G Model
AGG-3006; No. of Pages 7 Archives of Gerontology and Geriatrics xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Archives of Gerontology and Geriatrics journal homepage: www.elsevier.com/locate/archger
The long-term effect of community-based health management on the elderly with type 2 diabetes by the Markov modeling Jianqian Chao a, Mengmeng Zong a, Hui Xu b, Qing Yu b, Lili Jiang a, Yunyun Li a, Long Song a, Pei Liu c,* a b c
Department of Medical Insurance, School of Public Health, Southeast University, Nanjing, Jiangsu, China Hospital of Qinghuai, Nanjing, Jiangsu, China Department of Epidemiology and Biostatistics, School of Public Health, Southeast University, Nanjing, Jiangsu, China
A R T I C L E I N F O
A B S T R A C T
Article history: Received 13 May 2013 Received in revised form 4 May 2014 Accepted 8 May 2014 Available online xxx
The aim of this study was to assess the long-term effects of community-based health management on elderly diabetic patients using a Markov model. A Markov decision model was used to simulate the natural history of diabetes. Data were obtained from our randomized trials of elderly with type 2 diabetes and from the published literature. One hundred elderly patients with type 2 diabetes were randomly allocated to either the management or the control group in a one-to-one ratio. The management group participated in a health management program for 18 months in addition to receiving usual care. The control group only received usual care. Measurements were performed on both groups at baseline and after 18 months. The Markov model predicted that for every 1000 diabetic patients receiving health management, approximately 123 diabetic patients would avoid complications, and approximately 37 would avoid death over the next 13 years. The results suggest that the health management program had a positive long-term effect on the health of elderly diabetic patients. The Markov model appears to be useful in health care planning and decision-making aimed at reducing the financial and social burden of diabetes. ß 2014 Elsevier Ireland Ltd. All rights reserved.
Keywords: Markov model Long-term effect Health management Elderly diabetic patients
1. Introduction Diabetes has become a global health problem. New figures indicate that the number of people living with diabetes is expected to rise from 366 million in 2011 to 552 million by 2030 if no urgent action is taken (International Diabetes Federation, 2011). The prevalence of diabetes in China is increasing at a fast pace. According to the World Health Organization (WHO) Global Burden of Disease Study, the number of people with diabetes in China will rise from 20.8 million in 2000 to 42.3 million by 2030, ranking China second in the world in diabetes prevalence (Wild, Roglic, Green, Sicree and King, 2004). The financial and social burden of the disease is significant. In 2010, 11.6% of the world’s health expenditure was spent on prevention and treatment of diabetes (Chinese Diabetes Association, 2011). As an incurable chronic disease, diabetes management requires a lifetime commitment to healthy behaviors aimed at reducing risks for diabetic complications. Medical care by a physician and
* Corresponding author. Tel.: +86 025 86424437/138 13955976. E-mail address: [email protected] (P. Liu).
medication use are not sufficient to treat diabetes. Effective diabetes management requires individual responsibility; a patient with diabetes must decide daily whether to follow a regimen of diet, exercise, and medication compliance (Oglesby, Secnik, Barron, Al-Zakwani, & Lage, 2006; Schlundt, Pichert, Gregory, & Davis, 2003). A diabetes health management program could motivate individuals with diabetes to realize this objective. There have been a number of studies of diabetes health management (Drabik et al., 2012; Samoutis et al., 2010). In a randomized controlled trial (RCT), Samoutis et al. showed that implementation of a multifaceted quality improvement intervention for diabetic patients in primary health care settings resulted in improvements in blood pressure, total cholesterol, low density lipoprotein cholesterol, and three annual process of care measures (urine protein testing, dilated eye examination, and foot examination) compared with the control group at 18-month follow-up (Samoutis et al., 2010). RCTs to date have had limitations, such as short follow-up time (generally only a few weeks or months), failure to account for the natural history of the disease, and inability to detect rare events owing to small sample sizes (Hay, Jackson, Luce, Avorn, & Ashraf, 1999). Thus, analyzing data from RCTs will not fully reflect the role of health management on diabetes progression. Appropriate
http://dx.doi.org/10.1016/j.archger.2014.05.006 0167-4943/ß 2014 Elsevier Ireland Ltd. All rights reserved.
Please cite this article in press as: Chao, J., et al., The long-term effect of community-based health management on the elderly with type 2 diabetes by the Markov modeling. Arch. Gerontol. Geriatr. (2014), http://dx.doi.org/10.1016/j.archger.2014.05.006
G Model
AGG-3006; No. of Pages 7 J. Chao et al. / Archives of Gerontology and Geriatrics xxx (2014) xxx–xxx
2
scientific mathematical models may be used to compensate for the inherent defects of RCTs. The Markov model has been widely proven to be an effective model to assess the long-term effect(s) of an intervention or treatment (Zhu, Ni, & Sun, 2005). There have been studies on the long-term effects of diabetes screening, drug treatment, lifestyle changes, and yearly transitions of disability using the Markov model now (Centers for Disease Control and Prevention (CDC), 1998; Palmer et al., 2004; Raıˆche, He´bert, Dubois, Gueye, & Dubuc, 2012; Valentine, Tucker, Palmer, Minshall, & Silberman, 2009; Zhu et al., 2005); however, very little is known about long-term effects of a diabetes health management program. Assessment of the long-term effects is important prior to implementing a diabetes health management program. This study’s aim was to assess the long-term effects of community-based health management on elderly diabetic patients using a Markov model.
2. Methods 2.1. Subjects and data collection The study was a randomized, parallel-group, controlled trial. It was conducted in collaboration with the Nanjing Community Health Service Center. Nanjing is located in southeastern China; it is the provincial capital of Jiangsu province, one of the most developed provinces in China. We recruited patients with type 2 diabetes from the community health service center from January to July of 2009. Criteria for inclusion of participants were: (1) age 60 and over, (2) local permanent resident, and (3) diagnosed with type 2 diabetes according to the WHO 1999 criteria (WHO, 1999). The exclusion criteria were: (1) cognitive defect, severe psychological disorder or mental illness; (2) severe chronic diseases, such as heart failure, respiratory failure, liver cirrhosis, renal failure, or need for assistance in living; (3) limitations in physical activity; and (4) participating in or having participated in other trials within the last 30 days. People with these exclusion criteria were excluded either because study participation would be challenging for them, or because their inclusion might bias model predictions (e.g.,
increased deaths attributable to chronic diseases other than diabetes). One hundred elderly patients with type 2 diabetes eligible for study participation were randomly allocated to either the management or the control group on a one-to-one ratio using a random number table. All 100 patients signed informed consent forms. 2.2. Intervention The management group participated in an 18-month health management program that included the following components: health evaluation (including dietetic patterns, physical activity, psychological aspects, medication adherence, and self-care for diabetic complications), health management (including dietary advice, psychological counseling, a tailor-made exercise program based on earlier evaluation, education/skills training on diabetes self-management, telephone consultation, lectures on diabetes, distribution of health promoting materials, as well as regular monitoring of blood pressure, blood glucose, and longterm medication use). The components of the intervention were administered at least once per month by specially trained staff of the community health center and related researchers (Fig. 1). The control group received usual care. No study participants were lost to follow-up. After 18 months (December 2010), measurements were performed on both the management and control groups, including fasting blood glucose measurement using the glucose oxidation enzyme method (Ye, Wang, & Shen, 2006). 2.3. Data analyses Double data entry was performed by two independent operators on different computers using Epidata 3.1 software (http://www.epidata.dk/). General characteristics were compared between the management and control groups with t-tests and the chi-square (x2) test using SPSS17.0 (SPSS Inc., Chicago, IL, USA), with 0.05 as the required level of significance. A Markov model was calculated in Metlab 7.0.
Questionnaire Baseline (time 0)
Randomization
Health management group
Control group
During 18 month From baseline
Health management
usual care
usual care
health evaluation management lectures on diabetes
psychologi cal counseling
regular monitoring of blood pressure, blood glucose
monitoring of long-term medication use, so on
18 months
Measurement of outcomes
Measurement of outcomes
Fig. 1. Graphical depiction of the intervention.
Please cite this article in press as: Chao, J., et al., The long-term effect of community-based health management on the elderly with type 2 diabetes by the Markov modeling. Arch. Gerontol. Geriatr. (2014), http://dx.doi.org/10.1016/j.archger.2014.05.006
G Model
AGG-3006; No. of Pages 7 J. Chao et al. / Archives of Gerontology and Geriatrics xxx (2014) xxx–xxx
diabetes without complications
diabetes with complications
3
death
Fig. 2. Markov state transition model of diabetes natural history.
2.3.1. Markov model The first step to using the Markov model in decision analysis is to delineate the different health states according to the degree each affects health. Second, the model depicts the progression of the defined health states, and determines the transition probabilities between health states within a specified time (cycle length). The model estimates the outcome of disease progression by calculating the cumulative effect of health outcomes in each state over multiple cycles (Wang & Jin, 2000). Markov chain is a discrete stochastic process that has two important features: without after-effect (Markov property) and stability (Briggs & Sculpher, 1998; Sonnenberg & Robert, 1993). Markov property refers to the state when the system has been tested i times; it is only related to the state of i 1 times and is independent of previous states – i.e., the future evolution depends solely on the current state. Stability means that Markov property becomes more and more stable after a long time regardless of its initial state. Assuming that an event has undergone k states, the kth state is the absorbing state (random events cannot be transferred from the absorbing state to another state). In our study, the absorbing state is death. If we let any state be the i state, transitions can take place from between 1, 2 . . . i . . . k, with the k states being mutually exclusive (i.e., they could not occur at the same time). Its state random variable is defined as: i ¼ 1; 2; . . . k (1) : xt ¼ i t ¼ 1; 2; . . . Because the state transition is random, we must use probability to describe the possibility of state transition: Pij = P(Ej/ Ei) = P(Ei ! Ej) is used to describe the transition probability from i state to j state. The state transition probability has the following k X characteristics: 0 Pij 1, P i j ¼ 1; i; j ¼ 1; 2; . . . ; k. Under j¼1
certain conditions, it can only be transitioned from one state to another in the set state: Pil, Pi2, . . .. The transition probability matrix is: 2 6 6 6 4
p11 p21 .. .
p2k p22 .. .
.. .
3 p1k p2k 7 7 .. 7 . 5
pk1
pk2
pkk
the long-term effect of diabetes health management according to the multi-state characteristics of diabetes disease outcome. Diabetic patients were divided into three states based on the natural history of diabetes: diabetes without complications, diabetes with complications, and death (Ding, 2001). These three states could not exist at the same time (i.e., they are mutually exclusive). We only knew the patients state at a certain t time, in which the state prior to the t time had nothing to do with the current state (without after-effect). Death was the final absorbing state (Hong, He, & Chang, 2002). Taking into account the irreversibility of the diabetes progression, we developed the diabetic Markov state transition model under the assumption that study participants started in the state of diabetes without complications. A Markov model was used to simulate the transition process of diabetes without complications to diabetes with complications and then to death (Fig. 2). Fig. 3 illustrates the various states and possible transitions between states in the diabetes decision tree model with Markov process. In a Markov state transition model, time processing unit has a fixed length, which is ‘‘a stage.’’ In this study, one year is the cycle of each new stage because the related complications of diabetes often become apparent after years. Because average life expectancy in China is 73 years of age, and study participants were all 60 years of age, we assessed their risk of diabetic complications and death over the next 13 years. At each stage, the cohort was in a certain state. When each new stage began, participants could transfer from one state to another, or remain in the same state without any change. 2.4. Ethical approval This study was approved by the Medical Ethics Committee of Southeast University. All subjects signed written informed consent forms.
3. Results 3.1. General characteristics of patients
(2)
The decision tree model with Markov processes can be established based on the characteristics of the disease, the transition probability, and the purpose of the study. Decisions are then derived from the model’s result. 2.3.2. Markov state transition model of the diabetes In this study, a multi-state Markov decision model was used to simulate the natural history of diabetes to assess
In the management group of 50 patients at baseline, the mean age was 68.5 6.0 years, 54% were males, 60% were husband and wife living together, and 64% had a middle school education. Twentytwo (44%) had diabetes for 5 years or more (time from initial diabetes diagnosis), and 32 (64%) had experienced complications. In the control group of 50 patients at baseline, the mean age was 70.7 6.8 years, 44% were males, 48% were living with their children, and 48% had a primary school education or lower. Twenty-seven (54%) had diabetes for 5 years or more, and 31 (62%) had experienced complications. As shown in Table 1, the two groups were balanced and comparable – i.e., differences between groups were not statistically significant (P > 0.05).
Please cite this article in press as: Chao, J., et al., The long-term effect of community-based health management on the elderly with type 2 diabetes by the Markov modeling. Arch. Gerontol. Geriatr. (2014), http://dx.doi.org/10.1016/j.archger.2014.05.006
G Model
AGG-3006; No. of Pages 7 J. Chao et al. / Archives of Gerontology and Geriatrics xxx (2014) xxx–xxx
4
state transition model
diabetes
diabetes with complications
death
living
death
living
disease progress disease without change
diabetes with death
death
complications
death
diabetes with complications
diabetes
Fig. 3. Decision branching tree of Markov state transition.
3.2. Evaluation of the long-term effect 3.2.1. The transition probability The key point in Markov model application is the determination of the transition probability matrix. The state transition probability refers to the probability that patients in a particular state may transfer to another state during a certain period. Data from our RCT of the health management intervention’s effect on blood glucose (fasting blood glucose decreased 0.82 mmol/L in the management group compared with a 0.06 mmol/L increase in the control group), and data from three other studies (Chen, Cai, & Deng, 2009; Lu, 2008; Sacco, Bykowski, and Mayhew, 2012) were used to determine the parameters of transition probabilities. A 0.99
reduction (0.40, 1.58) in glycated hemoglobin (HbA1c) in the management group relative to the control group was observed (part of the test index is fasting blood glucose); we transformed it using the following formula: average blood glucose (mmol/ L) = [(1.5944 HbA1c) 2.5944] (Nathan et al., 2008). The progression of diabetes and its complications can be modeled as a function of glycemic levels (CDC Diabetes CostEffectiveness Study Group, 1998). One study showed that HbA1c improved 10% relatively, and the relative risk of complications reduced 40% when HbA1c was in the range of 7–11% (Clark, 1998). Complications of diabetes are categorized as macrovascular and microvascular. Column 2 of Table 2 shows the annual conversion rates of diabetes into macrovascular and
Table 1 General characteristics of study participants at baseline. Variables
Age(years) Mean SD Age range Gender Male Female Resident status Husband and wife living together Living alone Living with children Education Primary school or lower Middle school College or higher Disease course
AGG-3006; No. of Pages 7 Archives of Gerontology and Geriatrics xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Archives of Gerontology and Geriatrics journal homepage: www.elsevier.com/locate/archger
The long-term effect of community-based health management on the elderly with type 2 diabetes by the Markov modeling Jianqian Chao a, Mengmeng Zong a, Hui Xu b, Qing Yu b, Lili Jiang a, Yunyun Li a, Long Song a, Pei Liu c,* a b c
Department of Medical Insurance, School of Public Health, Southeast University, Nanjing, Jiangsu, China Hospital of Qinghuai, Nanjing, Jiangsu, China Department of Epidemiology and Biostatistics, School of Public Health, Southeast University, Nanjing, Jiangsu, China
A R T I C L E I N F O
A B S T R A C T
Article history: Received 13 May 2013 Received in revised form 4 May 2014 Accepted 8 May 2014 Available online xxx
The aim of this study was to assess the long-term effects of community-based health management on elderly diabetic patients using a Markov model. A Markov decision model was used to simulate the natural history of diabetes. Data were obtained from our randomized trials of elderly with type 2 diabetes and from the published literature. One hundred elderly patients with type 2 diabetes were randomly allocated to either the management or the control group in a one-to-one ratio. The management group participated in a health management program for 18 months in addition to receiving usual care. The control group only received usual care. Measurements were performed on both groups at baseline and after 18 months. The Markov model predicted that for every 1000 diabetic patients receiving health management, approximately 123 diabetic patients would avoid complications, and approximately 37 would avoid death over the next 13 years. The results suggest that the health management program had a positive long-term effect on the health of elderly diabetic patients. The Markov model appears to be useful in health care planning and decision-making aimed at reducing the financial and social burden of diabetes. ß 2014 Elsevier Ireland Ltd. All rights reserved.
Keywords: Markov model Long-term effect Health management Elderly diabetic patients
1. Introduction Diabetes has become a global health problem. New figures indicate that the number of people living with diabetes is expected to rise from 366 million in 2011 to 552 million by 2030 if no urgent action is taken (International Diabetes Federation, 2011). The prevalence of diabetes in China is increasing at a fast pace. According to the World Health Organization (WHO) Global Burden of Disease Study, the number of people with diabetes in China will rise from 20.8 million in 2000 to 42.3 million by 2030, ranking China second in the world in diabetes prevalence (Wild, Roglic, Green, Sicree and King, 2004). The financial and social burden of the disease is significant. In 2010, 11.6% of the world’s health expenditure was spent on prevention and treatment of diabetes (Chinese Diabetes Association, 2011). As an incurable chronic disease, diabetes management requires a lifetime commitment to healthy behaviors aimed at reducing risks for diabetic complications. Medical care by a physician and
* Corresponding author. Tel.: +86 025 86424437/138 13955976. E-mail address: [email protected] (P. Liu).
medication use are not sufficient to treat diabetes. Effective diabetes management requires individual responsibility; a patient with diabetes must decide daily whether to follow a regimen of diet, exercise, and medication compliance (Oglesby, Secnik, Barron, Al-Zakwani, & Lage, 2006; Schlundt, Pichert, Gregory, & Davis, 2003). A diabetes health management program could motivate individuals with diabetes to realize this objective. There have been a number of studies of diabetes health management (Drabik et al., 2012; Samoutis et al., 2010). In a randomized controlled trial (RCT), Samoutis et al. showed that implementation of a multifaceted quality improvement intervention for diabetic patients in primary health care settings resulted in improvements in blood pressure, total cholesterol, low density lipoprotein cholesterol, and three annual process of care measures (urine protein testing, dilated eye examination, and foot examination) compared with the control group at 18-month follow-up (Samoutis et al., 2010). RCTs to date have had limitations, such as short follow-up time (generally only a few weeks or months), failure to account for the natural history of the disease, and inability to detect rare events owing to small sample sizes (Hay, Jackson, Luce, Avorn, & Ashraf, 1999). Thus, analyzing data from RCTs will not fully reflect the role of health management on diabetes progression. Appropriate
http://dx.doi.org/10.1016/j.archger.2014.05.006 0167-4943/ß 2014 Elsevier Ireland Ltd. All rights reserved.
Please cite this article in press as: Chao, J., et al., The long-term effect of community-based health management on the elderly with type 2 diabetes by the Markov modeling. Arch. Gerontol. Geriatr. (2014), http://dx.doi.org/10.1016/j.archger.2014.05.006
G Model
AGG-3006; No. of Pages 7 J. Chao et al. / Archives of Gerontology and Geriatrics xxx (2014) xxx–xxx
2
scientific mathematical models may be used to compensate for the inherent defects of RCTs. The Markov model has been widely proven to be an effective model to assess the long-term effect(s) of an intervention or treatment (Zhu, Ni, & Sun, 2005). There have been studies on the long-term effects of diabetes screening, drug treatment, lifestyle changes, and yearly transitions of disability using the Markov model now (Centers for Disease Control and Prevention (CDC), 1998; Palmer et al., 2004; Raıˆche, He´bert, Dubois, Gueye, & Dubuc, 2012; Valentine, Tucker, Palmer, Minshall, & Silberman, 2009; Zhu et al., 2005); however, very little is known about long-term effects of a diabetes health management program. Assessment of the long-term effects is important prior to implementing a diabetes health management program. This study’s aim was to assess the long-term effects of community-based health management on elderly diabetic patients using a Markov model.
2. Methods 2.1. Subjects and data collection The study was a randomized, parallel-group, controlled trial. It was conducted in collaboration with the Nanjing Community Health Service Center. Nanjing is located in southeastern China; it is the provincial capital of Jiangsu province, one of the most developed provinces in China. We recruited patients with type 2 diabetes from the community health service center from January to July of 2009. Criteria for inclusion of participants were: (1) age 60 and over, (2) local permanent resident, and (3) diagnosed with type 2 diabetes according to the WHO 1999 criteria (WHO, 1999). The exclusion criteria were: (1) cognitive defect, severe psychological disorder or mental illness; (2) severe chronic diseases, such as heart failure, respiratory failure, liver cirrhosis, renal failure, or need for assistance in living; (3) limitations in physical activity; and (4) participating in or having participated in other trials within the last 30 days. People with these exclusion criteria were excluded either because study participation would be challenging for them, or because their inclusion might bias model predictions (e.g.,
increased deaths attributable to chronic diseases other than diabetes). One hundred elderly patients with type 2 diabetes eligible for study participation were randomly allocated to either the management or the control group on a one-to-one ratio using a random number table. All 100 patients signed informed consent forms. 2.2. Intervention The management group participated in an 18-month health management program that included the following components: health evaluation (including dietetic patterns, physical activity, psychological aspects, medication adherence, and self-care for diabetic complications), health management (including dietary advice, psychological counseling, a tailor-made exercise program based on earlier evaluation, education/skills training on diabetes self-management, telephone consultation, lectures on diabetes, distribution of health promoting materials, as well as regular monitoring of blood pressure, blood glucose, and longterm medication use). The components of the intervention were administered at least once per month by specially trained staff of the community health center and related researchers (Fig. 1). The control group received usual care. No study participants were lost to follow-up. After 18 months (December 2010), measurements were performed on both the management and control groups, including fasting blood glucose measurement using the glucose oxidation enzyme method (Ye, Wang, & Shen, 2006). 2.3. Data analyses Double data entry was performed by two independent operators on different computers using Epidata 3.1 software (http://www.epidata.dk/). General characteristics were compared between the management and control groups with t-tests and the chi-square (x2) test using SPSS17.0 (SPSS Inc., Chicago, IL, USA), with 0.05 as the required level of significance. A Markov model was calculated in Metlab 7.0.
Questionnaire Baseline (time 0)
Randomization
Health management group
Control group
During 18 month From baseline
Health management
usual care
usual care
health evaluation management lectures on diabetes
psychologi cal counseling
regular monitoring of blood pressure, blood glucose
monitoring of long-term medication use, so on
18 months
Measurement of outcomes
Measurement of outcomes
Fig. 1. Graphical depiction of the intervention.
Please cite this article in press as: Chao, J., et al., The long-term effect of community-based health management on the elderly with type 2 diabetes by the Markov modeling. Arch. Gerontol. Geriatr. (2014), http://dx.doi.org/10.1016/j.archger.2014.05.006
G Model
AGG-3006; No. of Pages 7 J. Chao et al. / Archives of Gerontology and Geriatrics xxx (2014) xxx–xxx
diabetes without complications
diabetes with complications
3
death
Fig. 2. Markov state transition model of diabetes natural history.
2.3.1. Markov model The first step to using the Markov model in decision analysis is to delineate the different health states according to the degree each affects health. Second, the model depicts the progression of the defined health states, and determines the transition probabilities between health states within a specified time (cycle length). The model estimates the outcome of disease progression by calculating the cumulative effect of health outcomes in each state over multiple cycles (Wang & Jin, 2000). Markov chain is a discrete stochastic process that has two important features: without after-effect (Markov property) and stability (Briggs & Sculpher, 1998; Sonnenberg & Robert, 1993). Markov property refers to the state when the system has been tested i times; it is only related to the state of i 1 times and is independent of previous states – i.e., the future evolution depends solely on the current state. Stability means that Markov property becomes more and more stable after a long time regardless of its initial state. Assuming that an event has undergone k states, the kth state is the absorbing state (random events cannot be transferred from the absorbing state to another state). In our study, the absorbing state is death. If we let any state be the i state, transitions can take place from between 1, 2 . . . i . . . k, with the k states being mutually exclusive (i.e., they could not occur at the same time). Its state random variable is defined as: i ¼ 1; 2; . . . k (1) : xt ¼ i t ¼ 1; 2; . . . Because the state transition is random, we must use probability to describe the possibility of state transition: Pij = P(Ej/ Ei) = P(Ei ! Ej) is used to describe the transition probability from i state to j state. The state transition probability has the following k X characteristics: 0 Pij 1, P i j ¼ 1; i; j ¼ 1; 2; . . . ; k. Under j¼1
certain conditions, it can only be transitioned from one state to another in the set state: Pil, Pi2, . . .. The transition probability matrix is: 2 6 6 6 4
p11 p21 .. .
p2k p22 .. .
.. .
3 p1k p2k 7 7 .. 7 . 5
pk1
pk2
pkk
the long-term effect of diabetes health management according to the multi-state characteristics of diabetes disease outcome. Diabetic patients were divided into three states based on the natural history of diabetes: diabetes without complications, diabetes with complications, and death (Ding, 2001). These three states could not exist at the same time (i.e., they are mutually exclusive). We only knew the patients state at a certain t time, in which the state prior to the t time had nothing to do with the current state (without after-effect). Death was the final absorbing state (Hong, He, & Chang, 2002). Taking into account the irreversibility of the diabetes progression, we developed the diabetic Markov state transition model under the assumption that study participants started in the state of diabetes without complications. A Markov model was used to simulate the transition process of diabetes without complications to diabetes with complications and then to death (Fig. 2). Fig. 3 illustrates the various states and possible transitions between states in the diabetes decision tree model with Markov process. In a Markov state transition model, time processing unit has a fixed length, which is ‘‘a stage.’’ In this study, one year is the cycle of each new stage because the related complications of diabetes often become apparent after years. Because average life expectancy in China is 73 years of age, and study participants were all 60 years of age, we assessed their risk of diabetic complications and death over the next 13 years. At each stage, the cohort was in a certain state. When each new stage began, participants could transfer from one state to another, or remain in the same state without any change. 2.4. Ethical approval This study was approved by the Medical Ethics Committee of Southeast University. All subjects signed written informed consent forms.
3. Results 3.1. General characteristics of patients
(2)
The decision tree model with Markov processes can be established based on the characteristics of the disease, the transition probability, and the purpose of the study. Decisions are then derived from the model’s result. 2.3.2. Markov state transition model of the diabetes In this study, a multi-state Markov decision model was used to simulate the natural history of diabetes to assess
In the management group of 50 patients at baseline, the mean age was 68.5 6.0 years, 54% were males, 60% were husband and wife living together, and 64% had a middle school education. Twentytwo (44%) had diabetes for 5 years or more (time from initial diabetes diagnosis), and 32 (64%) had experienced complications. In the control group of 50 patients at baseline, the mean age was 70.7 6.8 years, 44% were males, 48% were living with their children, and 48% had a primary school education or lower. Twenty-seven (54%) had diabetes for 5 years or more, and 31 (62%) had experienced complications. As shown in Table 1, the two groups were balanced and comparable – i.e., differences between groups were not statistically significant (P > 0.05).
Please cite this article in press as: Chao, J., et al., The long-term effect of community-based health management on the elderly with type 2 diabetes by the Markov modeling. Arch. Gerontol. Geriatr. (2014), http://dx.doi.org/10.1016/j.archger.2014.05.006
G Model
AGG-3006; No. of Pages 7 J. Chao et al. / Archives of Gerontology and Geriatrics xxx (2014) xxx–xxx
4
state transition model
diabetes
diabetes with complications
death
living
death
living
disease progress disease without change
diabetes with death
death
complications
death
diabetes with complications
diabetes
Fig. 3. Decision branching tree of Markov state transition.
3.2. Evaluation of the long-term effect 3.2.1. The transition probability The key point in Markov model application is the determination of the transition probability matrix. The state transition probability refers to the probability that patients in a particular state may transfer to another state during a certain period. Data from our RCT of the health management intervention’s effect on blood glucose (fasting blood glucose decreased 0.82 mmol/L in the management group compared with a 0.06 mmol/L increase in the control group), and data from three other studies (Chen, Cai, & Deng, 2009; Lu, 2008; Sacco, Bykowski, and Mayhew, 2012) were used to determine the parameters of transition probabilities. A 0.99
reduction (0.40, 1.58) in glycated hemoglobin (HbA1c) in the management group relative to the control group was observed (part of the test index is fasting blood glucose); we transformed it using the following formula: average blood glucose (mmol/ L) = [(1.5944 HbA1c) 2.5944] (Nathan et al., 2008). The progression of diabetes and its complications can be modeled as a function of glycemic levels (CDC Diabetes CostEffectiveness Study Group, 1998). One study showed that HbA1c improved 10% relatively, and the relative risk of complications reduced 40% when HbA1c was in the range of 7–11% (Clark, 1998). Complications of diabetes are categorized as macrovascular and microvascular. Column 2 of Table 2 shows the annual conversion rates of diabetes into macrovascular and
Table 1 General characteristics of study participants at baseline. Variables
Age(years) Mean SD Age range Gender Male Female Resident status Husband and wife living together Living alone Living with children Education Primary school or lower Middle school College or higher Disease course
