0
$\begingroup$

I would like to learn more about how unbalanced binary predictors affect type I or type II error in regression models. I am aware that having unbalanced binary outcomes can increase type II error.

I am using regression to test for an association between a binary predictor and continuous outcome. I am also testing if a binary predictor (ex. drug treatment yes/no) is associated with other binary predictors (ex. disease status yes/no). The regression model has sex, age, body mass index as covariates and then 1 binary predictor; I am iterating through each binary variable as predictors. So far I am using a case:control ratio of 1:2 for binary outcomes and the minimum sample size requirement is 200. I am not using over- or under-sampling techniques.

So should I also have my binary predictors have the case:control ratio of 1:2? I have looked at this and this thread but they focus on the situation when the unbalanced data is the outcome and not the predictor variable. I also read this list of assumptions on binary logistic regression from a university online resource and it does not touch upon unbalanced classes in the predictor data set.

I appreciate everyone's help!

Improve this question
$\endgroup$

1 Answer 1

Reset to default
0
$\begingroup$

One way to think about this is in the simplest case-- a continuous outcome variable and a binary predictor with no other covariates. This is a t-test. If you're unfamiliar with the notion of a t-test as a special case of a regression this post covers it in some detail. Specifically, a student's t-test with equal variance.

You'll note that in the case of a t-test we don't necessarily worry about unbalanced cases in the same way as we do when it is an outcome. So, most likely the reason you haven't heard any talk about bias around unequal group sizes is because mathematically... there aren't any. You do still have to worry about sample size. So, if you have once class that makes up 99.99% of your population, you're going to need to collect thousands of data points before you have enough data.

Improve this answer
$\endgroup$
2
  • $\begingroup$ This post is helpful. May you point me towards a resource about how there is no bias mathematically? $\endgroup$
    – WMorrisPrints
    Commented Jul 7, 2021 at 19:16
  • $\begingroup$ I'm having a hard time tracking down a proof of "no bias." It's kind of like saying "prove regression works with both integer and decimal numbers." It's kind of just true and no one has bothered exploring it too much. This page does talk about unbalanced t-tests. statisticshowto.com/unequal-sample-sizes $\endgroup$
    – Tanner Phillips
    Commented Jul 8, 2021 at 21:31

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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