On 2017 Mar 12, Andrea Messori commented:

Promoting the use of Markov simulation models to study outcomes of total knee arthroplasty

Andrea Messori

HTA Section, ESTAR Toscana, Regional Health Service, Firenze, Italy

Correspondence to: Dr. Andrea Messori, PharmD, HTA Unit, ESTAR Toscana, Regional Health Service, Via San Salvi 12, 50100 Firenze, Italy. andrea.messori.it@gmail.com Fax: +39-05-74701319

In patients receiving total knee arthroplasty (TKA), simulation studies employing Markov models are increasingly being used [1-4]. The aim of these studies is to determine the “typical” clinical outcomes expected on the long term and to generate estimates of cost/effectiveness. If we consider these modelling tools, most of the simulation software published thus far shares the following characteristics:

a) Health states. The model implements, with minimal variations across different models, the health-states shown in Figure 1 along with the corresponding transitions from one health state to another. The probabilities of individual transitions are shown in Figure 1; these probabilities can be adjusted depending on the specific intervention under examination;

b) Clinical outcomes after TKA. The following outcomes can occur after the first surgery: i) successful outcome; ii) complications; iii) death; the same outcomes can occur also after a repeat surgery for arthroplasty revision.

c) Life expectancy. The life-expectancy attributed to the simulated patients is determined by considering: a) the age-related and gender-related mortality of a healthy population [5]; b) the mortality attributable to arthroplasty surgery. These two factors are separately managed in different sections of the Markov model (see Figure 1).

d) Utilities and estimation of QALYs. Utility of patients is assumed to be around 0.72 [6] after surgery. Over the pre-specified time horizon (e.g. 20 years), QALYs are computed on the basis of the health states of the model, their utilities, and the corresponding transition probabilities.

e) Discounting. The annual discount rate (e.g. 3.5%) is incorporated in the calculation of QALYs according to standard discounting techniques [6].

As regards the practical use of these computer programs, the simulation models published in the past years are essentially based on two software tools: on the one hand, some researchers have used a general-purpose spreadsheet (namely: Excel by Microsoft) to develop these Markovian programs; on the other, other researchers [3] have used a specific, commercial program (in most cases: TreeagePro by Treeage Software Inc., Williamstown, Massachusetts, USA). The Markovian subroutines written under Excel, as well as the tools developed under Treeage, share a negative characteristic because they are not freely available. Even NICE does not provide these tools when a Technology Appraisal is released. The unavailability of these programming tools is a serious hurdle that limits the scientific advancement of cost-effectiveness research on TKA. Hence, in the present report we have tried to facilitate the application of Markov models in the setting of TKA by developing a simulation software which is an improved version of the tools previously employed for specific research projects [3]. Our simulation model, that can be downloaded from the following link http://www.osservatorioinnovazione.net/papers/total_knee_arthroplasty.trex, is designed to be run under TreeagePro version 2011 (or subsequent versions). The input variables for the model are shown in the legend to Figure 1. The output of the program is represented by the estimate of total QALYs per patient accrued over the pre-specified time horizon. The software manages only the clinical part of these simulations; however, cost data can be added quite easily by introducing new sections of programming.

References

[1] Losina E, Walensky RP, Kessler CL, Emrani PS, Reichmann WM, Wright[ EA, Holt HL, Solomon DH, Yelin E, Paltiel AD, Katz JN. Cost-effectiveness of total knee arthroplasty in the United States: patient risk and hospital volume. Arch Intern Med. 2009 Jun 22;169(12):1113-21.

[2] Bedair H, Cha TD, Hansen VJ. Economic benefit to society at large of total knee arthroplasty in younger patients: a Markov analysis. J Bone Joint Surg Am. 2014 Jan 15;96(2):119-26.

[3] Pennington M, Grieve R, Black N, van der Meulen JH. Cost-Effectiveness of Five Commonly Used Prosthesis Brands for Total Knee Replacement in the UK: A Study Using the NJR Dataset. PLoS One. 2016 Mar 4;11(3):e0150074.

[4] Mari K, Dégieux P, Mistretta F, Guillemin F, Richette P. Cost utility modeling of early vs late total knee replacement in osteoarthritis patients. Osteoarthritis Cartilage. 2016 Dec;24(12):2069-2076.

[5] ISTAT. Tavole di mortalità della popolazione italiana—Ripartizione: Italia—Maschi—Anno: 2005, Report of 2010. http://demo.istat.it/unitav2012/index.html?lingua=ita (last accessed 7 May 2014).

[6] Mason J, Drummond M, Torrance G. Some guidelines on the use of cost effectiveness league tables. BMJ. 1993 Feb 27;306(6877):570-2.

[7] Jørgensen CC, Kehlet H; Lundbeck Foundation Centre for Fast-track Hip and Knee Replacement Collaborative group.. Time course and reasons for 90-day mortality in fast-track hip and knee arthroplasty. Acta Anaesthesiol Scand. 2017 Apr;61(4):436-444.

Figure 1. States of the Markov model and transition probabilities.

The starting point of the simulation model is a Markov node (circled M) from which six branches originate. The explanation for these six branches is the following: 1) surgery for TKA; 2) follow-up after first surgery (and also the occurrence of revision surgery): 3) follow-up after revision surgery; 4) follow-up after first surgery with complications; 5) follow-up after revision surgery with complications: 6) death. Second-level branches regard events defined according to the accompanying labels. The symbols adopted in this scheme reflect the syntax required by the Treeage software: Ο, probabilistic node;◄, terminal node.

Abbreviations: RWD, reward (which in this model represents the incremental increase in quality- adjusted survival).

The graph of Figure 1 can be downloaded from the following link: http://www.osservatorioinnovazione.net/tenders/tka.gif

On 2017 Mar 12, Andrea Messori commented:

Promoting the use of Markov simulation models to study outcomes of total knee arthroplasty

Andrea Messori

HTA Section, ESTAR Toscana, Regional Health Service, Firenze, Italy

Correspondence to: Dr. Andrea Messori, PharmD, HTA Unit, ESTAR Toscana, Regional Health Service, Via San Salvi 12, 50100 Firenze, Italy. andrea.messori.it@gmail.com Fax: +39-05-74701319

In patients receiving total knee arthroplasty (TKA), simulation studies employing Markov models are increasingly being used [1-4]. The aim of these studies is to determine the “typical” clinical outcomes expected on the long term and to generate estimates of cost/effectiveness. If we consider these modelling tools, most of the simulation software published thus far shares the following characteristics:

a) Health states. The model implements, with minimal variations across different models, the health-states shown in Figure 1 along with the corresponding transitions from one health state to another. The probabilities of individual transitions are shown in Figure 1; these probabilities can be adjusted depending on the specific intervention under examination;

b) Clinical outcomes after TKA. The following outcomes can occur after the first surgery: i) successful outcome; ii) complications; iii) death; the same outcomes can occur also after a repeat surgery for arthroplasty revision.

c) Life expectancy. The life-expectancy attributed to the simulated patients is determined by considering: a) the age-related and gender-related mortality of a healthy population [5]; b) the mortality attributable to arthroplasty surgery. These two factors are separately managed in different sections of the Markov model (see Figure 1).

d) Utilities and estimation of QALYs. Utility of patients is assumed to be around 0.72 [6] after surgery. Over the pre-specified time horizon (e.g. 20 years), QALYs are computed on the basis of the health states of the model, their utilities, and the corresponding transition probabilities.

e) Discounting. The annual discount rate (e.g. 3.5%) is incorporated in the calculation of QALYs according to standard discounting techniques [6].

As regards the practical use of these computer programs, the simulation models published in the past years are essentially based on two software tools: on the one hand, some researchers have used a general-purpose spreadsheet (namely: Excel by Microsoft) to develop these Markovian programs; on the other, other researchers [3] have used a specific, commercial program (in most cases: TreeagePro by Treeage Software Inc., Williamstown, Massachusetts, USA). The Markovian subroutines written under Excel, as well as the tools developed under Treeage, share a negative characteristic because they are not freely available. Even NICE does not provide these tools when a Technology Appraisal is released. The unavailability of these programming tools is a serious hurdle that limits the scientific advancement of cost-effectiveness research on TKA. Hence, in the present report we have tried to facilitate the application of Markov models in the setting of TKA by developing a simulation software which is an improved version of the tools previously employed for specific research projects [3]. Our simulation model, that can be downloaded from the following link http://www.osservatorioinnovazione.net/papers/total_knee_arthroplasty.trex, is designed to be run under TreeagePro version 2011 (or subsequent versions). The input variables for the model are shown in the legend to Figure 1. The output of the program is represented by the estimate of total QALYs per patient accrued over the pre-specified time horizon. The software manages only the clinical part of these simulations; however, cost data can be added quite easily by introducing new sections of programming.

References

[1] Losina E, Walensky RP, Kessler CL, Emrani PS, Reichmann WM, Wright[ EA, Holt HL, Solomon DH, Yelin E, Paltiel AD, Katz JN. Cost-effectiveness of total knee arthroplasty in the United States: patient risk and hospital volume. Arch Intern Med. 2009 Jun 22;169(12):1113-21.

[2] Bedair H, Cha TD, Hansen VJ. Economic benefit to society at large of total knee arthroplasty in younger patients: a Markov analysis. J Bone Joint Surg Am. 2014 Jan 15;96(2):119-26.

[3] Pennington M, Grieve R, Black N, van der Meulen JH. Cost-Effectiveness of Five Commonly Used Prosthesis Brands for Total Knee Replacement in the UK: A Study Using the NJR Dataset. PLoS One. 2016 Mar 4;11(3):e0150074.

[4] Mari K, Dégieux P, Mistretta F, Guillemin F, Richette P. Cost utility modeling of early vs late total knee replacement in osteoarthritis patients. Osteoarthritis Cartilage. 2016 Dec;24(12):2069-2076.

[5] ISTAT. Tavole di mortalità della popolazione italiana—Ripartizione: Italia—Maschi—Anno: 2005, Report of 2010. http://demo.istat.it/unitav2012/index.html?lingua=ita (last accessed 7 May 2014).

[6] Mason J, Drummond M, Torrance G. Some guidelines on the use of cost effectiveness league tables. BMJ. 1993 Feb 27;306(6877):570-2.

[7] Jørgensen CC, Kehlet H; Lundbeck Foundation Centre for Fast-track Hip and Knee Replacement Collaborative group.. Time course and reasons for 90-day mortality in fast-track hip and knee arthroplasty. Acta Anaesthesiol Scand. 2017 Apr;61(4):436-444.

Figure 1. States of the Markov model and transition probabilities.

The starting point of the simulation model is a Markov node (circled M) from which six branches originate. The explanation for these six branches is the following: 1) surgery for TKA; 2) follow-up after first surgery (and also the occurrence of revision surgery): 3) follow-up after revision surgery; 4) follow-up after first surgery with complications; 5) follow-up after revision surgery with complications: 6) death. Second-level branches regard events defined according to the accompanying labels. The symbols adopted in this scheme reflect the syntax required by the Treeage software: Ο, probabilistic node;◄, terminal node.

Abbreviations: RWD, reward (which in this model represents the incremental increase in quality- adjusted survival).

The graph of Figure 1 can be downloaded from the following link: http://www.osservatorioinnovazione.net/tenders/tka.gif