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. 2016 Nov;36(8):952-64.
doi: 10.1177/0272989X16656165. Epub 2016 Jul 1.

Changing Cycle Lengths in State-Transition Models: Challenges and Solutions

Jagpreet Chhatwal  1 , Suren Jayasuriya  2 , Elamin H Elbasha  3
Affiliations

Changing Cycle Lengths in State-Transition Models: Challenges and Solutions

Jagpreet Chhatwal et al. Med Decis Making. 2016 Nov.

Abstract

The choice of a cycle length in state-transition models should be determined by the frequency of clinical events and interventions. Sometimes there is need to decrease the cycle length of an existing state-transition model to reduce error in outcomes resulting from discretization of the underlying continuous-time phenomena or to increase the cycle length to gain computational efficiency. Cycle length conversion is also frequently required if a new state-transition model is built using observational data that have a different measurement interval than the model's cycle length. We show that a commonly used method of converting transition probabilities to different cycle lengths is incorrect and can provide imprecise estimates of model outcomes. We present an accurate approach that is based on finding the root of a transition probability matrix using eigendecomposition. We present underlying mathematical challenges of converting cycle length in state-transition models and provide numerical approximation methods when the eigendecomposition method fails. Several examples and analytical proofs show that our approach is more general and leads to more accurate estimates of model outcomes than the commonly used approach. MATLAB codes and a user-friendly online toolkit are made available for the implementation of the proposed methods.

Keywords: Markov models; cost-effectiveness analysis; decision analysis; global health; mathematical models.

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Figures

Figure B1
Figure B1
Snapshot of the toolbox for cycle length conversion
Figure B2
Figure B2
Three-state Markov chain
Figure B3
Figure B3
Five-state Markov model
Figure B4
Figure B4
Four-state Markov model with two competing-risks states
Figure B5
Figure B5
Four-state Markov model with three competing-risks states
Figure B6
Figure B6
Five-state Markov model with four competing-risks states
Figure 1
Figure 1
State-transition model showing health states and transitions between states. DeCirr, decompensated cirrhosis; HCC, hepatocellular carcinoma.
Figure 2
Figure 2
Error in model outcomes using shorter cycle length from traditional approach in comparison to that obtained with eigendecomposition approach. We applied 3% discount rate and within-cycle correction to estimate total costs and quality-adjusted life years (QALYs). HCC, hepatocellular carcinoma.
Figure 2
Figure 2
Error in model outcomes using shorter cycle length from traditional approach in comparison to that obtained with eigendecomposition approach. We applied 3% discount rate and within-cycle correction to estimate total costs and quality-adjusted life years (QALYs). HCC, hepatocellular carcinoma.
Figure 2
Figure 2
Error in model outcomes using shorter cycle length from traditional approach in comparison to that obtained with eigendecomposition approach. We applied 3% discount rate and within-cycle correction to estimate total costs and quality-adjusted life years (QALYs). HCC, hepatocellular carcinoma.
Figure 2
Figure 2
Error in model outcomes using shorter cycle length from traditional approach in comparison to that obtained with eigendecomposition approach. We applied 3% discount rate and within-cycle correction to estimate total costs and quality-adjusted life years (QALYs). HCC, hepatocellular carcinoma.
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References

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