Which is more appropriate? Poisson or regular linear regression? I am working on a project to predict a range for patient length of stay.  My data consists of 215,000 rows of the following variables (30 total):


*

*LOS (length of stay in days)

*AGE (in years)

*GENDER 

*MARITAL

*DIAGNOSIS 1

*DIAGNOSIS 2

*DIAGNOSIS 3

*... and so on


With the exception of AGE and LOS, all the variables are binary.  The distribution for LOS is heavily skewed - almost all values are between 1-30, with extreme outliers from 50-370 that account for only 0.02% of the data.
My approach to modeling the relationship between LOS and the rest of the variables is as follows.  First, remove the 0.02% outliers for the dependent variable.  Second, do a simple log transform of the dependent variable.  After taking these two steps, the LOS data is normally distributed.  
My question is - is there any reason why I should not simply use plain old multivariate linear regression on this normalized LOS data?  
When I do this, I get highly significant p-values and an R-squared of 0.207.  Which, as I understand it, isn't horrible for complex health care data (please correct me if I am wrong).  This approach also results in nicely distributed residuals.
However, I was looking up different data distributions to see if I should be modeling in a different way.  Other length of stay models on the internet treat the data as a Poisson distribution, which led me here to inquire and hopefully acquire a greater understanding of how to treat this data!  
So, is my methodology sound in this case?  Any and all feedback is greatly appreciated!
 A: LOS is actually very difficult to work with due to its highly nontrivial tail structure. You will encounter many problems, including over dispersion and poor predictability for very long tails. The typical issue is that you will have patients with insanely long LOS who will severely affect your estimate predictions, and these should not be thrown out as outliers because they contain information about rare situations, as opposed to the average healthy patient. 
There have been many papers written on LOS prediction. To list a few:
Comparison of Regression Methods for Modeling Intensive Care Length of Stay
A review of statistical estimators for risk-adjusted length of stay: analysis of the Australian and new Zealand intensive care adult patient data-base, 2008–2009
I would suggest trying some of the techniques mentioned in the second reference. Generally speaking a log linked GLM model for LOS will give you acceptable performance for small LOS. Negative binomials are sometimes used to compensate for overdispersion but I doubt that the significant investment in computing them will give you better performance than a simple GLM. 
In the second reference, you'll also find some suggestions for potentially throwing out outliers. For example, throwing out the top 0.01 percent is sometimes used. For billing purposes, some insurance companies throw out LOS longer than a year because it instantiates a new billing cycle. 
A: I don't see any major problems with your approach.  But I don't count.  Does the audience for your report see any major problems with your approach?  Your sample size is enormous so the CLT is going to help you a lot. You are basically using a log-linear model.  
I would worry a bit about overdispersion (that different groups (represented by your predictors) do not ACTUALLY share a common underlying Poisson distribution).  You can test this by seeing whether the different (most common) predictor combinations actually generate simulated data that looks like your real data.  If they simulate data that looks narrow compared to your actual data, you have a problem.
It is not, by the way, difficult to model this as a Poisson regression without making the assumption of underlying normality.  This is just a generalized linear model.  Doing this would dispense with concern about overdispersion by modeling it as a negative binomial (which allows for considerable overdispersion).
One other thing to consider: R-square, etc. tend to focus on hitting the mark.  If your analysis is cost control, you may want to consider quantile-regression or other less-than/greater-than analyses or weighting the errors.  Your log-transform makes it difficult for you to control or even properly analyze this aspect of the data.  If your model predicts 3 days but the stay is 1 day, is that the same as if your model predicts 3 days but the stay is 9 days?  The log model says these are the same error!!!  Is that really what you mean to imply? 
