I was thinking of all of the lifestyle factors that might make one susceptible to tooth loss for >10 years prior to the study (this was a selection criteria for the participants): lack of education, nutrition, medical care, etc. The paper never controls for why these people lost their teeth.
(To be fair to the researchers of this paper, they do discuss some of this, but they focus on a causal relationship between tooth loss and the other factors. They never really consider that the relationship between these factors and tooth loss could be reversed.)