I've been performing some logistic regressions and found some great results. The problem is I'm unsure if my model is stable or not. This is mostly because I am confused about what people mean by cell size for logistic regression.

I keep reading inconsistent prescriptions. Some people say I need 10-15 observations per variable while some people say I need 10-15 observations per cell. I also get confused if people mean per cell when including all variables or just the main exposure/control vs event/ no event.

The overall N is 331.

Let's say I have data in a 2x2 table with the typical exposure/control by event/ no event:

.                        Event       No Event
.     Exposure             103          15
.  No Exposure             150          63

In this example, the smallest cell size would be 15. So, I could perform a logistic regression with 1 independent variable, right?

So let's say I wanted to add another variable to the same data, like Race (African American or not, 1 or 0) and here's the cell breakdown:

.     Clinic      Event    Race    N
.       0           1        1     121
.       1           1        1     92
.       0           0        1     46
.       0           1        0     29
.       0           0        0     17
.       1           0        1     14
.       1           1        0     11
.       1           0        0      1

Would this now mean that my smallest cell is 1? Or, would I still refer to the original 2x2 table and it would still be 15?

I'm asking because when I run my logistic model in SAS with 6 independent variables on this same data, I do not get any small cell warnings and the convergence criteria is met. Does this mean I'm okay and don't need to necessarily worry about cell size?

I have been running exact logistic regression models anyway but they take a VERY long time (whole other story). I'd rather just report the standard LR results to save time (assuming they are legitimate).

  • $\begingroup$ Could you explain what you mean by "stable"? Ordinarily one might think that refers to the standard errors of parameter estimates being satisfactorily small, but apparently not here--for otherwise you would just consult their values in the output. What sources are you referring to with the rules of thumb you are quoting? $\endgroup$ – whuber May 27 '16 at 20:34
  • $\begingroup$ I suspect there are several different things to worry about: 1) are estimates normally distributed so that est & SE makes sense, 2) is there a concern about overfitting, because a complex model is fitted on very little data. Plus perhaps something else? $\endgroup$ – Björn May 28 '16 at 5:20
  • $\begingroup$ @Björn 1) Yes I need to check the standard error estimates. If they are normal, things should be okay right? 2) Yes my concern is overfitting. Long story short, I just want to make sure I'm using the method correctly. I've done many LR's before but not many with small cell sizes. $\endgroup$ – Pete May 30 '16 at 16:25
  • $\begingroup$ @whuber Stable meaning that I don't have parameter estimates and confidence intervals that are gigantically huge (like an OR of 45 with 95% CI 25 - 65). I'm not at work where I have the source material handy, but here's one that I found just to give at least some sort of reasoning: citeulike.org/user/harrelfe/article/13467382 $\endgroup$ – Pete May 30 '16 at 16:29
  • $\begingroup$ Since (presumably) you do have CIs or standard errors for your parameter estimates, why then are you "unsure" about the stability of those estimates? $\endgroup$ – whuber May 30 '16 at 17:44

When they say "per Cell", generally in my experience people mean per cell in the larger NxM table created by adding your covariates.

This is however a very rough and informal guideline - as you're finding, logistic regression is fairly mechanically reliable, and can be made to do a great many things it probably shouldn't before running aground on convergence issues. For example, having one cell that violates that rule might not be a big deal, whereas having many may very well create problems.

There are two hazards with what you're currently doing:

  1. The model is essentially being asked to smooth over places where there isn't very much data, which carries the risk of missing things that exist in your exposure-disease relationship.
  2. It's possible (though not a problem in your example) that a cell size of zero is not merely due to stratification, but because something is impossible, and the regression model will also miss that.

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