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I have two outcomes given a population of people.

  • report a headache
  • report a migraine

And all those people are broken into two sets of groups.

  • by sex (male and female)
  • by deprivations score (1, 2, 3, 4, 5) - this is a measure of several factors, but think of it as a measure of poverty.

Each individual can only report a headache or a migraine, not both. And each individual can only be in one of the five deprivations groups, they can belong to multiple groups. Each individual can only be male or female.

As a reduced example, there are 200 males and 600 females reporting to their doctor. Of those males, 50 report a migraine, and 150 report a headache. A male can't report both headache and migraine. Of those females, 300 report a migraine and the other 300 report a headache. A female can't report both headache and migraine. Given the total numbers reporting to the doctor, are males overrepresented reporting a headache compared to females and how about for migraine?

The same for deprivation scores. Of the deprivation scores, which ones show a great propensity for reporting a migraine over a headache (or vice versa - I don't really mind)? An individual in the population can only belong to one of the deprivation groups.

I appreciate the question isn't well-defined, and I'm happy to provide further information. I used to know all of this, many years ago, so I really do appreciate being educated again. Many thanks :-)

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    $\begingroup$ Do you have one observation per individual? And does every individual either report headache or migraine? Or are both/none possible? $\endgroup$
    – COOLSerdash
    Commented Jul 21, 2023 at 17:57
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    $\begingroup$ Thanks! I think a logistic regression would be suitable. Code one outcome as 1 and the other as 0. The predictors would include the score and the sex. This will model the probability of reporting the outcome you coded as 1 in relation with the predictors. This will allow you to say something like: "The odds of reporting a headache vs. a migraine are 1.05 times higher in females compared to males, irrespective of the deprivation score." An important question is whether to treat the scores as categorical or continuous and whether you want to include an interaction between the two predictors. $\endgroup$
    – COOLSerdash
    Commented Jul 21, 2023 at 18:08
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    $\begingroup$ Thank you so much. This is certainly food for thought, and it's given me a direction. In greater detail, there is a huge amount of missing data for deprivation scores; not all clinical records have that data. Therefore, I would not add an interactioon between the two predictors, and simply highlight this as a study limitation. $\endgroup$
    – Anthony Nash
    Commented Jul 21, 2023 at 18:16
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    $\begingroup$ The missing data is a separate problem. Depending on what you judge the missing data mechanism to be (MCAR, MAR, MNAR), different solution exist. One popular method is multiple imputation. $\endgroup$
    – COOLSerdash
    Commented Jul 21, 2023 at 18:18
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    $\begingroup$ In addition to the comments by @COOLSerdash, if the deprivation score is ordinal (e.g. if the "distance" between level 1 of deprivation and level 2 isn't the same as the distance between levels 2 and 3), this answer mentions some possible strategies to deal with this variable as predictor/independent variable in your model: stats.stackexchange.com/a/195253/164936 $\endgroup$
    – J-J-J
    Commented Jul 21, 2023 at 18:19

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