There are two issues here. First, while DTI is a predictor of mortgage default, it is a fairly weak predictor. The reason is that it tends to be measured badly, for a variety of reasons. For instance, suppose someone applying for a loan has salary income and non-salary income. If the salary income is sufficient to obtain a mortgage, both the borrower and the lender have incentives not to report the more difficult to document non-salary income. The borrower's income will thus be understated, the DTI will be overstated, and the variable's measurement contaminated. There are a number of other examples that also apply.
Let's get more specific. Below are results from a linear default probability regression model based on the performance of all fixed rate mortgages purchased by Freddie Mac in the first quarter of 2004. This is a good year to pick, because it is rich in high DTI loans, and because its loans went through a (ahem) difficult period. The coefficients are predicting probability of not defaulting.
(I am happy to send code and results to anyone interested).
Update: if you want output files, please write directly to me at firstname.lastname@example.org. To obtain the dataset, which is freely available, you need to register with Freddie Mac at link referenced above.