I am seeking advice on penalized regression models for selecting covariates in epidemiological studies. A difficult tasks I face is feature selection while still attempting to account for confounding factors. During my academic studies, I have been taught various methods including stepwise and purposeful selection procedures; however, the later feels more like an "art" than science. I have recently learned of penalized regression models through independent studies, although applied to predictive purposes. I am wondering if there are credible sources that would suggest penalized regression for epidemiological studies to be an efficient feature selection procedure?
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1$\begingroup$ Will this method still be of use if you have shrunken estimates without standard errors? You might be interested in: stats.stackexchange.com/questions/7225/… $\endgroup$– charlesCommented Dec 10, 2013 at 19:19
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1$\begingroup$ In most textbooks there is a reference now to the LASSO or similar shrinkage methods. But the lack of consensus on how the estimates should be interpreted and CI estimated is a significant issue. Most references I see either don't mention this or relegate this to a brief aside (like the linked article). $\endgroup$– charlesCommented Dec 10, 2013 at 19:58
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$\begingroup$ Thanks, Charles. Sorry I was revising my comment about the CIs, but it appears I have deleted the comment. Given that a shrinkage model also includes bias and does not include SEs, then it would appear the shrinkage model would remain in the domain of prediction - for me anyway- as I wouldn't feel "confident" to extrapolate meaning from the coefficients... What are some other reliable feature selection methods than stepwise that might be useful for epidemiological studies? The populations I work with are indigenous and have little published available works. $\endgroup$– user2300643Commented Dec 10, 2013 at 20:17
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$\begingroup$ You are mixing penalization with variable selection. lasso does that but this needn't be the case, and in general the best predictions are made using shrinkage of all parameters without setting any parameters to zero. $\endgroup$– Frank HarrellCommented Dec 10, 2013 at 20:31
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$\begingroup$ @user2300643 Epidemiology as a field has been heavily influenced by several methodologists who are strongly against most selection algorithms. If you want a more systematic consideration of variable selection, consider directed acyclic graphs (DAGs)? A simple Google search will bring up a great many examples. $\endgroup$– FomiteCommented Dec 10, 2013 at 20:48
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Part of the problem is that in Epi one is more often interested in interpreting the coefficients, which penalization bias. Unpenalizing an exposure is possible, but it's unclear how to deal with changes in estimates caused by confounders in a penalized setting.
The Alen-Cady modified backward selection is based on hierarchically ranking candidate variables by their known/suspected a-priori importance, so in theory, there should be less Type I error than classical stepwise. But it's still stepwise with all the problems outlined by Harrell, Steyerberg and many others (I believe Steyerberg suggests using a liberal p<0.2-0.5 if you really must use stepwise).
I highly suggests Frank Harrell's book, or even better, taking his short courses. Steyerberg (2009) is another good book although more geared towards clinical prediction. Vittinghoff et al (2012) is easier and less rigorous and probably more epi oriented. I also suggests to read anything from Sander Greenland.
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$\begingroup$ +1 on Steyerberg and Vittinghoff. (Though I thought the Vittinghoff chapter of variable selection needed a bit more work and Steyerberg is focused on prediction modelling) I still have to get around to the Harrell book. $\endgroup$– charlesCommented Dec 11, 2013 at 16:05