Although many researchers in the field of health economics and quality of care compare the length of stay (LOS) in two inpatient samples, they often fail to check whether the sample meets the assumptions made by their chosen statistical test. In fact, LOS data show a highly right-skewed, discrete distribution in which most of the observations are tied; this violates the assumptions of most statistical tests.
To estimate the type I and type II errors associated with the application of 12 different statistical tests to a series of LOS samples.
The LOS distribution was extracted from an exhaustive French national database of inpatient stays. The type I error was estimated using 19 sample sizes and 1,000,000 simulations per sample. The type II error was estimated in three alternative scenarios. For each test, the type I and type II errors were plotted as a function of the sample size.
Gamma regression with log link, the log rank test, median regression, Poisson regression, and Weibull survival analysis presented an unacceptably high type I error. In contrast, the Student standard t test, linear regression with log link, and the Cox models had an acceptable type I error but low power.
When comparing the LOS for two balanced inpatient samples, the Student t test with logarithmic or rank transformation, the Wilcoxon test, and the Kruskal-Wallis test are the only methods with an acceptable type I error and high power.