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I have a biostatistics background and epidemiology interests me. I've never taken a course in epidemiology, so I'm not familiar with this field. My question is related to multivariate model construction in epidemiology.

Suppose that we want to analyse the relationship between one outcome and several explanatory variables which all are interesting individually. It appears to me that a common way to do it is to provide crude estimates for each predictor, estimate a multivariate model with all or a subset of the predictors, and provide the adjusted estimates with 95% CIs and possibly p-values.

With what I've learned, I would rather do some log likelihood ratio test, use AIC and BIC or use cross-validation to build the multivariate model. Maybe a model without all of the predictors is better. I assume the rationale for the initial approach is that each of the predictors is intended to control for potential cofounding. However, the approach strikes me as different from the approaches that are used in machine learning.

Is my understanding of multivariate modeling for diseases and exposures in epidemiology correct? If so, is it possible that a model selection approach based on AIC/BIC or cross-validation is more accurate/generalizable?

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    $\begingroup$ Your summary of epidemiological practice seems correct. We try to avoid variable selection where at all possible. $\endgroup$
    – mdewey
    Commented Dec 13, 2016 at 12:30
  • $\begingroup$ Also check out directed acyclic graph. Most epi models should have a causal framework in the background to support the inclusion of the confounding variables as independent variables. Aka, they may seem haphazardly put together, but the analysts should have a reason underneath. Variable selection is usually frowned upon in an explanatory epi analysis. $\endgroup$
    – Penguin_Knight
    Commented Dec 13, 2016 at 15:37

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There are a number of potential approaches to your question, all of which I've seen done in practice:

  1. Often, as @mdewey mentions, there is a tendency not to do variable selection at all. I'm actually slightly opposed to this, as if you're not paying attention it's easy to induce collider stratification bias.
  2. Many people use a "10% change in estimate" approach, where any variable that causes, as the name suggests, a 10% change in the effect estimate of interest is included in the multivariate model.
  3. There's also the use of causal models, such as DAGs, to provide a theoretical underpinning for what models you choose - these should identify the variables that you can control for to yield a theoretically unbiased estimate (with the usual caveats about unmeasured confounding).

In practice, I tend to use #3, and then to use #2 to narrow that set if there's too many variables for the size of the data set.

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