Low number of events in Firth logistic analysis

[Wouter Kiekens]

Hi,

First a little bit of background: I am working with a dataset with N = 90 cases. I have 14 dependent variables that are all binary and 4 independent variables (2 binary variables, 1 nominal variable, and 1 continuous variable). Because of the small number of cases, I am performing Firth logistic regression using the firthlogit command. For every dependent variable I am running a separate Firth logistic regression analysis.

The problem I run in to is the following: For some of the dependent variables, there is a very low number of events (the lowest number of events are 1, 2, 3, and 5). So my question is, does is make sense to run the Firth logistic regression analysis if the number of events is so low? Is there a certain cut of when it is not advisable to sun these analyses?

All models do run, but the 95% confidence intervals become very large.

Any help is appreciated!

Thanks!

Wouter

[Felix Bittmann]

I am not familiar with the command you use but the problem is general: you have a rather large number of predictors for the total N available. And this explains your large CIs. In that case you might want to consider to reduce the number of predictors, combine or coarsen them. Another alternative is to use an exact regression (exlogistic).

[Joseph Coveney]

I'm with Felix on this. It seems to me that you're asking a lot of your limited dataset, more than it can reasonably deliver.

-firthlogit- will attain convergence with as few as two observations, one success and one failure. (See below.) But that doesn't mean that you should be going that route. I don't recommend looking upon -firthlogit- as some kind of talisman, able to protect you against a poorly framed research question or an inadequately thought-out experimental design.

.ÿ
.ÿversionÿ16.1

.ÿ
.ÿclearÿ*

.ÿ
.ÿquietlyÿsetÿobsÿ2

.ÿ
.ÿgenerateÿbyteÿoutÿ=ÿ_nÿ-ÿ1

.ÿgenerateÿbyteÿkÿ=ÿ1

.ÿ
.ÿfirthlogitÿoutÿc.k,ÿÿ//ÿnolog
note:ÿkÿomittedÿbecauseÿofÿcollinearity
note:ÿkÿomittedÿbecauseÿofÿcollinearity

initial:ÿÿÿÿÿÿÿpenalizedÿlogÿlikelihoodÿ=ÿÿ-1.732868
alternative:ÿÿÿpenalizedÿlogÿlikelihoodÿ=ÿ-1.8256574
rescale:ÿÿÿÿÿÿÿpenalizedÿlogÿlikelihoodÿ=ÿÿ-1.732868
Iterationÿ0:ÿÿÿpenalizedÿlogÿlikelihoodÿ=ÿÿ-1.732868ÿÿ
Iterationÿ1:ÿÿÿpenalizedÿlogÿlikelihoodÿ=ÿÿ-1.732868ÿÿ

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿÿÿÿÿ2
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Penalizedÿlogÿlikelihoodÿ=ÿÿ-1.732868ÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿÿÿÿÿÿ.

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿoutÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿkÿ|ÿÿÿÿÿÿÿÿÿÿ0ÿÿ(omitted)
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ3.72e-09ÿÿÿ1.154701ÿÿÿÿÿ0.00ÿÿÿ1.000ÿÿÿÿ-2.263171ÿÿÿÿ2.263171
------------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file


.

[Wouter Kiekens]

Thank you for your answers.
I will look in to exact regression and see if this will be a viable option for me.

I could definitely reduce the number of independent variables in the model so I am going to try that see if that will help.

Thanks!