I have a dataset (N=350) for which I would like to regress a neuropsychological test score (continuous) on age, education, symptom severity (continuous), and diagnosis (binary). Symptom severity is censored: symptom severity score was only generated if a participant passed a screening item. It appears that a tobit model would work for predicting symptom severity as the dependent variable, but is there a defensible method to include my left-censored variable as a predictor?
One option is to include a variable that is 1 if symptom severity was not measured and 0 otherwise, then code all the symptom severities that were not measured as 0. The coefficient on the 0/1 variable will represent the average test score for those that did not have the severity measured and the slope for the severity will be computed based on those that had severity measures.