6.6 Power, precision and the size of the effect

The sample-size formula can be read in three directions. Fixing \(n\) and the effect gives the power; fixing \(n\) and the power gives the minimum detectable effect; fixing the effect and the power gives \(n\). In epidemiology the number of available cases is often fixed (all cases of a rare cancer in a region over five years), and the useful calculation is the second: what is the smallest risk ratio this study could reliably detect?

Two features of the formula govern design. The required size grows as the inverse square of the effect on the log scale, so halving \(\log \RR \) quadruples the study. And for a rare outcome or a rare exposure, the number of events in the rarer cell drives precision, which is why cohort studies of rare diseases and case-control studies of rare exposures are both inefficient.

An alternative to power is to design for precision: choose \(n\) so that the confidence interval for the measure of association has a given width. This is often more honest for an estimation study, whose aim is to measure an association rather than to test whether it is zero.

Questions on this section

Stuck on something here? Ask below and it stays attached to this topic.