Nonparametric Method for Estimation of Controlled Correlations in Studies of VEGF-Hypoxia Relationship

Abstract

It is known that vascular endothelial growth factor (VEGF) expression is a response to hypoxia. On the other hand hypoxia may be detected by oximetry parameters including venous CO-oximetry indices or corresponding partial pressures of O2 and CO2. However significant correlation ties between VEGF levels and oximetry parameters were not found in groups of patients with ischemic stroke and transient ischemic attack. At that some effect related to the relationship between VEGF and sO2 was observed at corresponding scatter plots. Correlation between VEGF and proteins S100 levels in serum existed only in group with severe hypoxia where sO2 is less threshold close to 39-40%. So the relationship between VEGF level and saturation index sO2 exists in conjunction with additional factor that is S100 level in serum. To assess statistical significance of observed regularity it is necessary to test three null hypotheses about independence of one of involved factors on two another. The relationship may be manifestation of hypoxia effect on VEGF. To assess significance of hypoxia effect as a whole all three null hypotheses were tested with the help of developed technique based on random permutations and involving nonparametric combinations of criteria related to single oximetry parameters. The statistical significance assessments also involved multiplicity adjustment aimed to take into account multiple search of additional factors among variety of biological indices from analyzed data set. As a result of developed technique application all three considered null hypotheses were rejected at adjusted level p < 0.02 when effect of hypoxia on correlation between VEGF and complement component C4 was evaluated.

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

“…This approach to assessing statistical significance is consistent with the concept of fully significant regularities discussed earlier in the works [1,2,3]. Ignoring the requirement to achieve full significance can lead to an erroneous conclusion about the existence of combined effects on data configurations arising from of simpler effects [1].…”

“…Standard statistical tools are found to be insufficient to assess full statistical significance. In the works [2,3], an approach is used in which the estimation of the statistical significance of the combined effect considered above should be reduced to the refutation of three null hypotheses:…”

“…This approach requires no additional assumptions. It was also used in the works [2,3] in the method of valid conditionally linear regularities(VCLR). At that, the maximum of the functional depending on the values of the correlation coefficients in the subgroups corresponding to the values of the third factor to the sides of the threshold and the sizes of these subgroups was used as the statistics of the test.…”

“…The disadvantage of this method is the impossibility of using it if the maximum of the functional corresponds to a threshold value that cuts off a small group. Research carried out in the work [2] showed that the maximum size of a cut-off group is 25 objects. This drawback did not allow adequately assessing the significance of the effect considered in present work, associated with the existence of a significant negative correlation between the serum levels of Factor VIII (FVIII) and levels of antibodies to NR2 subunits of the N-methyl-D-aspartate (NMDA) receptor, referred hereinafter to as ABNR2, in the group of patients with ischemic stroke (IS) and transient ischemic attack (TIA) after removal of 8 cases with an abnormally high vascular endothelial growth factor (VEGF).…”

“…Previously [2] introduced VCLR approach was used to prove the effect of hypoxia on the interrelations between VEGF and s100, between VEGF and the complement component c4. However VCLR approach did not allow the researches to assess the effect significance properly.…”