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It's not hard to reach statistical significance at all with small samples and logistic regression. What's hard is to see a meaningful result once you add in numerous 'control' variables
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Not sure I follow. Can you give an example of how their result could have been achieved by chance, at a probability >0.001?
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An example: there was underlying selection bias that led to a 'sicker' control group (however we define sicker). Given the small sample size, the logistic model cannot adequately control for this issue, and so the results are hard to interpret
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