## Abstract

The volume and technical complexity of both academic and commercial research using decision analytic modelling has increased rapidly over the last two decades. The range of software programs used for their implementation has also increased, but it remains true that a small number of programs account for the vast majority of cost-effectiveness modelling work. We report a comparison of four software programs: TreeAge Pro, Microsoft Excel, R and MATLAB. Our focus is on software commonly used for building Markov models and decision trees to conduct cohort simulations, given their predominance in the published literature around cost-effectiveness modelling. Our comparison uses three qualitative criteria as proposed by Eddy et al.: “transparency and validation”, “learning curve” and “capability”. In addition, we introduce the quantitative criterion of processing speed. We also consider the cost of each program to academic users and commercial users. We rank the programs based on each of these criteria. We find that, whilst Microsoft Excel and TreeAge Pro are good programs for educational purposes and for producing the types of analyses typically required by health technology assessment agencies, the efficiency and transparency advantages of programming languages such as MATLAB and R become increasingly valuable when more complex analyses are required.

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## Author information

### Affiliations

### Corresponding author

## Ethics declarations

### Funding

This study was funded through grants from the Canadian Institutes for Health Research (CIHR) and Genome Canada. Christopher McCabe is supported through a Capital Health Research Chair in Emergency Medicine Research.

### Conflicts of interest

Mike Paulden and Christopher McCabe have taught introductory courses on decision modelling using Microsoft Excel, but have no relationships with the developer and have received no financial benefits for using this software to teach these courses. Petros Pechlivanoglou has taught introductory courses on decision modelling using R and has contributed to decision modelling courses that use TreeAge, but has no relationships with any of the developers and has received no financial benefits for using this software to teach these courses. Chase Hollman, Mike Paulden, Petros Pechlivanoglou and Christopher McCabe have no other potential conflicts of interest to report.

### Author contributions

Mike Paulden built the TreeAge model used for the benchmark comparisons and rebuilt this model using Microsoft Excel. Chase Hollman rebuilt this model in MATLAB and R, with support from Petros Pechlivanoglou, and conducted the benchmarking exercise. Christopher McCabe supervised the project. Chase Hollman wrote the first draft of the manuscript. All authors contributed to subsequent drafts of the manuscript, responses to peer review, and preparation of the manuscript for publication.

### Data availability statement

We have provided the models used in our benchmarking exercise as supplementary material.

## Electronic supplementary material

Below is the link to the electronic supplementary material.

## Appendices

### Appendix 1: Search Strategy

### Appendix 2: Markov Chain versus Markov Tree Models in TreeAge

There are two ways of implementing a Markov model in TreeAge. The first is the standard Markov chain method, which in TreeAge is represented in the visual form:

The second is in the form of a Markov cycle tree, initially specified by Hollenberg [18] for aesthetic presentation of a Markov model:

The difference between the two is subtle yet can have a significant impact on the model specification.

Assume, for simplicity, that ‘Dead’ and ‘Diseased’ are absorbing states (this is a reasonable assumption for any currently incurable disease, such as multiple sclerosis). Then the Markov chain is fully described by the recurrence relations:

where *a*, *b* and *c* are the initial transition probabilities corresponding to healthy, diseased and dead, *X* is the transition matrix and *k* is the cycle number. The subscript (_{
i, j
}) indicates the row and column of the transition probability matrix at cycle *k*.

The Markov cycle tree is equivalently defined by:

These two methods produce different state distributions for the same initial probabilities *a*, *b* and *c*. If a Markov model is parameterized as a Markov cycle tree without accounting for this, the model will be incorrectly specified.

Note that the second state has the correct probability applied in the first cycle but that in all future cycles all states' distributions deviate from their true values.

To preserve the correct probabilities in this example would require defining

If the model has more hierarchical states, they too must be entered with care. Finally, time-dependent transition probabilities also must be corrected in every cycle.

To avoid ambiguity, we recommend that modellers use the Markov chain method.

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## About this article

### Cite this article

Hollman, C., Paulden, M., Pechlivanoglou, P. *et al.* A Comparison of Four Software Programs for Implementing Decision Analytic Cost-Effectiveness Models.
*PharmacoEconomics* **35, **817–830 (2017). https://doi.org/10.1007/s40273-017-0510-8

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### Keywords

- Health Technology Assessment
- Integrate Development Environment
- Health Technology Assessment Agency
- Debug Tool
- Markov Tree