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I am trying to develop the design for an observational study, but I am struggling with the number of observations that would allow us to estimate our model and generalize its results. As a dependent variable, we have a score of a psychological structure (varies between 1-100), and we have two families of predictors:

  1. Measurements of other psychological factors.
  2. Socio-economic controls.

We will probably be going to explore different specifications for the dependent variable (enter it as it is, enter it as a dummy variable for whether a person is placed among the highest 25 percentile of the distribution, etc.).

A popular thumb rule for deciding the required number of observations is the one-in-ten rule (or one of its variations), but it seems to better fit a classification problem, and even worse, oversimplistic. I came across this article, that presents a more scientific method, but it refers mainly to linear models with priors for the sizes of the expected coefficients.

Our main goal in this part of our research is to find which variables have the strongest predictive powers for $y$. We will have about ~50 predictors, and for most of them, we don't have any prior (there is no other article that correlated these measurements).
Is there any method to simulate the number of required observations under observational study, that does not require priors on the coefficients?

Thanks!

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See these two articles (choose which one depending on the nature of your outcome variable) https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.7993 and https://onlinelibrary.wiley.com/doi/10.1002/sim.7992

Note that power is almost irrelevant in this context.

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  • $\begingroup$ Hi, thanks for your answer. I am pretty new to power analysis and did not learn it in a class. Why isn't power relevant in this context? We want to make sure we would be able to consistently measure the parameters in the model. Thanks again! $\endgroup$
    – David Harar
    Nov 7, 2021 at 22:02
  • $\begingroup$ It does depend on the ultimate goal. If you are interested in the adjusted effect of a single special variable then power can be relevant, although IMHO precision is a better basis for sample size assessment (i.e., margin of error; width of key confidence interval). If you are interested in developing a prediction model or are interested in many variables at once then the two references I provided are more relevant. $\endgroup$
    – Frank Harrell
    Nov 7, 2021 at 22:50
  • $\begingroup$ Thank you very much, sir. $\endgroup$
    – David Harar
    Nov 8, 2021 at 4:14
  • $\begingroup$ On this site thanks is not expressed in a comment but rather by upvoting. $\endgroup$
    – Frank Harrell
    Nov 8, 2021 at 13:37

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