Probability waves: Adaptive cluster-based correction by convolution of p-value series from mass univariate analysis

Abstract

Background: Methods for p-value correction are criticized for either increasing Type II error or improperly reducing Type I error in large exploratory data analysis. This text considers patterns in probability vectors resulting from mass univariate analysis to correct p-values, where clusters of significant p-values may indicate true H0 rejection.

New method: We used ERP experimental data from control and ADHD boys to test the method. The Log10 of p-vector was convolved with a Gaussian window whose length was set as the shortest lag above which autocorrelation of each ERP wave may be assumed to have vanished. We realized Monte-Carlo simulations (MC) to (1) evaluate confidence intervals of rejected and non-rejected areas of our data, (2) to evaluate differences between corrected and uncorrected p-vectors or simulated ones in terms of distribution of significant p-values, and (3) to empirically verify the type-I error rate (comparing 10,000 pairs of mixed samples whit control and ADHD subjects).

Results: The differences between simulation or raw p-vector and corrected p-vectors were, respectively, minimal and maximal for window length set by autocorrelation in p-vector convolution.

Comparison with existing methods: Our method was less conservative while FDR methods rejected basically all significant p-values.The MC simulations presented 2.78 ± 4.83% of difference (20 channels) from corrected p-vector, while difference from raw p-vector was 596 ± 5.00% (p = 0.0003).

Conclusion: As a cluster-based correction, the present new method seems to be biological and statistically suitable to correct p-values in mass univariate analysis of ERP waves, which adopts adaptive parameters to correction.

Keywords: Cluster-based statistics; Convolution; False discovery rate; Mass univariate analysis; Multiple comparisons; Type-II error.