5.6.9Uncertainty
PSA was conducted, where probability distributions were assigned as per Table 5.. The normal distribution was used to model the patient-level variation in the pre-treatment SBP in each period and the SBP during the maintenance therapy. The HR of DM by drug was characterised by a lognormal distribution. The uncertainty in the occurrence of AEs was accounted for by using a beta distribution.
A lognormal distribution was assumed for the SBP lowering effect. For each drug, the SD of the SBP lowering effects was calculated by the weighted sum of the individual SDs, from the included studies in Wald et al’s and Wright et al’s reviews, and the number of participants (see Appendix 6). Assuming the SDs in the placebo arm and the active drug arm were independent and their variances were equal, the pooled SD of the mean difference between the placebo arm and the active drug arm was approximated using Equation 5.11[338]. Equation 5.11 was also used to calculate the SD of two or three combinations, which assumed that the SBP lowering effect had an additive effect of two or three single drugs.
SD = SQRT (SD1^2 + SD2^2) Equation 5.11.
Where 95% CIs or standard errors (SEs) were provided, they were transformed to SD using Equation 5.12, and then combined using Equation 5.11.
SE = (Upper limit –Lower limit)/3.92, where a normal distribution of SE is assumed.
SD = SE*SQRT(N) Equation 5.12.
As the hypertension SDDP model included randomness, the simulation produced results that changed randomly with each run. Therefore the final value of the objective function, f(π,) was estimated by the average total net benefit from 100 PSA runs for a specific policy π (i.e., G(π,ωi)) :
Equation 5.13.
where ω1, ω2, ..., ω100 is a random sample of 100 independent, identically distributed realizations of the random vector ω.
In principle, the simulation should average out the randomness after many runs; however, multiple runs for each sequential treatment policy increase the computation time considerably. Considering the given computational resources and time to implement all tests planed in this thesis, the number of replications was set to 100.
Table 5.. Parameters of key variables for PSA
Key parameters
|
Distribution
|
Parameters
|
Reference
|
Mean
|
SD
|
LB
|
UB
|
Population characteristics
|
Initial SBP
|
Lognormal
|
173.5
|
21.1
|
Burke et al, 2006[283]
|
TC, HDL, BMI
|
Fixed
|
Table 5.
|
.
|
.
|
HSE, 2011 (Raw dataset) [284]
|
Distribution of first-onset CVD
|
Fixed
|
|
.
|
.
|
ScHARR, 2007[286]; NICE, 2011[63]
|
Death
|
All-cause mortality
|
Fixed
|
Table 5.
|
.
|
.
|
ONS, 2011[287]
|
Non-circulatory death
|
Fixed
|
|
.
|
.
|
BHF, 2012[288]
|
Maintenance SBP
|
Male
|
Normal
|
134.89
|
16.85
|
HSE, 2011 (Raw dataset) [284]
|
Female
|
Normal
|
134.99
|
18.94
|
HSE, 2011 (Raw dataset)[284]
|
Baseline risk of primary and secondary CV events
|
Fixed
|
Table 5.
|
.
|
.
|
NICE, 2011[63]
|
HR of type 2 DM
|
Ds
|
Lognormal
|
0.91
|
0.73
|
1.13
|
Gress et al, 2000[261]
|
BBs
|
Lognormal
|
1.28
|
1.04
|
1.57
|
CCBs
|
Lognormal
|
1.17
|
0.83
|
1.66
|
ACEIs/ARBs
|
Lognormal
|
0.98
|
0.72
|
1.34
|
AEs
|
Ds
|
Beta
|
.
|
1
|
999
|
Law et al, 2003[282]
|
BBs
|
Beta
|
.
|
8
|
992
|
CCBs
|
Beta
|
.
|
14
|
986
|
ACEIs/ARBs
|
Beta
|
.
|
0
|
1000
|
RRs in the long-term CVD model
|
Fixed
|
Table 5.
|
.
|
.
|
NICE, 2011[63]
|
Drug costs
|
Ds
|
Gamma
|
11.86
|
11.86
|
50.74
|
NICE, 2011[63]
|
BBs
|
Gamma
|
13.17
|
13.17
|
485.45
|
CCBs
|
Gamma
|
18.64
|
18.64
|
431.22
|
ACEIs/ARBs
|
Gamma
|
21.77
|
21.76
|
183.21
|
CVD costs
|
Fixed
|
Table 5.
|
.
|
.
|
NICE, 2011[63]; ScHARR, 2007[286]; Currie et al, 2010[337]; http://www.slcsn.nhs.uk/cardiac-hf.html
|
Utility weight
|
Fixed
|
Table 5.
|
.
|
|
NICE, 2011[63]
|
5.6.10Other assumptions and limitations (1) Interaction between drugs
Clinical interaction between antihypertensive drugs can result in either additive, greater than additive or less than additive effects. Two different types of interactions exist in the framework of the hypertension SDDP: one is the SBP lowering effect of combining two drugs, and the other is the SBP lowering effect depending on the drug ordering. Based on the given evidence, this hypertension SDDP model assumed that the drugs combined were independent and had an additive SBP lowering effect, whereas the AEs were slightly less than the value estimated under the additive assumption. The CVD prevention effectiveness of combination treatment was assumed to be multiplicative.
The clinical interaction between the current drug and the next drug is also important to capture the sequential treatment effect. For example, the SBP lowering effect of Ds may be different depending on whether they are used initially or as a second, third or fourth-line treatment and which drug was used previously. The difference is possibly attributable to not just the patient’s characteristics (i.e., whether the patient is naïve or not), but also the impact of drug ordering. If someone starts treatment with a D and then adds a BB to the D as the second-line therapy, the clinical interaction between those drugs used in sequence is more complex to explain. Additional randomised intervention is not preferred in clinical trials because the efficacy would be confounded by the effects of the other treatments[339]. Furthermore, most existing evidence on the interactions between drugs used in sequence were described in terms of pharmacokinetic or pharmacodynamics, rather than clinical outcomes[340, 341]. Law et al showed that the blood pressure-lowering effect of a second-line drug was approximately 1 mm Hg less for each 10 mm Hg decrement in pre-treatment blood pressure[282]. The change of SBP lowering effect due to pre-treatment blood pressure was considered in this study by using the relative SBP lowering effect to the baseline SBP. However, the hypertension SDDP model was limited to consider the further incremental or decremented impact associated with the second, third or fourth-line drug in patients who have not controlled by the previous drug(s).
Hypertension is largely asymptomatic and is not a sufficiently serious disease to cause death directly; for this reason, compliance with antihypertensive treatment is generally poor. Some studies have found that more than half of all persons being treated by antihypertensive drugs did not take their drug properly[342-346]. This is one of the possible reasons that the patient may not respond to antihypertensive treatment[347, 348].
Good compliance is associated with better blood pressure lowering effect[349]. The relationship between better compliance and better clinical outcomes such as CHD and survival also has been confirmed[350, 351]. Regardless of the type of disease, however, the lack of reliable data is a common problem in CEAs when trying to consider the expected change in costs and health benefits resulting from compliance. Thus, the potential impact of compliance has been largely neglected in previous CEAs or relied on clinical opinions or assumptions[352]. With the same reason, this hypertension SDDP model did not consider the relationship between compliance and health outcomes (i.e., SBP lowering effect and CVD risk reductions).
(3) Lifestyle modification and other treatments
Lifestyle modification is recommended to patients with primary hypertension either before the start of pharmacological treatment or during the pharmacological treatment[8, 9, 63]. There is considerable evidence suggesting that lifestyle modification, such as smoking cessation, exercise, diet and relaxation, can reduce blood pressure and CVD risk[353-356]. Clinical guidelines also recommend the consideration of additional therapy, such as lipid-lowering drugs and antiplatelet therapy, for the patients at higher risk (i.e., with target organ damage, established CVD, DM, CKD or an estimated 10-year CVD risk ≥20%)[8, 9, 63]. The benefit of adding these drugs to antihypertensive treatment was well established[357-360]. To exclude the confounding effect and to reduce the complexity, however, the hypertension SDDP model assumed that the proportions of patients who adopted lifestyle modification or took lipid-lowering drugs and antiplatelet therapy were the same in each treatment option.
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