What They Didn’t Teach You About Decision Modeling

SMDM 2023 - 18th Biennial European Conference

Welcome to Berlin!

  • Introductions
  • Workshop Learning Objectives
  • Conceptual Framework

Workshop Overview

  • “Bag of tricks” to fill the gaps in CEA modeling.
  • Primary focus is discrete time Markov, but much of the material is also useful for discrete event simulation and microsimulation modeling.

Workshop Overview

  • Our primary aim is to provide you with intuition for why to use these methods.
  • We also aim to provide you with code.
  • We’ll move fast; don’t worry if everything doesn’t immediately resonate!

Learning Objectives (Morning)

  1. Fit a parametric mortality model to life table data to:
    • Net out cause-specific death from overall mortality (i.e., truly model background mortality).
    • Accurately simulate death times in a discrete event model.
    • Summarize background mortality for a discrete time Markov model in a few parameters.

Learning Objectives (Morning)

  1. Accurately construct a transition probability matrix.
  • The rate-to-probability (and probability-to-rate) conversion formulas you probably learned are technically correct, but only in a very narrow case with no competing risks like death.

Learning Objectives (Afternoon)

  1. Include non-markovian matrix elements to capture:

    • Counts of total events or counts of event transitions (single cycle) to/from certain states (e.g., how to deal with one-time costs).
    • Tunnel states to capture transitory health and/or cost dynamics.

Learning Objectives (Afternoon)

  1. Backwards-convert an existing Markov model
  • Facilitates adapation of existing models to accommodate new evidence, strategies, additional health states, different cycle lengths, etc.

Learning Objectives (Afternoon)

  1. Solve for PSA distribution parameters given sparse information from the literature (e.g., IQR of costs of $300-$750).

  2. Improve the efficiency of PSA analyses by sampling correlated PSA distributions using copulas.

Conceptual Framework

What They Taught You is (Technically) Wrong

  • A lot of the common methods taught for CEA are shortcuts, or may be technically correct for narrow cases—but are not generally.

  • This doesn’t mean everything published is totally wrong, however.

  • Because we often make comparisons across strategies, errors may (approximately) cancel out.

    • There is no guarantee of this, however.

The Big Picture

  • Decision thresholds methods, e.g. ICER, NMB, NHB all involve comparing a model run versus a reference run of the same model.
  • For example, a model of \(f_{cost}\) and \(f_{qaly}\) are run versus \(\theta_{ref}\) and \(\theta_{target}\).
  • These runs will have error due to misspecification, and in differencing the error can mostly cancel. Let \(g\) represent the truth, thus \(f(\theta) = g(\theta)+\epsilon_{\theta}\).

The Hopeful Big Picture

\[\text{ICER} = \frac{f_{cost}(\theta_{target}) - \epsilon_{ct} - f_{cost}(\theta_{ref}) + \epsilon_{cr}}{f_{qaly}(\theta_{target}) - \epsilon_{qt} - f_{qaly}(\theta_{ref}) + \epsilon_{qr}}\]

  • If \(\epsilon_{ct} \sim \epsilon_{cr}\) and \(\epsilon_{qt} \sim \epsilon_{qr}\) then the model errors cancel and this approaches the true model.
  • The decision threshold is robust in this case even when model run results are biased!

The Hopeful Big Picure

  • A similar theme will occur periodically today.
  • We’ll aim to highlight when these issues may be decision-relevant (i.e., errors may not cancel)

Questions?

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