I have an one-factor (5 levels of disease staging) expt. We were given whatever samples we could get, so even though it's rather unbalanced, there's not much we could do.

These are the # of samples:

Block size could be 5-10 (samples can be processed in such sized batches). So this is rather unbalanced. Further, about 60 samples are paired to about 25 patients (some patients have 2 samples from 2 separate visits, some have 3). Moreover, some paired samples are from the same stage, some have different stages (disease progressed over the visits).

We interest in finding the marker for disease progression. But what would be the best way to do this design? Should I deal with the unbalance just fill in some NA spots and randomly assign? Block size 10 would be convenient, and I would put paired samples in the same block but assigning stages will have to consider the overweight of some stages due to the paired samples, particularly in the case where 3 samples from the same pt has the same stage and in the same block, which will not be good. Should I just discard one sample?

Would limma still be good to analyze this? I guess if DOE is done well it should be fine? Thanks for any suggestion!

There is no need to do crazy stuff like adding fake NA samples. There is no need to discard samples. limma will handle unbalanced designs just fine. In fact, your table suggests that the number of samples is actually quite comparable across stages. I wouldn't consider a design to be strongly unbalanced unless we were looking at order of magnitude differences in sample sizes.

While I don't really understand the blocking setup, I would hope that the experimenters had the sense to avoid putting all samples from the same stage in a single processing block. If so, you can use limma with an additive model, probably something along the lines of ~block + stage in your design matrix, and specifying patient as the blocking factor in duplicateCorrelation.

If most or all of the blocks consist of samples from the same stage... then it becomes more difficult, as the stage and block effects will be confounded in the above design. To get around this, I would only keep one sample from each patient, use ~stage in the design matrix and use block in duplicateCorrelation.