Analysing the Time of Bed Availability in Intensive Care Unit of Accident and Orthopaedic Department Using Survival Analysis.

PurposeOptimizing the available resources in a hospital helps to improve the capacity utilization in the respective divisions. Predicting the length of stay (LoS) of patients admitted to Intensive Care Unit (ICU) gives a clear vision to the physicians and the administrative level to improve the productivity and to plan its staffing policy. MethodThe study was carried out for all the patients admitted to the ICU in Accident and Orthopaedic Service to estimate their LoS in ICU using survival analysis. Data obtained were identified as censored or non-censored data and were categorized based on their gender, age and the type of injury. Kaplan-Meier estimates were used to predict the LoS of patients based on the above categories. Finally, the best-fitted survival model, the logistic model was used to identify the significance of gender, age and the type of injury of the patients on their LoS. ResultsThe probability of discharging a female patient within less number of days was higher than that of male patients. Senior adults recorded the highest LoS. When patients were categorized based on the type of injury, highest LoS was recorded by the patients with facial injuries. According to the log-rank test only the levels of age (p value = 0.04) and injuries (p-value = 0.04) show a statistical difference between the respective variable levels. Gender does not show a significance relation with the LoS. ConclusionThe patients' age and the type of injury were significantly related to LoS of ICU patients.

The Number of Complex Roots of a Univariate Polynomial Within a Rectangle

Let f (z) be a nonzero complex univariate polynomialand let R be a rectangle in the complex plane. The number of complexroots of f (z) inside R is given by the winding number of f (z)on R if f (z) has no roots on the boundary of R. In this paper theresult is extended to all rectangles R even when f (z) has roots onthe boundary of R under the condition that f (z) is square-free. Itcan also be used to formulate an algorithm that isolates the complexroots of any polynomial