I am trying to run a model to estimate how well catastrophic illnesses such as TB, AIDS etc affect spending on hospitalization. I have "per hospitalization cost" as the dependent variable and various individual markers as independent variables, almost all of which are dummy such as gender, head of household status, poverty status and of course a dummy for whether you have the illness (plus age and age squared) and a bunch of interaction terms. 

As is to be expected, there is a significant amount -- and I mean a lot -- of data piled up at zero (i.e., no expenditure on hospitalization in the 12 month reference period). What would be the best way to deal with data such as these? 

As of now I decided to convert the cost into `ln(1+cost)` so as to include all observations and then run a linear model. Am I on the right track?