What statistics algorithm should be used to identify why something is increasing? I work at a hospital and have been asked to use statistical algorithms to identify an increase in Census which is really the number of patient days in a hospital. It has trended up about 15 percent in the past three months and we have not been able to identify why using basic descriptive statistics. I have dozens of fields to choose from such as PatientAge, DiagnosisCode, Physician who admitted patient, InsuranceType, ProcedurePerformed etc. There is an integer field called units and the overall units has increased which means there are more patients coming to the hospital. I want to analyze all of these fields and identify which field or combination of fields is producing an increase in Units. I tried simple correlations but nothing is standing out.  Could I use regression or decision trees to predict an increase in something? Thanks.
 A: First, it is important to consider the reference period when saying "trended up".  If the base period included winter months, then many medical centers have an increase because of the decrease caused by a severe winter (although this is more true for outpatient than inpatient visits).  But you've stated census as bed days which if I understand you may not include non-filled beds.  So first census needs to be precisely defined and perhaps separate occupancy from length of stay for those who were admitted.  If you want to consider just the number of patients admitted you may need to consider variables outside of individual patient characteristics.
On the other hand if you want to model length of stay for those admitted, as a function of patient characteristics, then you have perhaps an easier task and can use a regression model such as the Cox proportional hazards model to predict length of stay, possibly censoring on in-hospital death.
Another approach would be to consider differential frequencies of major admitting diagnosis, e.g., over time is one diagnosis increasing relative to others.  This is pertinent to winter increases in infectious diseases and summertime increase in trauma due to outside activities.
A: Sounds like you are working with patient level raw data. Without knowing much detail about your data, I would structure the problem like this (assuming you have at least several years of data):
1) Define the target variable as something at a higher level (higher level than patient-level), such as unique patients for a given day (one level up might be patients for a given week).
2) Aggregate all your candidate predictors up to the same level as the target you are predicting. So if your target is daily patients, you could create candidate model features like "insurance type A %", "insurance type B %", "diagnosis code 1 %", "diagnosis code 2%", "% male", "% age < 5", "% age 6-10" etc. etc. (where % = % of daily patients). You should start off with really wide data. As many different features you can join on that you think might have predictive power. If you are looking at only 1 hospital location, I would also join on daily temperature related features.
3) Perform some feature selection type exploration (scatter plots, histograms, box plots, correlations, trees, pca, etc.) and reduce predictors down to a manageable number.
4) Run some algorithms. I'm guessing for this particular problem, a simple stepwise regression would tell you enough if all you're interested in is descriptive analytics (as opposed to a more robust predictive model, which would require performing some train/test/validate tasks in addition).
