I see several problems with your analysis. First, LOS is not a normally distributed variable, and I am not sure that logging it gets you to a better place. If you are only looking at people who were hospitalized (thus, no zeros), then you probably have something like a Poisson distribution (with mostly 1 or 2 day stays but a few long stays as well). This suggests that your model should be a count model. You should be reviewing the dispersion of the data to help determine which count model it should be.

I don't know why you'd limit the data to a given percentile? It seems to me that doing so will move the bar from year to year, and thus you may have inconsistent measurements. Why not use all the data? An appropriate mode should accommodate the nature of the data.

Next, if you have multiple years, why are you comparing them in a piecemeal fashion, rather than in an appropriate time-series model (if the data are in the aggregate), or longitudinal model (if they are at the patient level)?

I am attaching a link to a paper I wrote on interrupted time series analysis that would answer your question, if your data is in the aggregate. If you use Stata, I have written a command that performs this analysis for you. It is available for download from within Stata by typing: ssc install itsa

I hope this helps

Ariel

Article Applying a propensity-score based weighting model to interru...

I'm adding consideration from Ariel answer. Are you sure that from 2009 till 2012 no changing in technology (drugs, pathways) occoured in the hospital? And the same no changing from personnel capacity?

Ciao

Davide

We are talking about total hip replacement surgery only.

Kisalaya.