Controlling test specificity for auditory evoked response detection using a frequency domain bootstrap

Statistical detection methods are routinely used to automate auditory evoked response (AER) detection and assist clinicians with AER measurements. However, many of these methods are built around statistical assumptions that can be violated for AER data, potentially resulting in reduced or unpredictable test performances. This study explores a frequency domain bootstrap (FDB) and some FDB modifications to preserve test performance in serially correlated non-stationary data.

The FDB aims to generate many surrogate recordings, all with similar serial correlation as the original recording being analysed. Analysing the surrogates with the detection method then gives a distribution of values that can be used for inference. A potential limitation of the conventional FDB is the assumption of stationary data with a smooth power spectral density (PSD) function, which is addressed through two modifications.

The FDB was compared to a conventional parametric approach and two modified FDB approaches that aim to account for heteroskedasticity and non-smooth PSD functions. Hotelling's T²(HT2) test applied to auditory brainstem responses was the test case.

When using conventional HT2, false-positive rates deviated significantly from the nominal alpha-levels due to serial correlation. The false-positive rates of the modified FDB were consistently closer to the nominal alpha-levels, especially when data was strongly heteroskedastic or the underlying PSD function was not smooth due to e.g. power lines noise.

The FDB and its modifications provide accurate, recording-dependent approximations of null distributions, and an improved control of false-positive rates relative to parametric inference for auditory brainstem response detection.