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I am using the residuals from a linear mixed effect model from the below formula ( having family structure as a random effect as the individuals are related.

 mod<- lmer(Genes ~ Age + Gender + Medication + (1|Familystructure)
 
 summary(mod)$res

I am then using these residuals in a glm to determine the association between the genes and the odds of disease

res<-glm(Disease ~ residuals, family=binomial)

If I am understanding this correctly- As an example, for gene 1, the odds ratio is 0.58, which shows that per unit increase in gene 1 there is a 58 % reduced odds of developing the disease.

 Logit odds = -0.49775
 Exp(logit odds) = 0.60
 Lower 95% CI= 0.3984
 Upper 95% CI= 0.927928

I know when running an lmer to look at how these genes change as a response to disease that this gene 1 significantly reduces in disease vs control, which is in accordance with the fact that an increase results in less of a likelihood of disease.

Could anybody advise please as to whether I can only infer that a unit decrease of this gene would result in an increased odds of disease? I was unsure whether exp(0.49775) ( changing the sign of the logit odds), yielding an odds of 1.645, corresponds to this?

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  • $\begingroup$ Could you add a reference describing this approach? $\endgroup$
    – Michael M
    Commented Jun 26, 2020 at 20:15
  • $\begingroup$ @MichaelM Please could you clarify what for ( the use of the residuals from lmer as a predictor in the glm?). If there may be any problems using this approach, please also comment if possible. $\endgroup$ Commented Jun 26, 2020 at 22:36

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How to calculate odds ratio per unit decrease of continuous variable

This link explains mathematically how this can be done in terms of working out the odds ratio per unit decrease by doing 1/exp(coef), which gets the same as exp(+ve logitodds).

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