Calculating Power for a logistic regression with 76 observations

[Patrick Abi Nader]

Hello All,

I have a sample of 76 participants that I am including in a logistic regression model. I am associating 7 independent variables with my outcome. Five of the seven variables are continuous, one is binary, and one is categorical. I am aware that usually the recommendation is to have 10-20 observations for each independent variable, but I cannot increase my sample. I would like to know the power that I am getting with the sample that I have.
I ran across the user written "Philip Ender" command

powerlog

but it is not what I am specifically trying to do. Do you folks have any suggestions?

Thank you
Patrick

[Clyde Schechter]

To answer your question would require more information than you have provided. What are the exact null and alternate hypotheses you want to tun a test on? And knowledge of the correlations among the variables is also required. Even when all of that information is given, I do not know if there is a Stata program that can do this kind of power calculation for you, but there is plenty of other software for sample size calculations.

That said. The recommendation of 10-20 observations per predictor is a fairly loose guideline; some would say that it should be more like 30 or even 50.

[Carlo Lazzaro]

Patrick:
You're right in stating that 10-20 observations per predictors are usually considered enough to play on the safe side of the (inferential) matter.¹
Clyde is right in highlighting that it is nothing more than a rule of thumb.

Reference:
1 Katz MH. Multivariable Analysis. Second Edtion. NY: Cambridge University Press, 2006: 81.

[Steve Samuels]

The rule of thumb is not for observations per predictor, but for events per predictor variable (EPV). with events defined as the smaller of the numbers of successes and failures.

[Carlo Lazzaro]

Steve is correct.
The rule of thumb of 10-20 observations per predictor refers to OLS, mainly.

[Marcos Almeida]

Hello Patrick,

Maybe the issue in your case will be the "effect size" - i.e., the odds ratio - for you have the sample size, and I guess you will work with alpha = 0.05 and power around 80% (for 90% would "bite" the estimation even more).

Once I had a similar case. Under ideal conditions, with mean = 0 and sigma = 1 (is this "real" in a logit model with several predictors?),considering the probability of X = 1 when Y = 1 is 20%, I gather you're bound to be able to detect Odds Ratio beyond 2.2. If this is feasible as well as reasonable for your study question, this may be the best you can get. The more variables you include, the lower the power, I fear.

Best,

Marcos