firth logestic regression

[rania]

I have sample size of 215 with 10 of them having disease positive and I have about 20 covariables that I want to examine. Can I do univariate logistic Regression for each and those with p- value more than 0.1 are to be included in Firth logistic regression ?
how can I interpret the results in SPSS ?
when I do this that appears

Conf. Interval Type Wald
Conf. Interval Level (%) 95
Estimation Method Firth penalized maximum likelihood
Output Dataset –NA–
Likelihood Ratio Test 38.0566
Degrees of Freedom 11
Significance 7.65335733629025e-05
Number of Complete Cases 176
Cases with Missing Data 39
Number of Iterations 26
Convergence Status Converged
Last Log Likelihood Change 6.3948846218409e-14
Maximum Last Beta Change 5.36667170504665e-06

what is the significance = 7.65335733629025e-05 , last log likelihood and maximum ones ??

 

[hlsmith]

With 10 cases you have just about enough to have an empty model with just an intercept. Anything else wouldnt be trustworthy internally or externally.

Just think about how you would try to think about interpreting a saturated model and it would likely have convergence (complete seperation) issues.

 

[rania]

With 10 cases you have just about enough to have an empty model with just an intercept. Anything else wouldnt be trustworthy internally or externally.

Just think about how you would try to think about interpreting a saturated model and it would likely have convergence (complete seperation) issues.

can you explain more what shall i do ?

 

[hlsmith]

You dont have enough data to support your question. Investigate how to do a sample size calculation to process your issue. So ten events and say 5 covariates. How do you generalize your results when you have no obs with all 5 variables (given you have some categorical variables). So say you have no women over the age of 30,without a job, lives in an apt, and is unmarried. You may not even have any subsets of the individuals. External validity is jacked, because even if you had 1 women like this how can you be confident she represents the other 36 million like this. You can't. Let me know if this doesnt make since!

 

[rania]

what is the proper solution for this situation ??

 

[noetsi]

either gather more data or use fewer predictors.

 

[hlsmith]

I would agree with @noetsi

But I think you would need more data regardless of using just one predictor. You just don't have enough events. An option some times is that if there is a lot of research in the area, you can run a Bayesian logistic model and you get to weight your priors with values from other studies. This process can assist with small sample sizes, but there has to be existing evidence (research results) to guide your selection of prior weights.