Hellow, again,

I’m working on the design of a longitudinal echocardiographic study in pediatrics, and I’d be very grateful for your input on a few statistical challenges I’m trying to resolve.

Let’s say I’ve already measured the within-subject standard deviation (SD) and intraclass correlation coefficient (ICC) for a given parameter (e.g., LV wall thickness or mitral inflow velocity), and I’ve optimized my protocols. I’ve decided that using, say, 10 repeated measurements per subject gives me the most realistic level of precision for that parameter.

Now, my main question is: - > How do I determine the number of patients I need to detect a true change over time, especially in children where within-group variability is inherently high due to age-related differences?

But here’s the catch:

• Within-subject variance may change over time. Some children have higher SD at baseline than at follow-up (or the opposite).
• The intrinsic variability of the parameter itself may evolve over time (e.g., during growth or puberty).
• Standard mixed-effects models often assume equal variance (homoscedasticity) over time — which could lead to misinterpretation.
• Using medians across replicates might reduce outliers, but could also mask true biological trends.

So I'm wondering:

• Is there a way to model or calculate the required sample size while accounting for the number of repeated measurements and the parameter’s intrinsic variability?
• If I’m measuring 25 different parameters, each with different CV or SD, could I optimize by adjusting replicates instead of just increasing n?
• And finally — could center-specific variability (equipment, staff, protocols) be factored in? Ideally, each center could measure its own reproducibility, and plug that into a formula that combines intrinsic variability and number of replicates per parameter.

Has anyone tackled something like this — or come across a modeling strategy, framework, or rule-of-thumb that would help?

Many thanks in advance for any thoughts or resources!