FITTING THE DISTRIBUTIONS OF LENGTH OF STAY BY PARAMETRIC MODELS

OBJECTIVES. The purpose of this study was to assess the adequacy of th ree widely used models-Lognormal, Weibull, and Gamma-for describing th e distribution of length of stay. This is a fundamental step in the de velopment of outliers resistant (robust) methods for the statistical a nalysis of this kind of data, where the main objective is to determine measures of average and total resource consumption of groups of patie nts. Current practice uses several types of trimming rules, many of wh ich are based on the Lognormal model, although theoretical and experim ental bases are still insufficient. METHODS. The three models were adj usted using robust procedures based on M-estimators to approximately 5 million stays grouped by Diagnosis-Related Groups (DRGs). The resulti ng 3,279 samples were collected in five European countries during 3 ye ars. RESULTS. Most Of the distributions observed could be fitted with one of these models. The descriptions provided by the Gamma and the We ibull models were similar, and the Gamma model could be omitted. The c asemix description provided by the Lognormal-Weibull family was, for c ertain countries, significantly better than the one provided by the si ngle Lognormal model. Often, for a given DRG and a given country, leng th of stay distributions could be described with the same model during several years. A given DRG, however, usually had to be described by m eans of different models for different countries. CONCLUSIONS. Practic al and conceptual consequences of the results are discussed. They can be extended to the analyses of other consumption variables used in hea lth services. Statistical procedures for casemix description, includin g current rules of trimming, should be improved by means of more flexi ble families of models.