Power Calculations in Longitudinal Mixed Effects - from two measurements to three measurements

Hi everyone. In recent weeks, I’ve been going down the rabbit hole about power calculations for longitudinal mixed effects.

One: in PAS software, it states that both in the GEE and mixed effects options, the power remains the same as we move from two measurements to three measurements

Second: The same results are yielded by the software WebPower - Statistical Power Analysis and Sample Size Planning for Linear mixed-effects model

Three: it appears that many of these calculations are based on the book Sample Size Calculations for Clustered and Longitudinal Outcomes in Clinical Research. Sponsored by LLMs, I was able to reproduce their table 5.3

.

Then I extended the codes to two, three, and four measurements. In that simulation, actually, the power increased a little bit, but almost no impact.

So questions are:

1. Are this references and code correct? I find it extremely counterintuitive and surprising that adding a third measurement has no/almost no impact on power.

I was expecting a 10 to 20% decrease on the sample size depending on the circumstances

1. On that note, does anyone have a verified R script that correctly calculates power for longitudinal designs in these scenarios?

I have attached some reports. Thank you

Rplot02.pdf (34.6 KB)

power_simulation_results_wide.pdf (236.3 KB)

Report6 gee.pdf (313.7 KB)