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Estimating healthcare expenditures is important for policymakers and clinicians. The expenditure of patients facing a life-threatening illness can often be segmented into four distinct phases: diagnosis, treatment, stable, and terminal phases. The diagnosis phase encompasses healthcare expenses incurred prior to the disease diagnosis, attributed to frequent healthcare visits and diagnostic tests. The second phase, following diagnosis, typically witnesses high expenditure due to various treatments, gradually tapering off over time and stabilizing into a stable phase, and eventually to a terminal phase. In this project, we introduce a pre-disease phase preceding the diagnosis phase, serving as a baseline for healthcare expenditure, and thus propose a five-phase to evaluate the healthcare expenditures. We use a piecewise linear model with three population-level change points and $4p$ subject-level parameters to capture expenditure trajectories and identify transitions between phases, where p is the number of covariates. To estimate the model’s coefficients, we apply generalized estimating equations, while a grid-search approach is used to estimate the change-point parameters by minimizing the residual sum of squares. In our analysis of expenditures for stages I–III pancreatic cancer patients using the SEER-Medicare database, we find that the diagnostic phase begins one month before diagnosis, followed by an initial treatment phase lasting three months. The stable phase continues until eight months before death, at which point the terminal phase begins, marked by a renewed increase in expenditures. 

Abstract Although sonodynamic therapy (SDT) has shown promise for cancer treatment, the lack of efficient sonosensitizers (SSs) has limited the clinical application of SDT. Here, a new strategy is reported for designing efficient nano‐sonosensitizers based on 2D nanoscale metal–organic layers (MOLs). Composed of Hf‐oxo secondary building units (SBUs) and iridium‐based linkers, the MOL is anchored with 5,10,15,20‐tetra(p‐benzoato)porphyrin (TBP) sensitizers on the SBUs to afford TBP@MOL. TBP@MOL shows 14.1‐ and 7.4‐fold higher singlet oxygen (¹O₂) generation than free TBP ligands and Hf‐TBP, a 3D nanoscale metal–organic framework, respectively. The¹O₂generation of TBP@MOL is enhanced by isolating TBP SSs on the SBUs of the MOL, which prevents aggregation‐induced quenching of the excited sensitizers, and by triplet–triplet Dexter energy transfer between excited iridium‐based linkers and TBP SSs, which more efficiently harnesses broad‐spectrum sonoluminescence. Anchoring TBP on the MOL surface also enhances the energy transfer between the excited sensitizer and ground‐state triplet oxygen to increase¹O₂generation efficacy. In mouse models of colorectal and breast cancer, TBP@MOL demonstrates significantly higher SDT efficacy than Hf‐TBP and TBP. This work uncovers a new strategy to design effective nano‐sonosensitizers by facilitating energy transfer to efficiently capture broad‐spectrum sonoluminescence and enhance¹O₂generation.