title: Sample size and optimal design for logistic regression with binary interaction.
abstract: There is no consensus on what test to use as the basis for sample size determination and power analysis. Some authors advocate the Wald test and some the likelihood-ratio test. We argue that the Wald test should be used because the Z-score is commonly applied for regression coefficient significance testing and therefore the same statistic should be used in the power function. We correct a widespread mistake on sample size determination when the variance of the maximum likelihood estimate (MLE) is estimated at null value. In our previous paper, we developed a correct sample size formula for logistic regression with single exposure (Statist. Med. 2007; 26(18):3385-3397). In the present paper, closed-form formulas are derived for interaction studies with binary exposure and covariate in logistic regression. The formula for the optimal control-case ratio is derived such that it maximizes the power function given other parameters. Our sample size and power calculations with interaction can be carried out online at www.dartmouth.edu/ approximately eugened.
authors.affiliation: Dartmouth Medical School, Hanover, NH 03755, U.S.A. eugened@dartmouth.edu
authors.forename: Eugene
authors.initials: E
authors.lastname: Demidenko
mesh_terms: D001249:Asthma / Q000235:genetics; D016022:Case-Control Studies; D004777:Environment; D005823:Genetics; D006801:Humans; D016013:Likelihood Functions; D016015:Logistic Models; D012107:Research Design; D018401:Sample Size