Repeated measurements with missing values

Question

The data is measured in two biological replicates with two technical replicates, each.

• Each variable might be detected only in one or more replicates, in the others it is considered missing at random.
• Each variable is measured with zero (missing) to dozens of data points in each experiment.
• Each measurement comes with its own estimated variance

The question for each variable (which was detected at least once): Does its mean deviate from 0? We can assume that the data is normally distributed.

What would be an appropriate test to apply to this data with randomness on many levels?

Answer 1

Let me propose an answer - I am happy to hear constructive criticism:

1. Merge measurements of technical replicates (taking the union)
   • I assume that the between-replicates variation is about the same as the within-replicate variation (for any variable).
2. Apply statistical tests of difference of mean for the combined data for each biological replicate and each variable. Apply multiplicity correction.
3. For variables detected in both biological replicate sets:
   • if direction of change is in both direction:
     • calculate combined p-values using Fisher's method
   • else, set p-value to 1
4. For variables seen in only one biological replicate set, use its original p-value (just penalize but don't remove them)

Do I miss any assumptions such that you would deem this procedure unsound?