We performed a retrospective cohort study that aimed to identify one or more groups that followed a pattern of chronic, high prescription use and quantify individuals’ time-dependent probabilities of belonging to a high-utilizer group. We analyzed data from 52,456 adults age 18–45 who enrolled in Medicaid from 2009–2017 in Allegheny County, Pennsylvania who filled at least one prescription for an opioid analgesic. We used group-based trajectory modeling to identify groups of individuals with distinct patterns of prescription opioid use over time. We found the population to be comprised of three distinct trajectory groups. The first group comprised 83% of the population and filled few, if any, opioid prescriptions after their index prescription. The second group (12%) initially filled an average of one prescription per month, but declined over two years to near-zero. The third group (6%) demonstrated sustained high opioid prescriptions utilization. Using individual patients’ posterior probability of membership in the high utilization group, which can be updated iteratively over time as new information become available, we defined a sensitive threshold predictive of sustained future opioid utilization. We conclude that individuals at risk of sustained opioid utilization can be identified early in their clinical course from limited observational data.
A new fourth-order difference method for solving the system of two-dimensional quasi-linear elliptic equations is proposed. The difference scheme referred to as off-step discretization is applicable directly to the singular problems and problems in polar coordinates. Also, new fourth-order methods for obtaining the first-order normal derivatives of the solution are developed. The convergence analysis of the proposed method is discussed in details. The methods are applied to many physical problems to illustrate their accuracy and efficiency. MSC: 65N06
This paper discusses a new fourth-order compact off-step discretization for the solution of a system of two-dimensional nonlinear elliptic partial differential equations subject to Dirichlet boundary conditions. New methods to obtain the fourth-order accurate numerical solution of the first order normal derivatives of the solution are also derived. In all cases, we use only nine grid points to compute the solution. The proposed methods are directly applicable to singular problems and problems in polar coordinates, which is a main attraction. The convergence analysis of the derived method is discussed in detail. Several physical problems are solved to demonstrate the usefulness of the proposed methods.
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