How many Christians were in the Roman Empire in the 4th century?

I’m continuing to read Adrian Goldworthy’s How Rome Fell (Yale University Press, 2009).  Goldsworthy makes the point throughout that our knowledge of ancient history is always as certain as some make it out to be.  For example, it is often taken for granted that Christians made up only c. 10% of the Roman population at the time of Constantine’s conversion.  Goldsworthy, however, observes:

….  All the evidence suggests that at the beginning of the fourth century Christians were a minority in the overall population.  It is also regularly asserted that they were a small minority, but this is by no means clear.  As usual, there are no reliable statistics, and, of course, we do not even know how big the empire’s population was.  One recent study suggested that Christians represented 10 per cent of the total, but this remains purely conjectural.

It is very unlikely that the numbers were smaller than this, and they may easily have been two or three times higher…. (p. 183).