A NOTE ON ESTIMATING A MEAN COST OF HOSPITAL STAY WITH INCOMPLETE INFORMATION pp. 309-317
Authors: (Isabella Locatelli and Alfio Marazzi, Institute of Social and Preventive Medicine (IUMSP), Centre Hospitalier Univ. Vaudois and Univ. of Lausanne, Switzerland)
Abstract: The estimation of a mean hospital cost has a great economic impact in hospital budgeting, funding and reimbursement. A typical feature of hospital data is that not all patients are followed up until the regular endpoint (home discharge). For example, a patient may die or be transferred to a different hospital before the end of his stay. In this case, his complete length of stay (LOS) and cost of stay are unobserved. In such situations cost and LOS are said to be “right censored”. Survival analysis techniques can be used in order to estimate the mean LOS in the presence of right censoring. These techniques are usually based on the assumption of independence between the unobserved complete LOS and the unobserved censoring time. Under this assumption, the censoring mechanism is said to be “non-informative”. Unfortunately, on the cost scale, the censoring mechanism is always informative, i.e., the unobserved complete cost and the unobserved censoring cost are generally correlated, due to the inherent patient heterogeneity with respect to cost accumulation. When standard survival analysis techniques - such as Kaplan Meier or Proportional Hazard models - are directly applied to cost data, the mean cost estimates are biased. In this note we discuss informative censoring and its effects on mean cost estimates. Moving from a very general and flexible model for the relationship between unit cost (e.g., daily cost) and LOS, we show that both a positive or a negative correlation can arise between the unobserved complete cost and the unobserved censoring cost. This result contradicts the general believe that the correlation between cost and censoring cost is always positive and, therefore, that the mean cost is generally overestimated. We explain why direct application of survival analysis techniques to the cost distribution can also lead to an underestimation of the mean cost.