Collaborators and Thanks

• Jinyi Zhu, Ph.D. (Vanderbilt)
• Ashley Leech, Ph.D. (Vanderbilt)
• Shawn Garbett, MS (Vanderbilt)
• Marie Martin, Ph.D. (Vanderbilt)

Summary

Summary

Extending the HTA/CEA Toolkit

Building Decision Analytic Capacity in LMICs

Challenges and Contributions

Challenges and Contributions

DALYs: Background

Years of Life Lost to Disease

For a given condition c,

YLD(c) = D_c \cdot L_c

Years of Life Lost to Premature Mortality

Life Expectancy & YLL

Exogenous vs. Endogenous

DALYs

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

Evolution of DALY Calculations

Overview of Decision Problem

Overview of Decision Problem

Overview of Decision Problem

life_table_year = 2019 
location = "United Kingdom"
cause_id = 491 # CVD
sex = "Both"
radix = 100000  # Population basis for life tables

Data Sources

Key Assumptions and Parameters

Key Assumptions and Parameters

Cause-Deleted Background Mortality

Cause-Deleted Background Mortality

Cause-Deleted Background Mortality

Solution

CVD-Deleted Life Table

Constructing the cause-deleted life table requires two necessary inputs:

Parametric Mortality

Figure 1: Fitted vs. Observed Mortality Using Heligman-Pollard Parametric Mortality Model

Checkpoint: Survival

Checkpoint: CVD Prevalence

Figure 2: Prevalence by Age, Model vs. GBD Data

Methods, Part 1: Structuring the Model

Approach 1: Markov Trace (Beginner)

Process

Summary and Comparison

Intensity Matrix: Approach 1 (Markov Trace)

Embedding

Probability Matrix: Approach 1 (Markov Trace)

Markov Trace

Markov Trace: Approach 1

• Must manually calculate changes in disease related deaths in Markov trace.

Approach 2: Transition States (Intermediate)

Process

Approach 1 vs. Approach 2

Summary and Comparison

Non-Markovian Elements

Non-Markovian Elements

Rate Matrix: Approach 2 (Transition States)

Embedding

Accumulator Transition State

• After embedding, trDCVD reflects an accumulator state (i.e., P(trDCVD trDCVD )=1)
• We must zero out the probability of remaining in the state to convert it to a transition state.
• We can do this because the Markovian submatrix remains closed!

Probability Matrix: Approach 2 (Markov Trace)

Markov Trace Comparison

Approach 3: Markov Chain with Rewards (Advanced)

Approach 3

Approach 3

Summary and Comparison

Methods, Part 2: Outcomes

1. Markov Trace (Beginner)

1. Markov Trace (Beginner)

2. Transition States (Intermediate)

Define payoff vectors for YLL & YLD:

• a_t is the cohort’s age at cycle t, i.e., a_t = a_0 +t \cdot \Delta_t
• r_{\Delta_t} is the cycle discount rate, i.e., r \Delta_t.

2. Transition States (Intermediate)

2. Transition States (Intermediate)

• Apply YLL payoff vector to calculate outcomes.
• YLL=\sum_{t=0}^{\omega-1} YLL(t)=\sum_{t=0}^{\omega-1}\left(\mathbf{s}'_0 \mathbf{P}_1\mathbf{P}_2\dots\mathbf{P}_t \mathbf{d}_{YLL,t} \times c_t \right)

3. Markov Chain with Rewards

YLL Reward Matrix (Transition)

• First define the first moment of remaining life expectancy as the vector \widetilde{\boldsymbol{\eta}}^{\top}.
• These life expectancies are drawn from the reference life table, or some alternative.

YLL Reward Matrix (Transition)

\widetilde{\mathbf{\eta}}=\left(\begin{array}{c} \eta_{11} \\ \vdots \\ \eta_{\tau 1} \\ \hline \vdots \\ \hline \eta_{1 \omega} \\ \vdots \\ \eta_{\tau \omega} \end{array}\right) where \eta_{i x} is remaining life expectancy for an individual in health state i at a given age x.

YLL Reward Matrix (Transition)

\widetilde{\mathbf{\eta}}=\left(\begin{array}{c} \eta_{H,0} = 88.87 \\ \eta_{CVD,0} = 88.87 \\ \hline \vdots \\ \hline \eta_{H,95} = 5.92 \\ \eta_{CVD,95} = 5.92 \\ \end{array}\right)

YLL Reward Matrix (Transition)

We next construct the reward matrices:

\begin{aligned} \widetilde{\mathbf{B}}_{1} & =\left(\mathbf{0}_{\tau \omega \times \tau \omega}\right) \\ \widetilde{\mathbf{C}}_{1} & =\left(\begin{array}{c} \widetilde{\boldsymbol{\eta}}_{1}^{\top} \\ \mathbf{0}_{1 \times \tau \omega} \end{array}\right) . \end{aligned} and

\widetilde{\mathbf{R}}^{YLL}_{1}=\left(\begin{array}{c|c} \mathbf{0}_{\tau \omega \times \tau \omega} & \mathbf{0}_{\tau \omega \times 2} \\ \hline \widetilde{\boldsymbol{\eta}}_{1}^{\top} & \mathbf{0}_{1 \times 2} \\ \mathbf{0}_{1 \times \tau \omega} & \mathbf{0}_{1 \times 2} \end{array}\right)

Expected YLD and YLL Outcomes

Expected YLD and YLL outcomes (Y) are estimated by

\begin{aligned} & \widetilde{\boldsymbol{\rho}}^{Y}_{1}=\widetilde{\mathbf{N}}^{\top} \mathbf{Z}\left(\widetilde{\mathbf{P}} \odot \widetilde{\mathbf{R}}^Y_{1}\right)^{\top} \mathbf{1}_{s} \end{aligned} where \widetilde{\mathbf{R}}^Y_{1} is the relevant reward matrix, \widetilde{\mathbf{N}} is the fundamental matrix, \widetilde{\mathbf{N}}=(\mathbf{I}-\widetilde{\mathbf{U}})^{-1}, and \mathbf{Z} is

\mathbf{Z}=\left(\mathbf{I}_{\tau \omega} \mid \mathbf{0}_{\tau \omega \times \alpha}\right)

Results, Part 1: Comparison of Approaches

Comparison of Approaches (No Discounting)

Comparison of Approaches (3% Discounting)

Results, Part 2: Comparison with DALY Shortcuts

DALY Shortcut 1

DALY Shortcut 2

• “QALY-like DALY”: defines the cycle occupancy payoff for the CVD state as one minus the disability weight
• No explicit accounting for YLL from premature deaths.

CEA: Comparison of Approaches

Results, Part 3: YLL and YLD by Cohort Starting Age

YLD by Model Starting Age

YLL by Model Starting Age

Results, Part 4: Exogenous (GBD) vs. Endogenous (Model) Life Expectancy

Incremental Outcomes: Exogenous vs. Endogenous Life Tables

Summary and Extensions

Summary of Approaches

DALY Shortcuts

DALY Shortcuts

Thanks!

john.graves@vanderbilt.edu