Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling; however, statistical dependence is not sufficient to demonstrate the presence of such a causal relationship (i.e., correlation does not imply causation).
Formally, dependence refers to any situation in which random variables do not satisfy a mathematical condition of probabilistic independence. In loose usage, correlation can refer to any departure of two or more random variables from independence, but technically it refers to any of several more specialized types of relationship between mean values. There are several correlation coefficients, often denoted ρ or r, measuring the degree of correlation. The most common of these is the Pearson correlation coefficient, which is sensitive only to a linear relationship between two variables (which may exist even if one is a nonlinear function of the other).
OBJECTIVE: In relapsing-remitting MS (RRMS) patients treated with natalizumab, the low level of L-selectin-expressing CD4+ T cells has been associated with the risk of progressive multifocal leukoencephalopathy (PML). In this study, our aim was to correlate the levels of soluble L-selectin and the anti-JCV antibody index in the sera of RRMS patients treated with natalizumab.
METHODS: This study included 99 subjects, including 44 RRMS patients treated with natalizumab, 30 with interferon beta (IFN-β) and 25 healthy controls. The levels of soluble l-selectin (sL-selectin) in sera were measured by ELISA, and the anti-JC Virus (JCV) antibody index was determined by the second-generation ELISA (STRATIFY JCV(TM) DxSelect(TM)) assay.
RESULTS: A significant correlation was found between the levels of sL-selectin and anti-JCV antibody indices in sera in the natalizumab-treated patients (r=0.402; p=0.007; n=44), but not in those treated with IFN-β. This correlation became even stronger in JCV seropositive patients treated with natalizumab for longer than 18 months (r=0.529; p=0.043; n=15).
CONCLUSION: The results support the hypothesis of sL-selectin being connected to the anti-JCV antibody index values and possibly cellular L-selectin. Measurement of serum sL-selectin should be evaluated further as a potential biomarker for predicting the risk of developing PML
L-selectin, also known as CD62L, is a cell adhesion molecule found on lymphocytes and the preimplantation embryo. It belongs to the selectin family of proteins, which recognize sialylated carbohydrate groups. L-selectin acts as a “homing receptor” for lymphocytes to enter secondary lymphoid tissues via high endothelial venules. Ligands present on endothelial cells will bind to lymphocytes expressing L-selectin, slowing lymphocyte trafficking through the blood, and facilitating entry into a secondary lymphoid organ at that point. The receptor is commonly found on the cell surfaces of T cells. Naive T-lymphocytes, which have not yet encountered their specific antigen, need to enter secondary lymph nodes to encounter their antigen. Central memory T-lymphocytes, which have encountered antigen, express L-selectin to localize in secondary lymphoid organs. Here they reside ready to proliferate upon re-encountering antigen. Effector memory T-lymphocytes do not express L-selectin, as they circulate in the periphery and have immediate effector functions upon encountering antigen. This can be shed and in this study, soluble L-selectin correlates with anti-JC virus antibody, which is an indication of whether you have had contact with JC virus, but the r=0.4.
This level of correlation in my mind has been the problem with many MRI outcomes, which have no clear pathological correlate.
So on a population level it may get a hint of a relationship, but for any individual it has no real meaning full outcome unless they are on of the extremes.
So when you see a paper saying this aspect correlates with that aspect, look at the r value to see how much confidence you can put in the conclusions.