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I have 6 out of 167 cases of cancer in the dependent variable. I would evaluate if three independent variables predicted the cancer. Are 6 cases enough? Is there a rule to determine this? Is there difference if the indipendent variables is nominal or numeric?

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  • $\begingroup$ What does "enough" mean? If I were to say "enough" then I would personally say "given prevalence x, how many samples do I need for the Jeffreys prior on the rate to be within the range x-r to x+r. Here is what a decent tool gives for your samples. (epitools.ausvet.com.au/…) $\endgroup$ – EngrStudent Aug 29 '16 at 14:36
  • $\begingroup$ 6 "Yes"s and 3 DVs will almost certainly produce complete separation in the data (which often manifests as huge coefficient estimates and standard errors). The rule of thumb usually says 5 or 10 cases per DV (depending on who you ask). $\endgroup$ – not_bonferroni Aug 29 '16 at 14:36
  • $\begingroup$ What do you mean by "6 out of 167"? Is is that 6 patients had cancer diagnosed ? $\endgroup$ – Tim Aug 29 '16 at 14:36
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    $\begingroup$ Related: stats.stackexchange.com/questions/26016/… $\endgroup$ – David R Aug 29 '16 at 14:42
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I think there is no minimal number of "cases" to perform logistic regression (well at least you need to have 2 classes.).

The only downside is that, if you have a very imbalanced data, you may model minority poorly.

Also you may get some warnings from R, glm, if you have perfect separably data, so you may consider adding regularization.

Regularization methods for logistic regression

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