Say, I have a biomarker that is strongly associated to a gene. This biomarker is also strongly associated to another trait, like glucose, but the gene is not.

  • If I perform a regression between the glucose and biomarker + gene I get the biomaker and gene both significant: Is this a spurious effect?
  • And what if I add an interaction term between the biomarker and gene on the glucose (biomarker*Gene+Gene+biomarker) and all the terms are significant?

What does it mean if when I add a third variable (biomarker) in the regression the second (gene) becomes significant all of the sudden? Does it mean that the second variable is then significantly associated with the dependent?

  • 2
    $\begingroup$ Are you familiar with mediating en.wikipedia.org/wiki/Mediation_(statistics) or moderating en.wikipedia.org/wiki/Moderation_(statistics) variables? Darn I cannot get those end brackets to form part of the link. $\endgroup$ – Michelle Feb 4 '12 at 3:02
  • $\begingroup$ Collinearity (which is often related to the topics Michelle mentioned) is a possible explanation. I suggest having a look at some of the dozens of questions on here related to this subject. $\endgroup$ – Macro Feb 4 '12 at 5:19

The most likely explanation is that the Biomarker is a suppressor variable. A suppressor variable is correlated with another predictor variable in such a way that the predictor is significant when both are entered into a model, but not when it is entered alone. Unfortunately, suppression is just one of those statistical phenomena that aren't very intuitive. This website is fairly long, but very clear and includes a discussion of all the relevant issues with a section on suppressor variables at the end. I also found this American Statistician paper, which is specific to suppressor variables. I haven't read it yet, but it looks quite good.

Another possibility is that the Biomarker is not a suppressor, but it accounts for enough of the residual variance in your response variable (glucose), that the weaker gene - glucose relationship becomes significant. Remember that 'significance' is assessed by the relationship between the variability that a predictor accounts for, and the residual variability. If the Biomarker accounts for a good deal of what would otherwise be residual variability, but consumes only, for example, 1 degree of freedom, this could increase the power of your analysis with respect to the gene. Under this interpretation, you would have simply needed more data to resolve the gene - glucose relationship, but there might not be any correlation between the gene and the Biomarker.

In neither case would it be correct to call this a spurious correlation. A spurious correlation is when there is a zero-order correlation between two variables, but no direct relationship. The classic situation is where two variables A and B are both caused by a third variable, C, but otherwise have no direct connection. A real-world example I once heard is that when the economy speeds up, it enhances both the birth rate and steel production, but that there is no direct connection between them.

An interaction is a third, distinct concept. An interaction obtains when you would describe a situation using the word 'depends'. For instance, if someone asked what is the effect of taking the birth control pill, you might say:

It depends, for women, it suppresses ovulation and so reduces the chance of pregnancy. But for men, since they don't ovulate, it has no effect.

(I acknowledge that this is a rather forced example.)

| cite | improve this answer | |
  • $\begingroup$ thank you, this is very clear. The gene has biologically to do with Glucose, but not directly associated (i tested it in a sample size of ~60.000 subjects). However, the gene is regulating a biomarker (something like Insulin) that is associated (and biologically relevant) to glucose levels and is the gene is significant if i add them both in the model, also their interaction. $\endgroup$ – Alex Feb 4 '12 at 16:55
  • $\begingroup$ I like these replies. These are very fundamental and fruitful topics. You also may want to look up the terms partial correlation and statistical control. $\endgroup$ – rolando2 Feb 5 '12 at 22:10

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.