A Comparison of Four Software Programs for Implementing Decision Analytic Cost-Effectiveness Models

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.

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:

$$X_{{\left( {1,1} \right)}}^{k} = a*X_{{\left( {1,1} \right)}}^{{\left( {k - 1} \right)}}$$

$$X_{{\left( {1,2} \right)}}^{k} = b*X_{{\left( {1,1} \right)}}^{{\left( {k - 1} \right)}} + X_{{\left( {1,2} \right)}}^{{\left( {k - 1} \right)}}$$

$$X_{{\left( {1,3} \right)}}^{k} = c*X_{{\left( {1,1} \right)}}^{{\left( {k - 1} \right)}} + X_{{\left( {1,3} \right)}}^{{\left( {k - 1} \right)}}$$

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:

$$X_{{\left( {1,1} \right)}}^{k} = X_{{\left( {1,1} \right)}}^{{\left( {k - 1} \right)}} *\left( {1 - b} \right)*\left( {1 - c} \right)$$

$$X_{{\left( {1,2} \right)}}^{k} = b*X_{{\left( {1,1} \right)}}^{{\left( {k - 1} \right)}} + X_{{\left( {1,2} \right)}}^{{\left( {k - 1} \right)}}$$

$$X_{{\left( {1,3} \right)}}^{k} = c*X_{{\left( {1,1} \right)}}^{{\left( {k - 1} \right)}} *\left( {1 - b} \right) + X_{{\left( {1,3} \right)}}^{{\left( {k - 1} \right)}}.$$

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

$$c^{\text{Corrected}} = \frac{{c^{\text{True}} }}{{\left( {1 - b} \right)}}.$$

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.