[Question] What fraction of breakthrough COVID cases are attributable to low antibody count?

To what extent are COVID cases in vaccinated people a result of low antibody count, vs other factors (e.g. initial viral load)? Where does most of the variance come from?

Motivation for this question: in a world where most breakthrough COVID cases hit people with low antibody count, one could get some kind of antibody test (probably of a particular type) and then either (a) get an extra vaccine if antibodies are low, or (b) just don’t worry if antibody counts are high. That makes antibody tests (of whatever the particular type is) very high value, since we can behave very differently in those two cases. In a world where most of the variance comes from other factors (like initial viral load), results of an antibody test don’t provide so much value.

Related: Is antibody testing to assess effects of vaccines on you a good idea?