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I have collected a dataset on a group of patients with a rare disease where not much is known. These patients can have an outcome, X, which has been seen in 50 of the 300 patients. I want to find out the risk factors associated with getting X in this rare disease. Since barely anything is known about this disease I barely have any hypotheses about which risk factors might have an influence except for the common stuff like smoking. I have over 30 variables collected (possible risk factors). I understand that you can only analyze one risk factor for every 10 events but I really only want to find possible risk factors so I can help these patients, just a clue for possible risk factors would help.

To minimize the amount of variables I input into the multivariable analysis I was thinking of doing something I've seen in several other studies where they do a univariable analysis for each risk factor, then they grab those with a p value of below 0.20 (where does that number come from?) and enter those into the multivariable analysis. In the table the results from both analyses are shown. I've seen this in reputable journals such as NEJM. What are some caveats of doing it this way? Or could I do it in another way? Any help is greatly appreciated.

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This type of approach is often used,* but it has some dangers. First are the problems inherent in any attempt at automated model selection like that. Second is the inherent omitted-variable bias in Cox models. As with logistic regression, omitting any predictor associated with outcome from a Cox model will tend to bias the magnitudes of coefficients of included predictors down toward zero. Unlike with linear regression, this is the case even if the omitted predictor is uncorrelated with the included predictors. So with the single-predictor analyses there is a risk of missing an important contributor on this account.

An approach based on knowledge of the subject matter is generally best. It might be possible to use such knowledge to combine multiple related risk factors into single combined predictors (without looking first at their relationships with outcome). Or you could take advantage of the penalization provided by ridge regression to allow a higher ratio of included predictors to events. The penalization might be omitted from predictors like smoking that you expect to be strongly associated with outcome.

These types of issues are explained in Frank Harrell's course notes and book, with illustrative examples.


*The single-predictor p-value cutoff for inclusion in that approach to Cox multiple regression is a rule of thumb to get the number of predictors down to a reasonable value. A value of 0.20 is not always the choice.

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