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

5.4The structure of the short-term drug switching model

There were three potential health states in the short-term drug switching model as structured in 1) d1-d4 represents the drug used for the specific health state in each period, given a policy π=(d1,d2,d3,d4).:

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  Success: including the patients who achieved the treatment goal.
  
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  Failure: including
  

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  The patients who did not achieve the treatment goal or
  
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  The patients who had a CVDs, DM or any other AEs.
  

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  Death
  

All patients started from Failure, which means uncontrolled hypertension. Every three months, a proportion of patients stayed at 1) Failure or moved to either 2) Success or 3) Death. Treatment success rate, which was the transition probability from Failure to Success, was dependent on SBP and the risk of CVDs, DM and other AEs. According to the NICE’s clinical guideline, treatment success of antihypertensive drugs was defined as following^[63]:

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  SBP<140 if 10-year CVD risk is higher than 20%, or
  
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  SBP<160 if 10-year CVD risk is less than 20%,
  
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  without CVD, DM or other AEs.
  

The treatment success rate was calculated by using a Monte Carlo sampling method. For each health state in each time period, the Monte Carlo simulation randomly generated 1,000 individual patients who have a set of sampled baseline SBP, SBP lowering effect and the risk of CVD, DM and AEs. 1,000 samples of baseline SBPs were generated based on the previous treatment results (i.e., the mean SBP and the SD after previous treatment). 1,000 samples of the level of SBP reductions and the occurrences of AEs including DM were also randomly generated based on the best available data and their distributions of the drug used. SBPs after treatment were calculated by subtracting the levels of SBP reduction from the baseline SBPs. CVD risks were calculated based on the SBPs after treatment, using a reported link between SBP and CVD risk (see discussion in section 5.6.1). The treatment was regarded as being successful if the set of sampled results meet the criteria of treatment success defined above. The treatment success rate was calculated based on the proportion of treatment success in the 1,000 sets of sampled results; and used for the transition probability from the current state to Success in the next period. The mean and SD of SBPs after treatment were saved separately for the patients whose treatment were successful and unsuccessful to use them to generate the baseline SBPs in the next time period depending on the health state evaluated.

This model assumed that the controlled patients took an appropriate maintenance therapy with regular check-up and kept their SBP around 128.8 mmHg (SE 0.36) for men and 122.3 mmHg (SE 0.43) for women, which were the mean SBP of general population aged over 60 in England^[221].

Total mortality was the sum of CVD mortality and non-CVD mortality. The CVD mortality was estimated by multiplying the CVD risk calculated by QRISK2^[285] and the proportion of CVD death of first-onset CVD (see Table ‎5.)^{[63, 286]}. Therefore CVD mortality was directly dependent on the changes in SBP and patients’ risk factors (e.g., age and gender) over time. On the other hand, non-CVD death, which was defined as the death caused by any other reasons, was calculated based on all-cause mortality estimated from the life tables between 2008 and 2010 in England and Wales (see Table ‎5.)^[287] and the proportion of non-circulatory death of all deaths (see )^[288].

Table ‎5.. Age and gender-specific proportions of first-onset CVD^{[63, 286]}

Age/Men	UA	MI	Stroke	CVD death	Other	Total
45	0.107	0.295	0.129	0.101	0.368	1
55	0.071	0.172	0.206	0.134	0.417	1
65	0.083	0.173	0.270	0.160	0.314	1
75	0.081	0.161	0.343	0.143	0.272	1
85	0.096	0.186	0.351	0.137	0.230	1
Age/Women	UA	MI	Stroke	CVD death	Other	Total
45	0.117	0.080	0.229	0.091	0.483	1
55	0.073	0.092	0.288	0.106	0.441	1
65	0.052	0.121	0.382	0.171	0.274	1
75	0.034	0.102	0.464	0.152	0.248	1
85	0.029	0.100	0.501	0.147	0.223	1

Table ‎5.. All-cause mortality between 2008 and 2010 in England and Wales^[287]

Age	Men	Women		Age	Men	Women
60	0.008503	0.005451		81	0.069174	0.048877
61	0.009045	0.005974		82	0.076246	0.054728
62	0.009867	0.006313		83	0.083825	0.061825
63	0.01113	0.007036		84	0.095148	0.069497
64	0.012319	0.007806		85	0.105922	0.078345
65	0.013317	0.008423		86	0.117177	0.087814
66	0.014845	0.009294		87	0.127952	0.098374
67	0.016206	0.010084		88	0.139538	0.111449
68	0.018296	0.011329		89	0.144657	0.118743
69	0.02	0.012508		90	0.155582	0.13526
70	0.021491	0.014067		91	0.164985	0.146217
71	0.023871	0.015183		92	0.186397	0.16876
72	0.026519	0.016759		93	0.206562	0.187047
73	0.029327	0.019023		94	0.227081	0.206707
74	0.031908	0.021312		95	0.247303	0.22523
75	0.035799	0.023388		96	0.266587	0.244006
76	0.040008	0.026653		97	0.283909	0.262298
77	0.044184	0.029737		98	0.300872	0.28506
78	0.049186	0.033709		99	0.312745	0.302419
79	0.054976	0.038206		100	0.341098	0.325999
80	0.061857	0.043509

Table ‎5.. Age and gender-specific non-circulatory deaths as a proportion of all deaths^[288]

Age group	Men	Women
55-64	0.71	0.83
65-74	0.69	0.76
75+	0.64	0.64

During the drug switching period, the proportion of patients who have CVD or DM was calculated using QRISK2^[285] (see Section 5.6.1). Assuming that the three-monthly event rate r is consistent over 10-years, the 10-year CVD risk was adjusted to three month basis using the following equation^[289]:

where P(t) is a cumulative probability for t. Equation 5.1.

To calculate the transition probabilities to individual CVDs (i.e., UA, MI, stroke and HF), the composite CVD risk was multiplied by the age and gender-specific distribution of first CVD in the UK (see Table ‎5.)^{[63, 286]}. The data originally came from the Bromley Coronary Heart Disease Register and Oxfordshire Community Stroke Project^{[290, 291]}.

The composite CVD risk calculated by QRISK2 did not include HF risk: therefore the HF risk was estimated by age and gender-dependent HF incidence in the UK (see Table ‎5.)^[288] and the RR of elevated SBP (>140 mmHg) for HF incidence in white population, which was 1.80 (1.27-2.55)^[292].

Table ‎5.. Incidence per 100,000 of HF in the UK^[288]

Age group	Men	Women
55-64	71.5	31.0
65-74	173.1	98.7
75+	287.5	239.8

The risk of new onset type 2 DM came from age and gender-specific type 2 DM incidence in the UK (see Table ‎5.)^[293] and the HR of the new onset DM in patients with hypertension by the class of antihypertensive drugs (see Table ‎5.Error: Reference source not found)^[261]. In order to apply the HR to the transition probability, the annual transition rate was calculated by Equation 5.2, and then the HRs were converted to RRs using Equation 5.3^[289]:

Equation 5.2.
Equation 5.3.

Table ‎5.. Type 2 DM annual risk per 100,000 population in the UK^[293]

Age group	Men	Women
60-64	1,233	915
65-69	1,486	1,142
70-74	1,656	1,338
75-79	1,625	1,380
80-84	1,411	1,252
85-89	1,189	1,060
90+	538	452

Table ‎5.. Risk of type 2 DM according to category of antihypertensive drug^[261]

Antihypertensive drugs	Relative Hazard (95% CI)
None	1
Ds	0.91 (0.73-1.13)
BBs	1.28 (1.04-1.57)
CCBs	1.17 (0.83-1.66)
ACEIs/ARBs	0.98 (0.72-1.34)