Assessing dependence between frequency and severity through shared random effects.

Research on the occurrence and the final size of wildland fires typically models these two events as two separate processes. In this work, we develop and apply a compound process framework for jointly modelling the frequency and the severity of wildland fires. Separate modelling structures for the frequency and the size of fires are linked through a shared random effect. This allows us to fit an appropriate model for frequency and an appropriate model for size of fires while still having a method to estimate the direction and strength of the relationship (e.g., whether days with more fires are associated with days with large fires). The joint estimation of this random effect shares information between the models without assuming a causal structure. We explore spatial and temporal autocorrelation of the random effects to identify additional variation not explained by the inclusion of weather related covariates. The dependence between frequency and size of lightning-caused fires is found to be negative, indicating that an increase in the number of expected fires is associated with a decrease in the expected size of those fires, possibly due to the rainy conditions necessary for an increase in lightning. Person-caused fires were found to be positively dependent, possibly due to dry weather increasing human activity as well as the amount of dry few. For a test for independence, we perform a power study and find that simply checking whether zero is in the credible interval of the posterior of the linking parameter is as powerful as more complicated tests.

Developing emergency department physician shift schedules optimized to meet patient demand.

OBJECTIVES: 1) To assess temporal patterns in historical patient arrival rates in an emergency department (ED) to determine the appropriate number of shift schedules in an acute care area and a fast-track clinic and 2) to determine whether physician scheduling can be improved by aligning physician productivity with patient arrivals using an optimization planning model. METHODS: Historical data were statistically analyzed to determine whether the number of patients arriving at the ED varied by weekday, weekend, or holiday weekend. Poisson-based generalized additive models were used to develop models of patient arrival rate throughout the day. A mathematical programming model was used to produce an optimal ED shift schedule for the estimated patient arrival rates. We compared the current physician schedule to three other scheduling scenarios: 1) a revised schedule produced by the planning model, 2) the revised schedule with an additional acute care physician, and 3) the revised schedule with an additional fast-track clinic physician. RESULTS: Statistical modelling found that patient arrival rates were different for acute care versus fast-track clinics; the patterns in arrivals followed essentially the same daily pattern in the acute care area; and arrival patterns differed on weekdays versus weekends in the fast-track clinic. The planning model reduced the unmet patient demand (i.e., the average number of patients arriving at the ED beyond the average physician productivity) by 19%, 39%, and 69% for the three scenarios examined. CONCLUSIONS: The planning model improved the shift schedules by aligning physician productivity with patient arrivals at the ED.