# Calculating confidence interval for average hospital length of stay, case-mix adjusted, in R

I'm looking for sample R code, or pointers to sample R code for the following. (Gentle) critique of the approach would also be appreciated. I'm not a statistician and I'm pretty new to R.

I have duration of hospitalization ("length of stay"=LOS) data for 2,000 patients from my hospital and 50,000 patients from a comparison data set. Each patient has a discharge year (YEAR) and is assigned to a diagnosis group (DG). My goal is to compare (with confidence intervals) the overall average LOS at my hospital to the expected average LOS if those patients had been part of the comparison data set.

Note that for a specific year and specific DG there may be anywhere from a few to 1,000s of patients, and, of course, the distribution of LOS is not normal. There could possibly even be a DG with 1 or more patients for a given year in my hospital's data but none in the comparison data set.

The approach I was considering was to create a comparison group where a random patient from the comparison data set is chosen for each patient from my hospital. The random patient would be matched by YEAR and DG. I would calculate the expected average LOS for this group and then repeat the process 10,000 times to determine the 2.5th to 97.5th percentile. I would repeat for each year and plot my hospital's average LOS versus the 95% CI for the expected average LOS.

To deal with the issue of there not being a match for a patient for a given DG for a given YEAR I was thinking of loosening the match criteria to pick patients from the previous or next year. I could keep broadening the match year until there were at least N patients from which to randomly pick.

Thoughts?

• have you seen the heritage health prize? It sounds uncommonly like your problem, so if you go to www.kaggle.com you may be able to find some suggestions as to how to deal with this kind of problem – richiemorrisroe May 26 '11 at 16:53

The suggestion by Jeff to consider nonparametric methods is a good one. Semiparametric models such as the Cox proportional hazards model may be even better because of their flexibility. The Cox model in particular will handle one feature of the problem that the other methods discussed will not: LOS is actually an incompletely observed random variable. Those patients dying in the hospital should not be considered to have a short LOS but to have their LOS right censored at the day of death.

From the Cox model you can estimate median and mean LOS, covariate adjusted. Examples are at http://biostat.mc.vanderbilt.edu/wiki/pub/Main/FHHandouts/slide.pdf with S code at http://biostat.mc.vanderbilt.edu/wiki/pub/Main/FHHandouts/model.s

You could set up a model that predicts LOS using YEAR, DG and other variables available (hospital datasets usually include age, gender and many other potential predictors).

One way of comparing your hospital to the comparison set is joining the two datasets and adding a hospital column (either 'my hospital' or 'comparison hospital'). If the conditions (linearity, independence, normality, homoscedasticity) of a linear model are met, you could use a simple ANCOVA. It looks reasonable to assume that LOS differences between your hospital and the comparison data may depend on DG, so you should probably include the DG hospital interaction term. Depending on the details more sophisticated models may be needed.R code sample:

model = lm(LOS ~ YEAR + DG * hospital, data=theJoinedTable)
summary(model)


Given that you're comparing n groups ($n > 2$) and that your count data are, as you say, likely non-normally distributed, I wonder if perhaps applying Kruskal–Wallis analysis of variance to your data might be an option.