# Interaction and correlation between two variables?

I fitted a generalised linear model to my medical retrospective data, in which there is

• a continuous variable x
• a binary variable y
• If y is TRUE, x will have high values. Because whatever causes y to be TRUE will also make x high.
• It doesn't work the other way round though. If x is high, y can be both FALSE and TRUE. In other words, there can be causes for x to be high that do not lead to y = TRUE.
• x is fairly reliably measured
• y is a more subjective measure (and binary) and I'd love to remove it from the model, but I think I cannot completely disregard its information because its presence has a meaningful, plausible and of course significant effect on the event.

My question

Is it correct to speak of an interaction in this situation?

There seems to be a correlation between x and y, but the fact that this is only present "in one direction" makes me a little bit helpless and I am not so sure what to do about it. Adding an interaction term seems to slightly increases the performance of the model (if judged by the AIC), but I have the feeling that it's not quite correct to speak of an interaction here.

If you have a better idea for question title, I'd be more than glad to hear. Thanks.

## This is the model output of my data, which are around 60k observations.
## Due to the event being fairly infrequent I found it difficult to create a representative sample,
## but I'd be willing to undergo that challenge if you should think that this would help you.

Call:
glm(formula = event ~ y * x, family = binomial, data = df)

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -4.53815    0.04829 -93.983  < 2e-16 ***
yTRUE        1.52285    0.17531   8.687  < 2e-16 ***
x            0.66225    0.05498  12.045  < 2e-16 ***
yTRUE:x     -0.64983    0.12033  -5.400 6.65e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 10114.4  on 60729  degrees of freedom
Residual deviance:  9879.7  on 60726  degrees of freedom
(79815 observations deleted due to missingness)
AIC: 9887.7

Number of Fisher Scoring iterations: 7
$$$$
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