Larger sample sizes will always be needed in order to account for multivariate associations. At least 20 observations per continuous outcome should be taken for every parameter (variable) entered into a multivariate model. At least 30-40 observations are needed for categorical outcomes due to the limited variance associated with measurement. Statistical power decreases with multivariate designs but these designs are desperately needed in the literature to better account for confounding on treatment effects.
Multivariate designs decrease statistical power and increase the needed sample size.
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