Modeling DALYs in Amua

Learning Objectives

  • Review of DALY health outcomes
  • Tips and tricks for modeling DALYs in Amua

Overview of DALY Outcomes

Common Outcomes

  1. Occupancy-based payoffs:
  • Utility/DALY weight applied for a time period / step.
  • Treatment/disease cost per time period / step.
  1. Transition-based payoffs:
  • One-time event-based cost (e.g., disease-related death, initial Dx, etc.).
  • One-time health outcome (e.g., years of life lost to premature mortality)

Disability-Adjusted Life Years (DALYs)

  • Reflect both occupancy- and transition-based payoffs.
  • There’s also very little guidance on how to structure a decision model for DALY outcomes.
  • We’ll show you how today!

DALYs

  • Origin story: Global Burden of Disease Study

  • Deliberately a measure of health, not welfare/utility

  • Similar to QALYs, two dimensions of interest:

    • Length of life (differences in life expectancy)

    • Quality of life (measured by disability weight)

DALYs

DALYs = YLL + YLD

  • YLL (Years of Life Lost)
  • YLD (Years Lived with Disability)

Years of Life Lost to Disease

For a given condition c,

YLD(c) = D_c \cdot L_c

  • D_c is the condition’s disability weight
  • L_c is the time lived with the disease.

Years of Life Lost to Premature Mortality

  • YLL are defined by by a “loss function.”
  • Drawn from a reference life table, indicating remaining life expectancy at age a.
  • YLL(a)= Ex(a)

Years of Life Lost to Premature Mortality

DALYs

DALY(c,a) = YLD(c) + YLL(a)

Evolution of DALY Calculations

  • Historical Practice: Initial GBD studies applied age-weighting and 3% annual time discounting.
  • Changes Post-2010: Discontinuation of these practices for a more descriptive DALY measure.

Current Discounting Practices

  • WHO-CHOICE: Time discounting of health outcomes.
  • Our Methodology: Continuous-time discounting from original GBD equations is retained.

Takeaways

  • Modeling DALYs in Amua is straightforward if you don’t use discounting.
    • For YLDs, use disability weight like you would a utility weight.
    • For YLLs, use one-time “cost” of remaining life expectancy.
      • YLL = tbl_reference_life_table[initial_age + t, 1]

Takeaways

  • But if you do need to discount …
    • You’re going to see some math expressions that take care of discounting for YLL outcomes.
    • This math adds some complexity but not much insight, so I’ll gloss over it a bit
    • We’ll provide you the formulas to use here and in the .amua model file.

Mathematical Formulation for DALYs in AMUA

  • YLD(c) = D_c.

  • YLL(a,t)= Ex(a)\exp(-\ln(1+r)*t).

    • a is the time of death

    • r is the discount rate you’re using in the model (e.g., 3%).

    • t is the cycle number at which premature death occurs.

Mathematical Formulation for DALYs in AMUA

  • YLD(c)= dw_c.

  • YLL(a,t)= tbl_ref_lt[initial_age+t,1] *\exp(-\log(1+ r_disc )* t).

Overview of Decision Problem

  • Progressive disease model (from case study)
  • Focus only on cohort of individuals who develop mild disease.
  • Follow until death (from disease-related or other causes)

Overview of Decision Problem

  • Major difference from case study: can ignore Healthy state.
  • Strategies: Status quo, prevention, treatment

Methods: Structuring the Model

State Transition Diagram

Defining Outcomes in Amua

  • YLD: New Outcome. Use disability weights instead of utility weights!
  • YLL: One-time “event” at time of death from disease.
    • “Cost”: present value of remaining life expectancy at age t in the model.
    • Intuition: we penalize premature death from disease using the remaining life expectancy at the age in which the person dies.
  • Need to also define the discount rate as a parameter r_disc

Interactive Amua Session

Occupancy-Based Payoff: YLD

  • YLD is an “occupancy-based” payoff (i.e., YLD increments by disability weight for each cycle in that health state).
    • Add dw_mild = 0.08
    • Add dw_progressive = 0.15
    • Add dw_progressive_treated = 0.13
  • Mild disease state: dw_mild
  • Progressive disease state: dw_progressive

Transition-Based Payoff: YLL

  • Remaining life expectancies are drawn from the reference life table, or from an endogenous life table.
  • Import reference life table as lookup table—just like we did with background mortality, etc.
  • Remember to use the “Truncate” option because the life table may not extend to the maximum age in the model.

Additional slides below (hit down button).

Life Expectancy & YLL

  • Contextual Choices: Remaining life expectancy values may vary by research context (Anand and Reddy 2019).
  • Historical Method: GBD uses an exogenous life table approximating maximum human lifespan.
  • Alternatives: Endogenous tables or models may be preferred in certain cases.

Exogenous vs. Endogenous Life Tables

  • Distinction: Source of life expectancy values (external vs. internal).
  • Exogenous: Independent mortality risks, using GBD’s reference table.
  • Endogenous: Specific to the population’s mortality risks and health states.

Incremental CEA

  • ICERs are based on cost per DALYs averted
  • Must export expected cost and DALY outcomes, then do ICER calculations outside Amua (e.g., Excel)
  • Alternative: define YLL and YLD outcomes as their negative values.
    • CEA will work, but expected values will be negative.

Thanks!

Draft manuscript (with R code) available online at https://graveja0.github.io/dalys/

References

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Anand, Sudhir, and Sanjay G. Reddy. 2019. “The Construction of the DALY: Implications and Anomalies.” SSRN Electronic Journal. https://doi.org/10.2139/ssrn.3451311.