Global poverty line is fine for comparing across countries. But, global poverty line can't be used at a disaggregate level. For example, Indian states are like countries. We have to use state level poverty levels derived from national poverty line (and not global poverty line).
Similarly, there is lot of talk about multi-dimensional poverty. But there are problems of aggregation etc.
These issues are discussed in a working paper of IGIDR, Mumbai.
See working paper C. Rangarajan and S.Mahendra Dev "Counting the poor and other issues", working paper no.048, Indira Gandhi Institute of Development Research, Mumbai, India