mash with multi-level conditions

[ghost]

Hello. Great package - however, I have a question about defining conditions.

In our experiment expression data and genotype data were obtained from 50 patients commencing drug treatment, The samples were obtained from three tissues (skin, blood, and synovium) at three time points (baseline, week 2, and week 4). Therefore, for each patient we have data for 9 "conditions":

Skin - baseline Skin - week 2 Skin - week 4 Blood - baseline Blood - week 2 Blood - week 4 Synovium - baseline Synovium - week 2 Synovium - week 4

eQTLs have been identified in each of these conditions and now there are two questions that we would like to answer with mash:

1. To what extent are eQTLs shared across time within a tissue? e.g. How many baseline skin eQTLs are shared with week 4 skin eQTLs?

2. To what extent are eQTLs shared across tissues within a time point? e.g. How many baseline skin eQTLs are shared with baseline blood eQTLs?

My question is whether it would be more appropriate to fit one mash model with all of the conditions to look at the above questions together, or to fit multiple mash models with subsets of the conditions to look at the questions separately?

i.e. Can a single mash model be used to investigate eQTL sharing across multi-level conditions? In this example the levels are tissue and time point.

Thank you.

[stephens999]

great question! With only 9 total conditions I would do them all at once.

if you had many more time points and many more tissues I might be more tempted by separate analyses to manage complexity and focus the analyses on the specific comparisons you are interested in. But 9 total is small enough I would just do them all at once.

[ghost]

Thank you! Sounds reasonable.

[AshleyRider]

@stephens999

Following on from OP's question about multi-level conditions, I'm wondering about how best to identify eQTLs with differential effects in these sort of studies.

The "mash with common baseline" approach seems useful for identifying eQTLs with differential effects across time within a tissue, but because there are three tissues (and therefore three baselines) I don't think this would work? A solution would be to subset the data and analyse each tissue separately; another would be to analyse everything and run three different mash models, each with a different baseline. Or is the "common baseline at mean" approach more appropriate here?

Sorry for the barrage of questions! I ask because we have a similar study and we are primarily interested in identifying eqtls with differential effects along different axes, like in OP's question, i.e. differences across time and differences between tissues. For looking at time, the common baseline approach seems right, but maybe in these multi-level situations it's just best to stick to e.g. "LFSR < 0.05 in at least one condition with effect within factor of 2" to define sharing between two conditions and define effects that don't meet these thresholds as unshared (i.e. differential).

[pcarbo]

@AshleyRider Your intuition is correct that the "common baseline" approach would be desirable, but unfortunately it isn't well suited for your situation. The complication that arises is that you need to account for measurement correlations amongst both (i) the time points and (ii) the tissues (skin, etc). The "common baseline" mash setup can handle (i) very well, but isn't flexible enough to also handle (ii). So, in short, the V matrix needs to model all those correlations — this is a hybrid situation that (as far as I am aware) we hadn't considered previously. For now, it may be best to proceed with the standard mash approach, which would be able to model (i), but not as accurately as the "common baseline" approach. Hope this helps.

[AshleyRider]

@pcarbo Thanks very much for your response - this is very helpful.