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I'm wondering how one determines the sample size needed to sufficiently analyze a three-way 2x2xcontinuous (logistic) regression interaction using observational data (association study)? Any references would be much appreciated. I'm finding it difficult to find any literature with a straightforward answer.

A similar question: how does one determine whether the sample size currently being used is sufficiently large to analyze a three-way 2x2xcontinuous interaction in a (logistic) regression model induced on observation data?

Thanks!

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  • $\begingroup$ there is no definite answer to this I'll posed question. The larger the sample size the more precise the estimate. $\endgroup$
    – utobi
    Commented Aug 30, 2023 at 15:38

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Simply to avoid overfitting, the rough rule of thumb for regression with a binary outcome is at least 15 members of the minority class per coefficient that you try to estimate. Section 4.4 of Frank Harrell's Regression Modeling Strategies provides a somewhat more detailed estimate.

In your 3-way interaction situation (if there is a simple linear model for the continuous predictor) there is one coefficient for each of the 3 predictors, 3 two-way interaction coefficients, and one 3-way interaction coefficient, for 7 coefficients beyond the intercept. So unless you have at least 7*15 = 105 cases in the minority class you are in danger of overfitting.

That doesn't even start to address the issue of how large the effects are that you would like to be able to detect or the precision of the resulting estimates. See Section 10.2.3 of the Harrell reference for an introduction to how to take those design issues into account. This linked question also shows some ways to proceed.

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