I read that it is recommended that

for LR, a useful rule of thumb comes from simulation experiments which suggest that the number of the less common of the two possible outcomes (“events”) divided by the number of predictor variables should be at least 10, and preferably greater.

I'm not sure if I quite understand this. Does this mean say if the result was death, there were 7 predictor variables, and one of the predictor variables was playing baseball, which 4/100 people did, that 4/7 < 10, and therefor this criteria is not met? If this is not what is meant; is there any other condition for the number of events?

  • 1
    $\begingroup$ If you have say 100 subjects, 20 of whom die and 80 survive, then according to this rule of thumb you should have no more than 2 covariates (predictor variables) in your model. In fact, with 2 covariates the condition is satisfied: $\frac{\min(20,80)}{2} \ge 10$, while with 3 covariates it is not $\frac{\min(20,80)}{3}<10$ $\endgroup$
    – boscovich
    Dec 23, 2014 at 21:55
  • $\begingroup$ Thank you for clearing that up! Is there a condition for number of events for a given predictor? $\endgroup$
    – Cenoc
    Dec 23, 2014 at 23:10
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    $\begingroup$ In my experience you need more than 15 events per candidate predictor. And note that you need 96 subjects just to estimate the intercept within a margin of error of +/- 0.1 on the risk scale. $\endgroup$ Dec 23, 2014 at 23:13
  • $\begingroup$ @FrankHarrell, do you mean you need 96 instances of the lesser of the two events? Eg, intuitively it seems to me N=100, but p(Y=1)=.01, wouldn't likely yield a good estimate. $\endgroup$ Dec 23, 2014 at 23:40
  • $\begingroup$ $n=96$ total number of observations. Thanks for alert on SO. $\endgroup$ Dec 24, 2014 at 3:44


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