Dear researchers, in real world, a "reasonable" sample size for a logistic regression model is: at least 10 events (not 10 samples) per independent variable. My question is: does this rule refer to the final model that we finally produced or the predictor selection (model development) step where we select and put the candidate predictors (independent variables) into the model which we are going to run using a stepwise manner? For example, my sample size is 100 patients with 40 outcomes, and I select 20 predictors (independent variables) and put them in a logistic regression model, after I run the model using backward selection, I get 4 predictors (independent variables) remaining in the model as they are statistically significant (P
First logistic regression doesn't ask about the number of independent variable, if it is only 1 then the value of exp B provides unadjusted odds ratio, but if the independent variable is more than 1 it provides Adjusted odds ratio by adjusting the other variables.
Now what your question is that how many variables to keep in your study having 100 samples.
So according to my suggestion why you are making a single model make 3-4 models in 1st you can include 4-5 variables and then in 2nd model add 4-5 variables more according to your objective and so on.
Whatever you was doing is also correct but there will be so much loss of information that you don't want too loose.
So one other thing you can do is to do factor analysis, it will decrease your number of variables.
There was a related question some time ago, you may want to have a look there for useful clues: https://www.researchgate.net/post/Whats_the_minimum_sample_size_for_logistic_regression
According to Hsieh (paper referenced in the thread above) in order to detect an OR=2 in a univariate logistic regression with p=.25 alpha=.05 and power=.80 you need about 100 i.i.d. observations. If you include a second covariate with a given correlation rho with your existing one, ceteris paribus, n has to increase to 100/(1-rho^2). Mind that the more covariates you include the higher the correlation you should expect among you Xs and so the larger your sample size should be in order to achieve a desired level of precision in your estimates. Bottomline is: with n=100 you better keep your model very simple, possibly choosing your covariates according to some a priori model you have in mind rather than relying on backward selection devices.
Hi Guys, finally, I have to answer my own question. The "10 events per predictor" rule refers to the model development step (predictor selection step), NOT the final model. Therefore, my example is NOT an adequate practice. In that example, selecting four (instead of 20) predictors to include in the logistic regression model would be adequate as there are 40 events. The following post is a good one as it is really RELEVANT to my question. Thank you!
https://www.statalist.org/forums/forum/general-stata-discussion/general/5060-variable-selection-in-a-logistic-regression-model-with-a-small-number-of-outcomes
Dear Ning,I am no physician/clinician but apart from that the advice you got in this Researchgate thread does not look to me much different from what Clyde Schecther' wrote in his Statalist post. Anyway it's good you got the answer you were looking for at last.
Hi Ning,
As i have earlier said that there are no hard and fast rule for the number of independent variables to select while going to apply logistic regression. While there isjust a thumb rule that you should have atleast 10 cases per independent variables. So if you have 20 predictors the sample should be more than 200.
But this is not true always, you can even use 5 cases per predictor variable by little compermising with the quality of your result.
See this publication in detail. I hope it helps.
Thanks
@ Ravi Prakash Jha, Dear Ravi, thank you so much, but my question is: does this rule refer to the final established model or the model development (predictor selection) process? My question is NOT whether this rule is correct. If you could help me with my question, I would really highly appreciate that. Thank you sir!
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