Modelling decay in effectiveness for evaluation of behaviour change interventions: a tutorial for public health economists

Paolo Candio, Koen B. Pouwels, David Meads, Andrew J. Hill, Laura Bojke, Claire Williams

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Background and purpose
Recent methodological reviews of evaluations of behaviour change interventions in public health have highlighted that the decay in effectiveness over time has been mostly overlooked, potentially leading to suboptimal decision-making. While, in principle, discrete-time Markov chains—the most commonly used modelling approach—can be adapted to account for decay in effectiveness, this framework inherently lends itself to strong model simplifications. The application of formal and more appropriate modelling approaches has been supported, but limited progress has been made to date. The purpose of this paper is to encourage this shift by offering a practical guide on how to model decay in effectiveness using a continuous-time Markov chain (CTMC)-based approach.

A CTMC approach is demonstrated, with a contextualized tutorial being presented to facilitate learning and uptake. A worked example based on the stylized case study in physical activity promotion is illustrated with accompanying R code.

The proposed framework presents a relatively small incremental change from the current modelling practice. CTMC represents a technical solution which, in absence of relevant data, allows for formally testing the sensitivity of results to assumptions regarding the long-term sustainability of intervention effects and improving model transparency.

The use of CTMC should be considered in evaluations where decay in effectiveness is likely to be a key factor to consider. This would enable more robust model-based evaluations of population-level programmes to promote behaviour change and reduce the uncertainty surrounding the decision to invest in these public health interventions.
Original languageEnglish
JournalEuropean Journal of Health Economics
Early online date16 Dec 2021
Publication statusE-pub ahead of print - 16 Dec 2021

Bibliographical note

Funding Information:
PC was supported through the White Rose PhD Studentship Network scheme as part of the National Institute for Health Research Collaboration for Leadership in Applied Health Research and Care Yorkshire and Humber.

Publisher Copyright:
© 2021, The Author(s).


  • Decision-making
  • Effect decay
  • Mathematical modelling
  • Public health
  • Structural uncertainty

ASJC Scopus subject areas

  • Economics, Econometrics and Finance (miscellaneous)
  • Health Policy


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