Power and sample size calculations for studies involving linear regression

This article presents methods for sample size and power calculations for st udies involving linear regression. These approaches are applicable to clini cal trials designed to detect a regression slope of a given magnitude or to studies that test whether the slopes or intercepts of two independent regr ession lines differ by a given amount. The investigator may either specify the values of the independent (x) variable(s) of the regression line(s) or determine them observationally when the study is performed. In the latter c ase, the investigator must estimate the standard deviation(s) of the indepe ndent variable(s). This study gives examples using this method for both exp erimental and observational study designs. Cohen's method of power calculat ions for multiple linear regression models is also discussed and contrasted with the methods of this study. We have posted a computer program to perfo rm these and other sample size calculations on the Internet (see http: //ww w.mc.vanderbilt.edu/prevmed/psintro.htm). This program can determine the sa mple size needed to detect a specified alternative hypothesis with the requ ired power, the power with which a specific alternative hypothesis can be d etected with a given sample size, or the specific alternative hypotheses th at can be detected with a given power and sample size. Context-specific hel p messages available on request make the use of this software largely self- explanatory. Controlled Clin Trials 1998;19:589-601 (C) Elsevier Science In c. 1998.