# Effective sample size reduction for correlated data analyses

In power and sample size calculations, and minimum detectable effect analyses for GEE, I have often seen an effective sample size reduction used to account for correlation. The idea is that the more correlated certain clusters are, like labs within a patient, or people within a town, the less precision you have to measure an effect. The effective sample size reduction is given as a constant scalar (less than 1) that multiplies the power expression for independent data. So the n is reduced by a constant, the power by a constant, and the minimum detectable effect (by the inverse of) a constant.

Is this a rigorous approach? Is there an accepted method for calculating this value? Has it been discussed in the literature? Does it matter if the modeling approach is linear, logistic, or survival models?

• Do you mean the design effect (pdf), $DE = 1+\rho(m-1)$? – gung - Reinstate Monica Apr 11 '18 at 13:31
• @gung yes! Thanks for the link. Are you able to speak to whether the DE (or DEFF) quantitatively relates to power expression(s) for common modeling approach(es)? – AdamO Apr 11 '18 at 13:36
• AFAIK, it is the same for OLS, logistic / Poisson / other GLMs, proportional hazards models, etc. I'm not sure how it works for a GEE. – gung - Reinstate Monica Apr 11 '18 at 13:41
• @gung I'm not following. What is the same? Do you mean that the design effect is calculated in the same fashion for all models based on the intracluster variance? The GEE is a general case of all those models, but allows explicit specification of correlation structures, so it seems relevant. But I'm still failing to connect the DE to power in an intelligent way. – AdamO Apr 11 '18 at 15:15
• I mean it works the same--you use the same formula, above. Generally, you have some actual N, but your effective N is less than the amount of data you have due to clustering. So you divide N/DE to get your effective N. For purposes of power analyses, you can work backwards. – gung - Reinstate Monica Apr 11 '18 at 15:35