An explanatory bi-variate model for surgery-duration and its empirical validation

Modeling the distribution of surgery-duration has been the subject of much research effort. A common assumption of these endeavors is that a single distribution is shared by all (or most) subcategories of surgeries, though parameters’ values may vary. Various distributions have been suggested to empirically model surgery-duration distribution, among them the normal and the exponential. In this paper, we abandon the assumption of a single distribution, and the practice of selecting it based on goodness-of-fit criteria. Introducing an innovative new concept, work-content instability (within surgery subcategory), we show that the normal and the exponential are just two end-points on a continuous spectrum of possible scenarios, between which surgery-duration distribution fluctuates (according to subcategory work-content instability). A new explanatory bi-variate stochastic model for surgery-duration is developed, which reflects the two sources affecting variability—work-content instability and error. A newly defined extended exponential distribution is used to model the former, and a multiplicative normal/lognormal error to model the latter. The family of distributions, spanned by the new model, is shown to describe well existent diversely shaped distributions. The new model is statistically explored and empirically validated, using a database of ten thousand surgeries. Incorporating covariates in the model is discussed.