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In simple logistic regression i noticed that many researcher neglect the constant part of the logistic regression equation.

Log(odds) = a + b Gender (say that 0 = Female and 1 = Male) So the log of the odds of cancer when the case is male is b ... and odds of course is exp(b)

but shouldn't the log of the odds equals b + a? because log(odds) = a + b x 1 = a + b

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My guess is that you've misinterpreted what someone wrote and they meant that males have $b$ higher log-odds than females.

$$ \log(odds) = a+bx\\ \log(odds) = a+b\text{ (male)}\\ \log(odds) = a+0\text{ (female)}\\ $$

Then subtract to see that $\log(odds)$ for males is $b$ higher than $\log(odds)$ for females.

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  • $\begingroup$ Yeah I understand it like what you said. But I in many articles it's just interpreted as: odds of cancer for males is exp(b), without taking care of a $\endgroup$
    – Hussain
    Commented Feb 1, 2022 at 15:53

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