Simple and multiple linear regression: sample size considerations

ObjectiveThe suggested “two subjects per variable” (2SPV) rule of thumb in the Austin and Steyerberg article is a chance to bring out some long-established and quite intuitive sample size considerations for both simple and multiple linear regression.Study Design and SettingThis article distinguishes two of the major uses of regression models that imply very different sample size considerations, neither served well by the 2SPV rule. The first is etiological research, which contrasts mean Y levels at differing “exposure” (X) values and thus tends to focus on a single regression coefficient, possibly adjusted for confounders. The second research genre guides clinical practice. It addresses Y levels for individuals with different covariate patterns or “profiles.” It focuses on the profile-specific (mean) Y levels themselves, estimating them via linear compounds of regression coefficients and covariates.Results and ConclusionBy drawing on long-established closed-form variance formulae that lie beneath the standard errors in multiple regression, and by rearranging them for heuristic purposes, one arrives at quite intuitive sample size considerations for both research genres.