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Using this study as an example, I am wondering if the size of different study groups run in the same models impacts the conclusions we can draw from statistical tests.

In this study, the researchers were looking at pulse oximetry discrepancies between Black and White patients. They found that Black patients were more likely to have something called Occult (or Hidden) Hypoxemia, which is when the pulse oximeter incorrectly measures the peripheral oxygen levels as higher than they truly are. These mistakes are illuminated by running a more invasive test of arterial blood oxygen saturation.

In this study, the study population is 73% White (N = 21,918), 21.6% Black (N = 6,498), and 5.4% Hispanic (N = 1,623). They found that Black patients had a significantly higher probability of being given a mistakenly high reading of peripheral blood oxygen saturation than White and Hispanic patients, which could potentially lead to worse health outcomes for those patients.

My question is, given the large difference in sample sizes of White v. Black and Hispanic patients, how is this accounted for in running statistical tests and drawing conclusions? For example, in this study the researchers used a multivariable logistic regression model to predict the odds of occult hypoxemia, and adjusted for patient characteristics like age, race, sex, etc. Is this adjusting enough to account for the differences in sample size, or are there other methods one should use to bolster statistical models run on groups of different sizes?

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Try this experiment. Double the size of your data set by exactly duplicating every case. Then rerun your logistic regression. You should find that for every predictor term the estimates of coefficient and odds ratio turn out the same as before. What will change are the p-values and the standard errors on which they depend. These standard errors will all be smaller than before by a factor of the square root of 2.

So the procedure adjusts standard errors in light of sample size; it does not change estimates of the relationships of interest. And when I say "sample size" that includes the sample sizes for the subgroups defined by your predictor variables. Each comparison of one subgroup to another will have its standard error affected by those subgroups' sizes. If your study's group of Hispanic patients had numbered 160 instead of 1,623, you would have seen dramatically larger standard errors and p-values for the corresponding comparisons.

There are some statistical procedures for which differently sized subgroups typically require special design considerations. Logistic regression is not one of them.

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  • $\begingroup$ Got it, thanks for the information. Very helpful! $\endgroup$ May 1, 2023 at 15:21
  • $\begingroup$ You're welcome! Glad it's helpful. $\endgroup$
    – rolando2
    May 1, 2023 at 20:43

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