was not biased. Similarly, our proposed mean-log-ratio method faithfully reflected true increases in spectral power.

We recommend against log-ratio baseline correction due to its negative bias. Even when analyses primarily examine differences between conditions rather than absolute spectral change from baseline, a biased baseline correction method can influence how results are interpreted. For researchers compelled by the advantages of log-ratio correction, we recommend mean-log-ratio correction.