Nonlinearity testing in the case of non Gaussian surrogates, applied to improving analysis of synchronicity in uterine contraction

Surrogates are commonly used to test a particular hypothesis on time series. The parameter commonly used in the literature to test these hypotheses is the z score. The z score assumes that the distribution of the statistics obtained on the surrogates is Gaussian. In this paper, we propose the use of a more general parameter than the z score that will also work in the case of non-Gaussian distribution of the statistics. We also derive a statistical test, based on the fitting of the distribution of the surrogate measure profile, in order to test the initial hypothesis. We validate the proposed approach on both synthetic signals and real uterine EMG signals by using the nonlinear correlation coefficient as initial statistic. We further show that this corrected nonlinear correlation coefficient can discriminate between pregnancy contractions and labor in a monkey, but the uncorrected nonlinear correlation coefficient cannot. This makes the corrected nonlinear correlation coefficient a promising candidate in a future application for preterm labor prediction in humans.