Extending effective multiplicity for independent designs in multichannel fNIRS studies

Recent advancements in multichannel functional near-infrared spectroscopy have led to an expansion in the number of measurement channels. This increase in multiplicity necessitates appropriate multiple-comparison correction. The effective multiplicity ( $M_{\mathrm{eff}}$ ) method has been introduced to control family-wise error rate while accounting for correlation between channels. However, the application of this method has been limited to a one-sample design, and its performance has only been compared with Bonferroni correction.

We aimed to evaluate the applicability of the $M_{\mathrm{eff}}$ method to independent designs in channel-wise analysis and to compare its performance with other conventional multiple-comparison correction methods.

Using simulated datasets, we conducted resampling simulations to examine the relationship between the number of channels and $M_{\mathrm{eff}}$ values and between the number of channels and the number of significant channels for each correction method. In addition, we performed exploratory analyses using actual experimental datasets with 44-channel measurements from $\sim 60$ participants, which had been analyzed within regions of interest in previous studies.

In resampling simulations, as the number of channels increased, $M_{\mathrm{eff}}$ values converged at around 25 for the 44-channel datasets, and the number of significant channels remained relatively constant regardless of the number of total channels, in contrast to other correction methods. In the exploratory analyses on actual experimental datasets, channels identified as significant were similar to the regions of interest defined in the previous studies.

We demonstrated that, in channel-wise analysis, when the total number of participants exceeds the number of channels, the $M_{\mathrm{eff}}$ approach is effective for balancing type I and II errors in independent designs and that it is applicable to both exploratory and confirmatory analyses.