Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Aging and mortality of persons with HIV: a novel Kalman Filtering and DMD framework

Alex Viguerie, Elisa Iacomini

TL;DR

A novel variant of the Dynamic Mode Decomposition (DMD), nonnegative DMD is introduced and it is shown that nonnegative DMD provides physically-consistent projections of mortality and HIV diagnosis while remaining purely data-driven, and not requiring additional assumptions.

Abstract

Due to the widespread availability of effective antiretroviral therapy (ART) regimens, average lifespans of persons with HIV (PWH) in the United States have increased significantly in recent decades. In turn, the demographic profile of PWH has shifted. Older persons comprise an ever-increasing percentage of PWH, with this percentage expected to further increase in the coming years. This has profound implications for HIV treatment and care, as significant resources are required not only to manage HIV itself, but associated age-related comorbidities and health conditions that occur in aging PWH. Effective management of these challenges in the coming years requires accurate modeling of the PWH age structure. In the present work, we introduce several novel mathematical approaches related to this problem. We present a workflow combining a PDE model for the PWH population age structure, into which publicly-available HIV surveillance data is assimilated using the Ensemble Kalman Inversion (EKI) algorithm. This procedure allows us to rigorously reconstruct the age-dependent mortality trends for PWH over the last several decades. To project future trends, we introduce and analyze a novel variant of the Dynamic Mode Decomposition (DMD), nonnegative DMD. We show that nonnegative DMD provides physically-consistent projections of mortality and HIV diagnosis while remaining purely data-driven, and not requiring additional assumptions. We then combine these elements to provide forecasts for future trends in PWDH mortality and demographic evolution in the coming years.

Aging and mortality of persons with HIV: a novel Kalman Filtering and DMD framework

TL;DR

A novel variant of the Dynamic Mode Decomposition (DMD), nonnegative DMD is introduced and it is shown that nonnegative DMD provides physically-consistent projections of mortality and HIV diagnosis while remaining purely data-driven, and not requiring additional assumptions.

Abstract

Due to the widespread availability of effective antiretroviral therapy (ART) regimens, average lifespans of persons with HIV (PWH) in the United States have increased significantly in recent decades. In turn, the demographic profile of PWH has shifted. Older persons comprise an ever-increasing percentage of PWH, with this percentage expected to further increase in the coming years. This has profound implications for HIV treatment and care, as significant resources are required not only to manage HIV itself, but associated age-related comorbidities and health conditions that occur in aging PWH. Effective management of these challenges in the coming years requires accurate modeling of the PWH age structure. In the present work, we introduce several novel mathematical approaches related to this problem. We present a workflow combining a PDE model for the PWH population age structure, into which publicly-available HIV surveillance data is assimilated using the Ensemble Kalman Inversion (EKI) algorithm. This procedure allows us to rigorously reconstruct the age-dependent mortality trends for PWH over the last several decades. To project future trends, we introduce and analyze a novel variant of the Dynamic Mode Decomposition (DMD), nonnegative DMD. We show that nonnegative DMD provides physically-consistent projections of mortality and HIV diagnosis while remaining purely data-driven, and not requiring additional assumptions. We then combine these elements to provide forecasts for future trends in PWDH mortality and demographic evolution in the coming years.

Paper Structure

This paper contains 16 sections, 45 equations, 8 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methods
  3. Mathematical model
  4. Ensemble Kalman Inversion
  5. Nonnegative DMD
  6. Standard DMD
  7. Nonnegative DMD algorithm
  8. Application to PWDH age structure model
  9. Mathematical analysis
  10. Results
  11. Reconstruction of age-dependent PWDH mortality curves, 2009-22
  12. Forecasting PWDH mortality, new diagnoses and PWDH population age-structure, 2023-30
  13. Future PWDH mortality
  14. Future HIV diagnoses
  15. PWDH population age structure, 2023-30
  16. ...and 1 more sections

Figures (8)

  • Figure 1: Age distribution of the diagnosed PWH population in the United States over the years 2008-22.
  • Figure 2: The comparison of surveillance (top) and simulated (bottom) mortality.
  • Figure 3: Annual probability of mortality at a given age, in time. Note the consistent decrease in time, punctuated by increases in the upper age ranges in 2020-22 caused by the COVID-19 pandemic.
  • Figure 4: Mortality curves by age for several years, plotted side-by-side. The left panel shows mortality probability over the entire age range; the right panel focuses more closely on the important 40-80 age range.
  • Figure 5: Projection of age-dependent mortality through 2030. The maximum eigenvector is the asymptotic limit of the projected future age-dependent PWDH mortality.
  • ...and 3 more figures