7.3Markov model-based optimisation: Enumeration 7.3.1Base-case 1) Enumeration results
The total computational time to enumerate 4,128 sequential treatment policies in parallel was 12.20 hours where 12 Intel X5650 processors were used. The evaluation of one sequential policy was 10.64 seconds on average (note each evaluation of a policy option includes 100 Monte Carlo simulation replications to estimate the mean and CIs of the objective function). The maximum total net benefit was achieved by the sequential treatment policy starting with ACEIs/ARBs, followed by Ds+ACEIs/ARBs, Ds+CCBs+ACEIs/ARBs and Ds+BBs+ACEIs/ARBs as second, third and fourth-line treatments. The total expected net benefit for this optimal sequential treatment policy was £330,080 (95% CI £330,013-£330,147). The estimated total net benefits of the top seven policy options were not significantly different at the 5% significance level (see Table 7.).
Table 7.. Optimal solutions using enumeration in the base-case
No.
|
Solutions
|
TNB
|
SD
|
(p-value)
|
1st
|
2nd
|
3rd
|
4th
|
3720
|
ACEIs/ARBs
|
Ds+ACEIs/ARBs
|
Ds+CCBs+ACEIs/ARBs
|
Ds+BBs+ACEIs/ARBs
|
330,080
|
342.58
|
|
621
|
Ds
|
Ds+ACEIs/ARBs
|
Ds+CCBs+ACEIs/ARBs
|
BBs+ACEIs/ARBs
|
330,000
|
371.88
|
(p=0.15)
|
622
|
Ds
|
Ds+ACEIs/ARBs
|
Ds+CCBs+ACEIs/ARBs
|
CCBs+ACEIs/ARBs
|
329,990
|
359.81
|
(p=0.09)
|
623
|
Ds
|
Ds+ACEIs/ARBs
|
Ds+CCBs+ACEIs/ARBs
|
Ds+BBs+CCBs
|
330,030
|
374.12
|
(p=0.34)
|
624
|
Ds
|
Ds+ACEIs/ARBs
|
Ds+CCBs+ACEIs/ARBs
|
Ds+BBs+ACEIs/ARBs
|
330,020
|
349.05
|
(p=0.27)
|
625
|
Ds
|
Ds+ACEIs/ARBs
|
Ds+CCBs+ACEIs/ARBs
|
BBs+CCBs+ACEIs/ARBs
|
329,990
|
310.92
|
(p=0.05)
|
3719
|
ACEIs/ARBs
|
Ds+ACEIs/ARBs
|
Ds+CCBs+ACEIs/ARBs
|
Ds+BBs+CCBs
|
330,020
|
411.57
|
(p=0.28)
|
3721
|
ACEIs/ARBs
|
Ds+ACEIs/ARBs
|
Ds+CCBs+ACEIs/ARBs
|
BBs+CCBs+ACEIs/ARBs
|
330,030
|
343.33
|
(p=0.40)
|
1) The optimal solution, which had the highest total net benefit, is in grey.
Figure 7. graphically shows the estimated mean total net benefits of 4,128 policies. The range of the total net benefits was between £296,250 (policy number 3257, treatment sequence starting with ACEIs/ARBs, followed by CCBs, Ds and BBs) and £330,080, which is the total net benefit of the optimal solution as shown in Table 7. (policy number 3720, treatment sequence starting with ACEIs/ARBs, followed by Ds+ACEIs/ARBs, Ds+CCBs+ACEIs/ARBs and Ds+BBs+ACEIs/ARBs). The difference in total net benefit between the best solution and the worst solution was over £30,000, which is more than one full QALY gained. The enumeration results are also shown in Figure 7. as four separate figures by initial drug. Regardless of the initial treatment, Figure 7. shows that the total net benefits can vary substantially depending on the choice of subsequent treatments. The estimated total net benefits of the sequential treatment policy appear to be considerably associated with the additive effect of the four single drugs.
Figure 7. shows that the percentage of the patients who used the third or fourth-line drug at the end of the drug switching period was low, where the percentage of the patients who used the second-line drug was high. The percentage of the patients who used only the first-line drug during the drug switching period was very low from a minimum of 0.06% (policy number 767, whose total net benefit was £320,760) to a maximum of 0.28% (policy number 2007, whose total net benefit was £320,820). The percentage of the patients who used the second-line drugs at the end of the drug switching period was from a minimum of 0.65% (policy number 3143, whose total net benefit was £324,520) to a maximum of 67.68% (policy number 1725, whose total net benefit was £316,570). The percentage of the patients who used the third-line drugs at the end of the drug switching period was from a minimum of 13.44% (policy number 1691, whose total net benefit was £313,160) to a maximum of 80.07% (policy number 209, whose total net benefit was £314,670). The percentage of the patients who used all four lines of treatments during the drug switching period (also used forth-line drug at the end of the drug switching period) was from a minimum of 0.08% (policy number 2795, whose total net benefit was £320,070) to a maximum of 76.95% (policy number 170, whose total net benefit was £315,900).
Figure 7.. Total net benefit of 4,128 policies where enumeration was used
Figure 7.. Total net benefits of 4,128 sequential treatment policies depending on the initial drug
Figure 7.. The percentage of the patients who were using first, second, third or fourth-line drug at the end of the drug switching period
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