Determining Subgroups of Significant Correlation in Analyzing Relation between NR2 Antibodies and Factor VIII in Acute Neurological Diseases

The paper considers a new method for finding correlations distorted by the influence of a third factor. In other words, the method is designed to search for effects consisted in the existence a significant correlation between two variables in a group of observations received from the main sample by removal of the observations with extremal values of a third factor. Testing for such effects should include both an assessment of the statistical significance of the correlation in the subgroup and the significance of the influence of the third factor. Potentially, this can be done using the previously developed method of valid conditional linear regularities (VCLR). The statistics used in the VCLR method is the maximum of the functional, which depends on the correlation coefficients in the subgroups identified using the threshold for the third factor and the sizes of these subgroups. The disadvantage of this method is that it cannot be used if the maximum of the functional corresponds to a threshold value that cuts off a small group. This drawback did not allow to adequately assess the significance of the effect associated with the existence of a significant negative correlation between the serum levels of antibodies to factor VIII and NR2 in the group of patients with ischemic stroke and transient ischemic attack after excluding patients with abnormally high levels of vascular endothelial growth factor. An alternative method was proposed, which is based on a permutation test. At that the statistics of the test is a minimum p-value from those characterizing the correlation coefficients calculated using the normal approximation of the Fisher's z-transform corresponding to all possible threshold values for the third factor. The use of the new criterion made it possible to adequately assess the significance of the observed effect.