Short Communication

Markov Prediction Model for the Main Complications of Type 2 Diabetes Mellitus

Maurílio Souza Cazarim1, Ana Carolina de Oliveira Gonçalves2, André de Oliveira Baldoni2, Cristina Sanches2, Leonardo Régis Leira Pereira1
1Faculty of Pharmaceutical Sciences of Ribeirão Preto, University of São Paulo (FCFRP-USP). Av. Bandeirantes, 3,900 Monte Alegre. Ribeirão Preto Brazil, Phone: (16) 3315-4000.
2Federal University of São João Del-Rei (UFSJ). Rua Sebastião Gonçalves Coelho, 400 - Bairro Chanadour - Divinópolis - MG – Brazil.
*Corresponding author:

Maurílio de Souza Cazarim, Center for Research in Pharmaceutical Care and Clinical Pharmacy (CPAFF), Faculty of Pharmaceutical Sciences of Ribeirão Preto, University of São Paulo, Ribeirão Preto - SP, Brazil- 14040-903, Phone: +55 016 3315-4236, E-mail: maurilio.jf@gmail.com

It is estimated that currently 415 million people live with diabetes mellitus in the world and and there is the trendof this number to increase. . Monitoring of patients over a long period of time often becomes impracticable due to the difficulty in keeping the environment controlled for follow-up in the absence of bias, and also due to the loss of patients in follow-up and the cost of carrying out a prolonged study. This study proposes a schematic diagram for Markov modeling in predicting the major complications of Type 2 Diabetes Mellitus (T2DM)over time. The main steps of the Markov model are: to define health states; to determine the transitions between health states; to define the temporal extent and quantity of each cycle; and to estimate the probabilities, costs, and outcomes associated with each state. In Markov model proposed, the diabetic cohort of patients starts in a stable state, early diagnosed patients with T2DM, without complications. Over time, measured annually, certain portions of the patient cohort can be allocated to the following health states: pressure ulcer, diabetic foot, retinopathy, neuropathy, cardiovascular disease, and chronic kidney disease, according to the probabilities defined by the glycated hemoglobin level of each patient. This study proposed a diagram for predictive models of health states in T2DM to be tested in clinical trials or projection studies, This model is to be used only for research purposes and not in clinical settings.

Chronic diseases play an increasingly important role in the public health scenario around the world, since the phenomenon of epidemiological transition has characterized a change in the profile of population morbidity and mortality [1]. In addition, it is estimated that currently 415 million people live with diabetes mellitus in the world and and there is the trendof this number to increase.Because of this the diabetes mellitus has occupied a relevant place among the chronic diseases that affect the world population. [1,2]. Type 2 Diabetes Mellitus (T2DM) can lead to several macro and microvascular complications for the patient [3,4]. Because it is a chronic disease, many patients become incapacitated due to the severity of these complications, which result in clinical, financial and social consequences [5,6]. According to data from the National Health and Nutrition Examination Survey, which was conducted between 2007 and 2010, 40 % of Americans with T2DM failed to achieve adequate glycemic control [7].This high prevalence of uncontrolled patients increases the occurrence of complications [8,9].

Complications related to T2DM can be divided into acute and chronic complications. Acute complications include hyperglycemia (casual glycemia> 250 mg/dL), with or without ketoacidosis, and hypoglycemia (casual glycemia<60 mg/dL). Chronic complications can be divided into microvascular complications related to the natural evolution of T2DM, and macrovascular complications, which are not necessarily related to T2DM, but are usually more severe in patients with this clinical condition. Microvascular complications include retinopathy, pressure ulcers, diabetic foot, nephropathy and neuropathy. Macrovascular complications are represented by cardiovascular diseases: ischemic heart disease, stroke and peripheral arterial disease [3].

Glycated hemoglobin (A1c) is the method that allows estimating the patient's glycemic profile for a period of approximately 90 to 120 days. A study of 183 patients who had A1cmonitored in the laboratory found A1c values at a mean of 10.2 % and a range of 3.9 - 19.1 %. Another study considered only T2DM patients who were in treatment for the disease. The average found among the 193 patients belonging to the study wasA1c of 7.7 % [10,11]. The main complications that can result from the lack of glycemic control are pressure ulcers, diabetic foot, retinopathy, neuropathy, cardiovascular diseases,and chronic kidney disease [3,12]. Retinopathy is the leading cause of blindness in adults, and after 20 years of illness approximately 60 % of T2DM patients will already have some visual impairment. T2DM continues to be the main cause of chronic kidney disease (CKD), about 1/5 patients with T2DM have a decreased glomerular filtration rate (GFR), that is, they have some degree of diabetic nephropathy. Neuropathy also has a high prevalence among patients with T2DM. In T2DM, some degree of neuropathy can usually be verified at the time of diagnosis. All of these T2DM complications directly impact the patient's quality of life [3,12].

Patients with A1c within the considered adequate values, that is, less than 6.5 % present a relative risk of developing complications (neuropathy, retinopathy, nephropathy and microvascular problems), similar to that of a patient who does not have diabetes. When we consider the A1c values close to 8 % the relative risk approaches three [3]. With a value of A1c between 11 and 12 %, the patient with T2DM is 20 times more likely to present these complications when compared to a patient without diabetes. The reduction of 1 % in A1c values implies a 43 % reduction in the risk of amputation, a 14 % risk of acute myocardial infarction and a 37 % reduction in microvascular complications [2,3,10,11]. Monitoring of patients over a long period of time often becomes impracticable due to the difficulty in keeping the environment controlled for follow-up in the absence of bias, and also due to the loss of patients in follow-up and the cost of carrying out a prolonged study. These factors compromise the efficiency of achieving long-term outcomes for the diabetic patient. This makes it impossible or difficult to visualize the results of health interventions or technologies in the face of the main complications of T2DM over time. In this sense, the use of modeling methods are very valid to consolidate predictive models [2,13]. The mathematical model that is used for chronic diseases is Markov modeling, since it can be projected together with the decision tree constituting more complex outcomes related to health status over a long period of time. Because it is a predictive model grounded in probabilities linked to epidemiological indicators like relative risk, incidence tax, mortality tax. Its application allows individuals to be assigned different health states that are defined as Markov health states, and it also makes it possible to establish transition states for the individual over time by assigning costs and utility measures to quality of life, denoted transition states of Markov. The time horizon is usually defined over years, and each year determines a Markov cycle. Through prior knowledge about the disease, including epidemiological issues such as incidence and mortality, it becomes possible to jointly apply statistical tools to modeling to distribute the probabilities to each patient's state, including their transition over time. Thus is possible to simulate a hypothetic cohort along the years only using the real data from small number of patients [14, 15,16]. This study proposes a schematic diagram for Markov modeling in predicting the major complications of T2DM over time. The main steps of the Markov model are: to define health states; to determine the transitions between health states; to define the temporal extent and quantity of each cycle; and to estimate the probabilities, costs, and outcomes associated with each state. The schematization of these steps is paramount to the development of the model, and is called diagramming.

The diagram should represent the transition states for the morbidity in question and for this there must be specific knowledge of the disease and its possible prognoses and complications. The transition between health states should be diagrammed before entering a Markov model, because it is possible to visualize the possibilities of transition within the real perspective of the disease, reducing the chance of errors occurring in the modeling. Temporal extension is fundamental in modeling, because in it is predicted a curve of probability distribution in which time is a preponderant factor for the occurrence of events. The temporal extension can be represented in the diagram, therefore, it facilitates the interpretation of the prognosis before certain morbidities that develop throughout the disease [13,14]. The estimation of probabilities should come from real data, whether obtained from previous studies or even from the consensus of experts based on their practice. The probabilities will be fundamental within the survival function for each Markov modeling state, and through them, the chances of the patient being allocated to each state of health throughout the projection will occur. At the end of each health state, the cost and utility of that health state can be attributed, which allows us to measure outcomes such as quality adjusted life years - QALY and years of life saved - YLS, as well as pharmacoeconomic analyzes such as cost of illness, cost-effectiveness, cost-utility, and budget impact of completed intervention or health technology [14].

Transition probabilities may vary over time, thus stochastic methods become essential, in which they will predict within a probability distribution curve the variation of probabilities for health states in the scenario proposed in the diagram [13,16]. For this, we must consider a survival function for health states. Survival functions can be defined according to the clinical data and the knowledge provided for the morbidity in question. The general function for survival in a given health state is related to the occurrence of the event (F), which determines the survival (S) in

clyto access

For chronic diseases the most predatory models of survival function are associated with exponential and weibull distribution [17]:

Exponential


clyto access

Note: S (t) = survival function; h (t) = risk function; f (t) = density function of the probabilities for the failure time according to the distribution. Where λ is a positive parameter, often called rate, and where t> 0. Note also that the exponential distribution has mean 1 / λ and variance 1 / λ2. The shape of the density is the same for all λ, and 1 / λ acts as a scale parameter.

Weibull


clyto access

Note: S (t) = survival function; h (t) = risk function; f (t) = density function of the probabilities for the failure time according to the distribution.Where t> 0 and α and η are set as positive parameters, being α a scale parameter and η a shape parameter. Note that when η = 1, we obtain an exponential distribution with parameter λ = 1 / α. The transition state diagram model that is being proposed is more strongly associated with an exponential distribution, since it fits the transition of all Markov health states, the main states of T2DM complications, during the Markov cycle. Thus, it is preferable that the risk be constant as determined by the exponential distribution. Patients are allocated throughout the annual cycles according to the risk-weighted odds, relative to presenting the particular complication of the disease. If on the timeline the patient presents more complications, the care intensifies, and the chances of better glycemic indexes and A1c rates are balanced by the more complex care model, which does not decrease or increase the risk [3,11]. However, these distributions compose a model that works as an overall picture and difficult to give individual actual estimates. Then, when there is the need to use individual data is recommended to input the probabilities of each patient in the model and follow a proper distribution to the database [14]. The diagram shows that the cohort of diabetic patients starts in a stable state, taking care only of T2DM. Over time, measured annually, certain portions of the patient cohort can be allocated to the following health states: pressure ulcer, diabetic foot, retinopathy, neuropathy, cardiovascular disease (CVD), and chronic kidney disease (CKD), according to the probabilities defined by the A1c level of each patient. In each state the patient is likely to be on treatment or die. Death is a state of absorption for Markov modeling, so the patient does not return to participate in the cycles. Also, for the patient being treated, the year following theymay continue to cope with the T2DM complication or to die from that complication.

It is noteworthy that the health states of pressure ulcer, and the specific cardiovascular diseases of stroke, peripheral arterial disease, and ischemic heart disease are states that present the probability of recurrence for the respective complication. For diabetic foot there is the likelihood of the patient suffering an amputation and returning for secondary or recurrent treatment, or death.Retinopathy can progress to blindness and the patient still has a chance of death in this state. In neuropathy there is the possibility of compromising a vital organ, and then the patient begins to treat this condition with a new probability of death. In CVD states, the patient goes on to a tertiary prevention in order to avoid recurrence of the disease; in this state of tertiary prevention there is a likelihood that the patient will continue to be prevented or die. For CKD, the disease may be severe and the patient may undergo renal dialysis, in the latter state the patient may remain on dialysis or die (Figure 1).

clyto access
Figure 1. State transition diagram for analytical decision Markov model of type 2 diabetes mellitus. Legend: CKD = Chronic kidney disease; CVD = cardiovascular disease; IHD = Ischemic heart diseases; PAD = Peripheral artery disease; ; ST = Stroke; T2DM = Type 2 diabetes mellitus. In each branch there is a specific transition probability for the respective health condition. Note: when the patient is affected by the complication in this model, is necessary to use the incidence probability of that complication and to assign the hospitalization cost and emergency cost weighted by their hospitalization rates in diabetic patients for each health state.that year must incorporate the hospitalization cost and emergency cost. Highlights that the next years that the patient will be in that state the specific cost will be only to secondary prevention for that he is not affected in a second time.

Markov models are important methods to predict outcomes and costs in the health system [18].This study proposed a diagram for predictive models of health states in T2DM to be tested in clinical trials or projection studies. Thus, this diagram allows to generate the hypothesis that the Markov model structured according to it, tends to measure costs and health outcomes over time for patients with T2DM.However, it is a model that can be applied in some clinical studies, then the researcher need get knowledgement in pharmacoeconomics area to apply this model. This model is important to be applied in studies with elevated evidence degree like trials and meta-análises because the pharmacoeconomics is a branch of the sciences that has contributed to improving the evidence level for incorporating new technologies, procedures, services, drugs in the health system. Summarising, this model can be useful for saving resources in the health due it predict outcomes and expenditure in the T2DM care.

1. Malta Dc, Cezário Ac, Moura L, Neto Olm, Junior Jbs (2006) A construção da vigilância e prevenção das doenças crônicas não transmissíveis no contexto do Sistema Único de Saúde. Epidemiologia e Serviços de Saúde 15: 47-65.
2. American Diabetes Association (ADA). Standards of Medical Care in Diabetes –2016 (2016)Diabetes Care 39 (Suppl 1).
3. Brazilian Society Of Diabetes (SBD). Diretrizes da Sociedade Brasileira de Diabetes: 2014-2015 (2015)São Paulo: AC Farmacêutica.
4. http://www.diabetesatlas.org/content/diabetes.
5. Silva IJ, Pais-Ribeiro H, Cardoso HR (2003) Efeitos do Apoio Social na Qualidade de Vida, Controlo Metabólico e Desenvolvimento de Complicações Crónicas em Indivíduos com Diabetes. Psicologia, Saúde & Doenças 4: 21-23.
6. Pereira DS, Nogueira JAD, Silva CAB (2015) Qualidade de vida e situação de saúde de idosos: um estudo de base populacional no Sertão Central do Ceará. Rev. Bras. Geriatr. Gerontol. Rio de Janeiro 18: 893-908.
7. Casagrande SS, Fradkin JE, Saydah SH, Rust KF, Cowie CC (2013) The prevalence of meeting A1c, blood pressure, and LDL goals among people with diabetes, 1988-2010. Diabetes Care 36: 2271-2279.
8. Lachin JM, Orchard TJ, Nathan DM (2014) Update on Cardiovascular Outcomes at 30 Years of the Diabetes Control and Complications Trial/Epidemiology of Diabetes Interventions and Complications Study. Diabetes Care 37: 39-46.
9. Casagrande SS, Fradkin JE, Saydah SH, Rust KF, Cowie CC (2013) The Prevalence of Meeting A1C, Blood Pressure, and LDL Goals Among People With Diabetes, 1988–2010. Epidemiology/Health Services Research. Diabetes Care 36: 2271-2279.
10. Velasquez PA, Agnes C, Svidzinsk TI (2011) Hemoglobina Glicada como ferramenta na avaliação do controle glicêmico de pacientes. Rev bras anal clin 43: 21-25.
11. Obreli-Neto PR, Marusic S, Guidoni CM, Baldoni AD, Renovato RD, et al. (2015) Economic evaluation of a pharmaceutical care program for elderly diabetic and hypertensive patients in primary health care: a 36-month randomized controlled clinical trial. Journal of managed care & specialty pharmacy. 21:66-75.
12. Barrile SR, Ribeiro AA, Costa APR, Viana AA, De Conti MHS, et al. (2013) Comprometimento sensório-motor dos membros inferiores em diabéticos do tipo 2 Fisioter Mov 26:537-548.
13. Drummond MF, Sculpher MJ, Claxton K, Stoddart GL, Torrance Gw (2005) Methods for the economic evaluation of health care programmes. 3 th ed. Oxford: Oxford university press 379.
14. Rascati Kl (2014) Essentials of Pharmacoeconomics. 2nd ed. Baltimore, MD: Lippincott Williams & Wilkins 289p.
15. Stevanovic J, Postma MJ, Pechlivanoglou P (2012) A systematic review on the application of cardiovascular risk prediction models in pharmacoeconomics, with a focus on primary prevention. Euro J Preventive Cardiology 19: 42–53 Strom Bl (2005) What is Pharmacoepidemiology? In: Strom BL,editor. Pharmacoepidemiology. 3rd ed. Chichester (UK): John Wiley & Sons Ltd 3-15.
16. Cazarim MS, Einarson TR (2017) New Prediction Methods of Indicators and Costs Capable of Increasing the Efficiency of Pharmacoeconomic Studies for Health Decision Analysis. Pharmaceutica analytica acta. 8:556.
17. Pagano M, Gauvreau M (2012) Princípios de Bioestatística. 2. ed. São Paulo, SP: Cengage Learning, 506.
18. Cazarim MS, Goncalves ACO, Maduro LCS, Pereira LR (2016) Perspectives of Pharmacoeconomics to improve access to the Brazilian Public Health System. J Appl Pharmaceut Sci 3: 3-6.

Citation: Cazarim MS, Oliveira Goncalves AC, Baldoni AO, Sanches C, Leira Pereira LR (2017) Markov Prediction Model for the main Complications of Type 2 Diabetes Mellitus. J Diabetes Care Endocrinolo 1:004

Published: 29 November 2017

Reviewed By : Dr. Hanan El-Sayed Badr, Dr. Teresa Arora,

Copyright:

© 2017 Cazarim et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.