A simple method to improve regression and correlation coefficient estimates with noisy neural data

Linear regression and Pearson correlations are bedrock statistical analyses in neuroscience: correlations between neurons are a signature of collective information coding and computation, and linear regression quantifies the linear or nonlinear (e.g., polynomial) relationships among, e.g., neurons or brain regions. However, noise can bias the regression and correlation coefficient estimates towards zero, an effect known as regression dilution. While averaging over trials, time, or neurons--a widespread practice to mitigate noise in neuroscience--reduces the effects of noise, it does not generally eliminate such effects.

Here, we present a simple bootstrap-based method to correct for the effects of independent noise on regression and correlation coefficients when the quantities of interest are averages (or other metrics) of the data, regardless of the modality (including electrophysiology, fMRI, calcium imaging, behavioural). We demonstrate the efficacy of the method on simulated data: applied to noisy data, including model neural responses to oriented gratings, our method results in nearly unbiased estimates of the ground truth. In contrast, estimates obtained directly from the averaged data are biased towards zero.

Finally, we apply our method to publicly available experimental data. By re-analyzing open-source data that estimate the intersubject correlations (ISCs) of brain regions across multiple subjects, we find that the correlations can be considerably (~1.5-2x) larger than originally reported. Similarly, we find that some regression coefficient estimates reported in a recent calcium-imaging experiment are substantially biased towards zero. This regression dilution obscured whether the neural responses changed across days, as a lack of change--responses on day 2 being the same as on day 1--corresponds to a regression coefficient of 1. Our method avoids such bias, allowing us to find that the neural responses systematically change across days for one stimulus type, but not for another, consistent with other results reported in the experiment.