Fitting the distributions of length of stay by parametric models

The purpose of this study was to assess the adequacy of three widely used models--Lognormal, Weibull, and Gamma--for describing the distribution of length of stay. This is a fundamental step in the development of outliers resistant (robust) methods for the statistical analysis of this kind of data, where the main objective is to determine measures of average and total resource consumption of groups of patients. Current practice uses several types of trimming rules, many of which are based on the Lognormal model, although theoretical and experimental bases are still insufficient.

The three models were adjusted using robust procedures based on M-estimators to approximately 5 million stays grouped by Diagnosis-Related Groups (DRGs). The resulting 3,279 samples were collected in five European countries during 3 years.

Most of the distributions observed could be fitted with one of these models. The descriptions provided by the Gamma and the Weibull models were similar, and the Gamma model could be omitted. The casemix description provided by the Log-normal-Weibull family was, for certain countries, significantly better than the one provided by the single Lognormal model. Often, for a given DRG and a given country, length of stay distributions could be described with the same model during several years. A given DRG, however, usually had to be described by means of different models for different countries.

Practical and conceptual consequences of the results are discussed. They can be extended to the analyses of other consumption variables used in health services. Statistical procedures for casemix description, including current rules of trimming, should be improved by means of more flexible families of models.