On 2016 Sep 27, Andrea Messori commented:

Modeling the economic consequences of inhibitor development in previously untreated patients with severe hemophilia A

By Andrea Messori, HTA Unit, Regional Health System, 50100 Firenze (Italy)

Background

If one performs a PubMed search using the keywords “Markov AND (haemophilia OR hemophilia) AND inhibitors”, only 4 articles are retrieved (published in 2013, 2003, 2003, and 2000). This demonstrates that, despite its potential advantages, the use of Markov models in haemophilia patients is still very limited. In the past 10 years, the study by Farrugia and co-workers (Haemophilia. 2013 Jul;19:e228-38.) is the only example of a Markov model designed to handle the data of patients with severe disease and inhibitors. Quite recently, we have developed a similar model that has not yet been formally published. Hence, this Comment has the purpose to describe the main characteristics of our model.

Model description

Our model is represented in Figure 1 (link to display this figure: http://www.osservatorioinnovazione.net/papers/markov-hemophilia-figure1.gif ). A commercial software (TreeagePro, Treeage Software Inc., 2011 version, Williamstown, MA, USA) has been employed for its development. Briefly, the core of the model is a decision node (not shown in Figure 1) from which two branches originate, the first describing the patients assigned to recombinant factor VIII (Panel A in Figure 1) and the second those assigned to plasma-derived factor VIII (Panel B in Figure 1). A total of 10 health states are included in the Markov model (see the Appendix reported below for further details). The purpose of the model is to carry out a budget impact analysis in which the replacement therapy and the treatment of inhibitors are the main cost items. The transition probabilities that manage how patients move across the health states are also presented in Figure 1 (Panels A and B). Probabilities with values of 0 or 1 are self-explanatory; accordin to the syntax of TreeagePro, the symbol “#” identifies a probability equal to the value needed to reach 100% after taking into account the other probability/probabilities directly expressed in numerical form and assigned to the other branch(es) of the same node. In each of the two main sections of the model (i.e. recombinant factor VIII [Panel A] and plasma-derived factor VIII [Panel B]), the Markov analysis incorporates the adjustment for annual discount rates and traces the number of cycles evaluated in the iterative process. According to the Markov approach, costs incurred in the model are iteratively summed upon each cycle. Three items participate in the cost analysis, namely the annual cost per patient treated with recombinant factor VIII (denoted as “annualcostric”), the annual cost per patient treated with plasma-derived factor VIII (denoted as “annualcostpd”), and the cost per patient of immunotolerance therapy (denoted as “costofIT”). As regards the syntax of the Treeage software, cost data are handled as “incremental rewards” (denoted as “Incr Rwd”). In other words, the variable “Rewards” was used to cumulate the various cost data at each cycle. The TreeagePro code needed for running the model is available from th author upon request.

Appendix. Detailed description of the 10 health states included in the Markov model

The main health states included in the recombinant branch of the model (ordered bottom-up according to Panel A of Figure 1) are the following: a) state denoted as “Without” in which patients assigned to heath-state ( c) are assumed not to develop high-titer inhibitors and then move to the health state “all-people-final-ric”; b) state denoted as “With” in which patients assigned to heath-state ( c) are assumed to develop high-titer inhibitors and then move to the health state “IT-ric”; c) state denoted as “all people ric” in which patients treated with recombinant factor VIII proceed in their Markov iterative process and are exposed to the risk of developing high-titer inhibitors; d) state denoted as “all-people-final-ric” in which patients treated with recombinant factor VIII (irrespective of whether they have developed or not high-titer inhibitors) proceed in their Markov iterative process until the end of the time horizon without being any longer exposed to the risk of developing high-titer inhibitors; e) state denoted as “IT-ric” in which patients treated with recombinant factor VIII who have developed high-titer inhibitors receive immune-tolerance therapy and move to the health state “post-IT-ric” and then to the health state “all-people-final-ric”. The main health states included in the plasma-derived branch of the model (ordered bottom-up according to Panel B of Figure 1) are the following: f) state denoted as “Without” in which patients assigned to heath-state (h) are assumed not to develop high-titer inhibitors and then move to the health state “all-people-final-pd”; g) state denoted as “With” in which patients assigned to heath-state (h) are assumed to develop high-titer inhibitors and then move to the health state “IT-pd”; h) state denoted as “all people ric” in which patients treated with recombinant factor VIII proceed in their Markov iterative process and are exposed to the risk of developing high-titer inhibitors; i) state denoted as “all-people-final-pd” in which patients treated with recombinant factor VIII (irrespective of whether they have developed or not high-titer inhibitors) proceed in their Markov iterative process until the end of the time horizon without being any longer exposed to the risk of developing high-titer inhibitors. j) state denoted as “IT-pd” in which patients treated with recombinant factor VIII who have developed high-titer inhibitors receive immune-tolerance therapy and move to the health state “post-IT-pd” and then to the health state “all-people-final-pd”. The model was designed to predict in these cohorts the expected expenditures, that were quantified on the basis of the (different) cumulative incidence of high-titer inhibitors and the (different) cost of the replacement products between the cohorts. It should be noted that some health states assigned, in Figure 1, to the first-level branches of both Panels A and B (governed by the Markov node) are not reachable at the first cycle of the Markov process (i.e. probability = 0 at this cycle), but are designed to be reached from the second-level branches, associated with the development or not of high-titer inhibitors. Finally, although the Treaage software allows to manage other variables participating in the calculation of rewards (namely: initial reward denoted as “Init Rwd”, which is summed upon entry in the health state; and: final reward denoted as “Fin Rwd”, which is summed upon exit from the health state), these were not necessary for the purposes of our model and were therefore kept at 0 (as illustrated in the two panels of Figure 1).

On 2016 Sep 27, Andrea Messori commented:

Modeling the economic consequences of inhibitor development in previously untreated patients with severe hemophilia A

By Andrea Messori, HTA Unit, Regional Health System, 50100 Firenze (Italy)

Background

If one performs a PubMed search using the keywords “Markov AND (haemophilia OR hemophilia) AND inhibitors”, only 4 articles are retrieved (published in 2013, 2003, 2003, and 2000). This demonstrates that, despite its potential advantages, the use of Markov models in haemophilia patients is still very limited. In the past 10 years, the study by Farrugia and co-workers (Haemophilia. 2013 Jul;19:e228-38.) is the only example of a Markov model designed to handle the data of patients with severe disease and inhibitors. Quite recently, we have developed a similar model that has not yet been formally published. Hence, this Comment has the purpose to describe the main characteristics of our model.

Model description

Our model is represented in Figure 1 (link to display this figure: http://www.osservatorioinnovazione.net/papers/markov-hemophilia-figure1.gif ). A commercial software (TreeagePro, Treeage Software Inc., 2011 version, Williamstown, MA, USA) has been employed for its development. Briefly, the core of the model is a decision node (not shown in Figure 1) from which two branches originate, the first describing the patients assigned to recombinant factor VIII (Panel A in Figure 1) and the second those assigned to plasma-derived factor VIII (Panel B in Figure 1). A total of 10 health states are included in the Markov model (see the Appendix reported below for further details). The purpose of the model is to carry out a budget impact analysis in which the replacement therapy and the treatment of inhibitors are the main cost items. The transition probabilities that manage how patients move across the health states are also presented in Figure 1 (Panels A and B). Probabilities with values of 0 or 1 are self-explanatory; accordin to the syntax of TreeagePro, the symbol “#” identifies a probability equal to the value needed to reach 100% after taking into account the other probability/probabilities directly expressed in numerical form and assigned to the other branch(es) of the same node. In each of the two main sections of the model (i.e. recombinant factor VIII [Panel A] and plasma-derived factor VIII [Panel B]), the Markov analysis incorporates the adjustment for annual discount rates and traces the number of cycles evaluated in the iterative process. According to the Markov approach, costs incurred in the model are iteratively summed upon each cycle. Three items participate in the cost analysis, namely the annual cost per patient treated with recombinant factor VIII (denoted as “annualcostric”), the annual cost per patient treated with plasma-derived factor VIII (denoted as “annualcostpd”), and the cost per patient of immunotolerance therapy (denoted as “costofIT”). As regards the syntax of the Treeage software, cost data are handled as “incremental rewards” (denoted as “Incr Rwd”). In other words, the variable “Rewards” was used to cumulate the various cost data at each cycle. The TreeagePro code needed for running the model is available from th author upon request.

Appendix. Detailed description of the 10 health states included in the Markov model

The main health states included in the recombinant branch of the model (ordered bottom-up according to Panel A of Figure 1) are the following: a) state denoted as “Without” in which patients assigned to heath-state ( c) are assumed not to develop high-titer inhibitors and then move to the health state “all-people-final-ric”; b) state denoted as “With” in which patients assigned to heath-state ( c) are assumed to develop high-titer inhibitors and then move to the health state “IT-ric”; c) state denoted as “all people ric” in which patients treated with recombinant factor VIII proceed in their Markov iterative process and are exposed to the risk of developing high-titer inhibitors; d) state denoted as “all-people-final-ric” in which patients treated with recombinant factor VIII (irrespective of whether they have developed or not high-titer inhibitors) proceed in their Markov iterative process until the end of the time horizon without being any longer exposed to the risk of developing high-titer inhibitors; e) state denoted as “IT-ric” in which patients treated with recombinant factor VIII who have developed high-titer inhibitors receive immune-tolerance therapy and move to the health state “post-IT-ric” and then to the health state “all-people-final-ric”. The main health states included in the plasma-derived branch of the model (ordered bottom-up according to Panel B of Figure 1) are the following: f) state denoted as “Without” in which patients assigned to heath-state (h) are assumed not to develop high-titer inhibitors and then move to the health state “all-people-final-pd”; g) state denoted as “With” in which patients assigned to heath-state (h) are assumed to develop high-titer inhibitors and then move to the health state “IT-pd”; h) state denoted as “all people ric” in which patients treated with recombinant factor VIII proceed in their Markov iterative process and are exposed to the risk of developing high-titer inhibitors; i) state denoted as “all-people-final-pd” in which patients treated with recombinant factor VIII (irrespective of whether they have developed or not high-titer inhibitors) proceed in their Markov iterative process until the end of the time horizon without being any longer exposed to the risk of developing high-titer inhibitors. j) state denoted as “IT-pd” in which patients treated with recombinant factor VIII who have developed high-titer inhibitors receive immune-tolerance therapy and move to the health state “post-IT-pd” and then to the health state “all-people-final-pd”. The model was designed to predict in these cohorts the expected expenditures, that were quantified on the basis of the (different) cumulative incidence of high-titer inhibitors and the (different) cost of the replacement products between the cohorts. It should be noted that some health states assigned, in Figure 1, to the first-level branches of both Panels A and B (governed by the Markov node) are not reachable at the first cycle of the Markov process (i.e. probability = 0 at this cycle), but are designed to be reached from the second-level branches, associated with the development or not of high-titer inhibitors. Finally, although the Treaage software allows to manage other variables participating in the calculation of rewards (namely: initial reward denoted as “Init Rwd”, which is summed upon entry in the health state; and: final reward denoted as “Fin Rwd”, which is summed upon exit from the health state), these were not necessary for the purposes of our model and were therefore kept at 0 (as illustrated in the two panels of Figure 1).