Sequential drug decision problems in long-term medical conditions: a case Study of Primary Hypertension Eunju Kim ba, ma, msc

Z(HS)=27
Z(HS1)=3^0 Z(HS2)=3^1 Z(HS3)=3^2 Z(HS4)=3^3
The size of the search space Z(SS)	Z(SS)=6		Z(SS1)=3 Z(SS2)=3 Z(SS3)=3
The size of the decision space Z(DS)	Z(DS)=6*4*27=648		Z(DS1)=3^0x3=3 Z(DS2)=3^1x3=9 Z(DS3)=3^2x3=27
The calculation of reward	Equation 2.4-2.5		Equation 3.4-3.5	Equation 3.7
The number of search	6	15	39	30,000
Computational intensity	Low	Medium	High	High
Optimal drug sequence	π6 =(drug3,drug2,drug1)		See Table 3.5.	See Table 3.5.
Total net benefit from the optimal solution	£85,716		£86,004	£85,804

1) Computational time was not provided as it was very short for all methods in this small size problem.

Table ‎3.. Optimal treatment pathway obtained from the different optimisation approaches

	Possible disease pathways at t	Enumeration	Simulated annealing	Dynamic programming	Q-learning
t=1	Hu	drug3	drug3	drug3	drug3
t=2	Hu-Hu	drug2	drug2	drug3	drug2
	Hu-He	drug2	drug2	drug1	drug1
	Hu-Hn	drug3	drug3	drug1	drug3
t=3	Hu-Hu-Hu	drug1	drug1	drug3	drug1
	Hu-Hu-He	drug1	drug1	drug1	drug1
	Hu-Hu-Hn	drug2	drug2	drug1	drug2
	Hu-He-Hu	drug1	drug1	drug3	drug2
	Hu-He-He	drug1	drug1	drug1	drug2
	Hu-He-Hn	drug2	drug2	drug1	drug1
	Hu-Hn-Hu	drug2	drug2	drug3	drug2
	Hu-Hn-He	drug2	drug2	drug1	drug1
	Hu-Hn-Hn	drug3	drug3	drug1	drug3
Total net benefits		£85,716	£85,716	£86,004	£85,804

1) The solutions in grey are infeasible, which are against the assumptions made in the hypothetical case study.

Chapter 4.Modelling sequential drug decision problem for hypertension: Overview

4.1Chapter overview

This chapter includes a general description about hypertension and the pharmacological treatment of primary hypertension. A literature review of previous economic evaluations of antihypertensive drugs in primary hypertension summarises the cost-effectiveness results of major antihypertensive drugs and discusses the structures of previous CEA models and their limitations regarding the consideration of drug switching. A conceptual framework of the hypertension SDDP model is presented graphically based on the major clinical guidelines and the previous CEA model structures in primary hypertension. The decision problem is defined with the elements used for the mathematical description of SDDPs in section 2.4.

4.2Hypertension and pharmacologic management

4.2.1Epidemiological aspects of hypertension

Hypertension is a common chronic condition in which the arterial blood pressure is consistently elevated above systolic blood pressure (SBP) 140 mmHg or diastolic blood pressure (DBP) 90 mmHg (see Table ‎4.). Globally, 40% of the adult population aged 20 years or older had hypertension in 2008^[220]. In England, the hypertension prevalence was 31% of men and 28% of women in 2011 in those aged 16 and over^[221]. The prevalence increases with advancing age (see Figure ‎4.).

Table ‎4.. Blood pressure classification from the NICE guideline^[63]

	Clinic BP^1)	ABPM^2) or HBPM^3)BP
Normotensive	< 140/90 mmHg	< 135/85 mmHg
Stage 1 hypertension	≥140/90 mmHg	≥135/85 mmHg
Stage 2 hypertension	≥160/100 mmHg	≥150/95 mmHg
Stage 3 hypertension	≥180/110 mmHg	≥180/110 mmHg

1) BP represents blood pressure; 2) Ambulatory blood pressure monitoring (ABPM) represents daytime average blood pressure; 3) Home blood pressure monitoring (HBPM) represents average blood pressure


1) Hypertensive controlled: SBP below 140 mmHg and DBP below 90 mmHg, currently taking medication specifically prescribed to treat their high blood pressure; Hypertensive uncontrolled: SBP at least 140 mmHg or DBP at least 90 mmHg, currently taking medication specifically prescribed to treat their high blood pressure; Hypertension untreated: SBP at least 140 mmHg or DBP at least 90 mmHg, not currently taking medication specifically prescribed to treat their high blood pressure.
Figure ‎4.. The prevalence of hypertension in 2011, by age and gender^[221]
Figure ‎4.. Mean SBP in 2011, by age and gender in England^[221]

Figure ‎4.. Mean DBP in 2011, by age and gender in England^[221]

The majority of patients with hypertension have primary (or essential) hypertension. Key causal factors identified are excess body weight, excess dietary sodium or alcohol intake, reduced physical activity, inadequate intake of fruits, vegetables and potassium^[9]. Other factors are sympathetic nervous system hyperactivity, abnormal cardiovascular development, rennin-angiotensin system activity and defect in natriuresis, intracellular sodium and calcium^[222].

5-10% of the hypertension is secondary hypertension, which has a specific identified cause for the elevated blood pressure, such as chronic kidney disease (CKD), chronic steroid therapy and Cushing’s syndrome, renovascular disease, pheochromocytoma, aldosteronism and so on. Secondary hypertension is more likely to worsen suddenly and to respond poorly to treatment, but the causes of secondary hypertension are potentially correctable.

Hypertension is not a disease itself, but is one of the most significant risk factors that may increase the chance of cardiovascular morbidity and mortality^[223]. The strong relationship between blood pressure and cardiovascular risk is firmly established for those with and without existing heart disease. MacMahon et al performed an analysis of nine observational studies, involving 420,000 individuals, and found that long-term reductions in usual DBP of 5-10 mmHg were associated with 34-56% reduction in the relative risk (RR) of stroke and 21-37% reduction in the RR of CHD^[224]. The similar relationship between DBP and CHD and stroke was also found in Collins et al’s systematic review of 14 randomised trials of antihypertensive drugs^[225]. With 5-6 mmHg reduction in DBP over 5 years, the reduction in the odds of stroke and CHD were 42% and 14%, respectively. Even in persons whose blood pressure was in the normal range, CV event rates increased with an increase in DBP^[226]. Compared with optimal blood pressure (i.e., BP<120/80 mmHg), the hazard ratio (HR) for cardiovascular disease (CVD) was 2.5 among women and 1.6 among men in the high normal group (i.e., 130/85≤BP≤139/89 mmHg). A stronger relationship between blood pressure and vascular mortality was observed in middle age than in old age^[227]. Given a 20 mmHg SBP or 10 mmHg DBP reduction, the HR in stroke mortality was 0.36 at ages 40-69 years, whereas 0.67 at ages 80-89 years.

4.2.2Antihypertensive drugs¹

(1) Thiazide-type diuretics

Thiazide-type diuretics (Ds) lower blood pressure initially by decreasing plasma volume (by suppressing tubular reabsorption of sodium, thus increasing the excretion of sodium and water) and cardiac output, but during long-term therapy their major hemodynamic effect is reduction of peripheral vascular resistance. Generally they are well tolerated and achieve the treatment goal at low dosages. They are especially effective in the elderly.

The thiazides, which are a type of diuretics, are the most widely used antihypertensive drugs for primary hypertension. A further type, loop-diuretics, may lead to electrolyte and volume depletion more readily than the thiazides and have short durations of action. Therefore, loop Ds should not be used in hypertension except in the presence of renal dysfunction.

Metabolic changes in blood glucose, triglycerides, low-density lipoprotein cholesterol (LDL) and plasma insulin are dose related. These effects are relatively minor during long-term low-dose therapy, but were problematic when high doses of older drugs were used (e.g., hydrochlorothiazide 100 to 200mg per day). If higher doses of Ds are required, the drug should be used in combinations with a potassium-sparing agent or with an angiotensin converting enzyme inhibitor (ACEI) or angiotensin II receptor blocker (ARB).