I've built a parametric survival model (survreg in R) to predict injury recovery duration using features such as age and treatments. I'm looking at trying model-based boosting using mboost with Weibull, loglog, or lognormal distribution (as described here). Can anyone recommend other alternatives? Has anyone tried neural network methods to predict time to event / duration data?
Yes, neural-network modeling of survival data dates back about 3 decades at least. You might want to consult this PubMed entry and its links.
Such survival analysis suffers from the difficulty, inherent in neural-network modeling, of understanding how particular predictors contribute to the differences in outcomes.
Boosting can be useful, as you can let the data help take into account interactions among predictors that you might not have considered. You at least get some estimate of which predictors are important. You don't, however, know the specific forms of their associations with outcome.
Semi- or fully parametric survival regression models typically provide much better interpretability, and with them you can use your understanding of the subject matter to address specific hypotheses of interest.