Relative poverty measures aren't the best for measuring poverty. For example, in the US, the poverty line is based on US income and not some absolute measure of poverty.
The question is what is poverty trying to measure, and I think it tries to paint a picture of how the poor are living. One way to get a better picture is to look at the income of the individuals in a particular country at the 10th percentile. The following picture shows where the US is in this respect against other developed countries.
Another question is at what level do you measure poverty - individual or household? An extension to this is how do demographics drive this train? For example, a divorce can split a household that is above the relative poverty line and create two households that below poverty.
I think most treatments of the issue tends to devolve into inequality discussions (although inequality is best discussed over time, and so the real issue here is income level mobility).