I am not sure what specifically you want to compare when comparing two regression models across groups: The difference of a specific regression coefficient, the difference of explained variance, ... ?

But whatever your goal may be: If there are no simple formulas to calculate power for more complex models, you always can use Monte Carlo simulations. A very helpful example of how to do is shown in a recent Stata blog (see https://blog.stata.com/2019/01/10/calculating-power-using-monte-carlo-simulations-part-1-the-basics/ ) that will be extended within the next weeks to show how to write a simulation program for more complex models. Even if you have no access to Stata, the blog will show you how to set up Monte Carlo simulations to calculate power from first principles.

Hope that helps!

I suggest that you use Minitab software to estimate sample size in your study. Very useful.

Hi Brendan,

From what you describe, the Likelihood Ratio Chi-Square Test (using Shieh-O'Brien approximation) works fine.

You can either use this fast calculator:

https://www.dartmouth.edu/~eugened/power-samplesize.php?

Or if you have access to SAS software, you can use proc power (I am giving you a personal code just as a template):

proc power;

logistic

alpha = 0.05

vardist('predictor 1') = binomial(0.08, 1)/*distribution of a dichotomous variable X for "high risk group, yes/no" , (proportion of people with x, n trials [do not change])*/

vardist('predictor 2') = binomial(0.11, 1)/*distribution of a dichotomous variable Y for "high risk group, yes/no" , (proportion of people with x, n trials [do not change])*/

vardist("covariate 1") = normal(33,7)/*mu=mean, sigma=sd. "e.g. age"*/

vardist("covariate 2") = normal(114, 12)/*mu, sigma. "e.g. SBP"*/

vardist("covariate 3") = normal(12, 6)/*mu, sigma. "duration of symptoms"*/

vardist('covariate 4') = binomial(0.12, 1)/*(proportion with microalbuminuria, 1)*/

/*you can add as many as you want, following this format [I recommend sticking to normal or dichotomous covariates]*/

testpredictor = 'aab_pos'

testoddsratio = 2.4 /*Odds ratio between risk strata*/

covoddsratios = (2 2 2 2) /*odds ratio for each covariate, needs to be (# of vardist statements -1) should come from our 'pilot' data*/

responseprob = 0.12/* prevalence of your outcome*/

ntotal = 800 /*total cohort size*/

power = .;/*leave blank, will output power*/

run;

Hopefully this helps.

Best,

Giovane

The sample size used in multiple regression is perhaps the single most influential element under the control of the researcher in designing the analysis. The effects of sample size are seen most directly in the statistical power of the significance testing and the generalizability of the result.

The size of the sample has a direct impact on the appropriateness and the statistical power of multiple regression. Small samples, usually characterized as

having fewer than 30 observations, are appropriate for analysis only by simple regression with a single independent variable. Even in these situations, only strong relationships can be detected with any degree of certainty. Likewise, large samples of 1,000 observations or more make the statistical significance tests overly sensitive, often indicating that almost any relationship is statistically significant. With such large samples the researcher must ensure that the criterion of practical significance is met along with statistical significance.

In multiple regression power refers to the probability of detecting as statistically significant a specific level of R2 or a regression coefficient at a specified significance level for a specific sample size. Sample size plays a role in not only

assessing the power of a current analysis, but also in anticipating the statistical power of a proposed analysis.

The attached table illustrates the interplay among the sample size, the significance level chosen, and the number of independent variables in detecting a significant R2. The table values are the minimum R2 that the specified sample size will detect as statistically significant at the specified alpha level with a power (probability) of 0.80.

For more info, check Multiple Regression Chapter

https://www.amazon.com/Multivariate-Data-Analysis-Joseph-Hair/dp/9332536503/ref=sr_1_1?s=books&ie=UTF8&qid=1547637001&sr=1-1&keywords=Multivariate+Data+Analysis