Rate-adjusted spike–LFP coherence comparisons from spike-train statistics

Coherence is a fundamental tool in the analysis of neuronal data and for studying multiscale interactions of single and multiunit spikes with local field potentials. However, when the coherence is used to estimate rhythmic synchrony between spiking and any other time series, the magnitude of the coherence is dependent upon the spike rate. This property is not a statistical bias, but a feature of the coherence function. This dependence confounds cross-condition comparisons of spike-field and spike-spike coherence in electrophysiological experiments. Taking inspiration from correction methods that adjust the spike rate of a recording with bootstrapping ('thinning'), we propose a method of estimating a correction factor for the spike-field and spike-spike coherence that adjusts the coherence to account for this rate dependence. We demonstrate that the proposed rate adjustment is accurate under standard assumptions and derive distributional properties of the estimator. The reduced estimation variance serves to provide a more powerful test of cross-condition differences in spike-LFP coherence than the thinning method and does not require repeated Monte Carlo trials. We also demonstrate some of the negative consequences of failing to account for rate dependence. The proposed spike-field coherence estimator accurately adjusts the spike-field coherence with respect to rate and has well-defined distributional properties that endow the estimator with lower estimation variance than the existing adjustment method.