Deep learning does not do this.
Data with less noises are what most deep learning and non statistical models does well. Meaning that image, nlp, etc.. deep learning does well. But data with lots noises/uncertainty/variance or even data that isn't large enough, such as time series, currently statistical models are still king (https://en.wikipedia.org/wiki/Makridakis_Competitions).
Even with healthcare you're answering a question/ hypothesis. This is where statistical models strength lies because all statistical models are hypothesis tests and vice versa. There are very little opportunity in healthcare where you would use deep learning compare to statistic. I've seen NLP can be of use but the majority of work in healthcare are inference/casuality base (this is why they use propensity model so much). I'm in this space public healthcare.