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

c=(1,2,3,4), where 1=3months, 2=6months, 3=9months and 4=12months.

Y=SLE₄-SLE₁

X=EXP(1/Y*LN(4))

SLE_c=SLE_c-1+LOG(c,X) Equation 5.5.
Table ‎5.. Absolute SBP lowering effects accumulated over one year

	SLE at three months observed in the Wald’s study	Expected SLEs at 6 and 9 months		SLE at 12 months observed in the Wright et al’s study
	3 months	6 months	9 months	12 months
Ds	7.3	10.17	11.85	13.04
BBs	9.3	9.41	9.47	9.51
CCBs	8.4	8.65	8.80	8.90
ACEIs/ARBs	6.8	13.97	18.16	21.14

1) SLE stands for SBP lowering effects.
The current hypertension SDDP model assumes that the BBs and CCBs have little incremental SBP lowering effect after three months, whereas Ds and ACEIs/ARBs gradually drop SBP over one year. Many factors Wald et al’ and Wright et al’s systematic reviews were suspected of causing this difference in the SBP lowering effect at three months and 12 months. Whereas the Wald et al’s systematic review included more trials but short-term with less participants (i.e., 42 trials including 10,968 participants), the Wright et al’s systematic reviews included less trials but long-term with more participants (24 trials with 58,040 participants). Crossover studies were included in the Wald et al’s systematic review, while excluded in the Wright et al’s systematic review, which would have the effect of minimising differences between estimates of treatments. The average initial SBP of participants was 156.14 mmHg in Wald et al’s review and 168.88 mmHg in the Wright et al’s review. No clinical evidence was identified to support the different speed of SBP lowering effect across antihypertensive drugs.

Another way to estimate the time-dependent SBP lowering effects is using the SBP data observed in clinical trials. The Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial (ALLHAT) reported the annual change in SBP during the five years of using Ds (chlorthalidone), CCBs (amlodipine) and ACEIs (lisinopril)^[317]. The Dutch-TIA trial also provided information about the change in SBP over 5.5 years where an atenolol-based regimen was compared with placebo^[318]. These RCTs have the advantage of providing the observed data over a long time in a controlled population, but the result can be sensitive depending on the study design and the characteristics of participants. However, no RCT tested the four single treatment options included in this study at the same study design. Furthermore, the participants in both studies are not similar to the population in the hypertension SDDP model. As both methods had a certain level of uncertainty, the base-model was built using the estimated SBP lowering effects based on the Wald’s and Wright et al’s systematic review and sensitivity analyses were undertaken with the values reported in ALLHAT and Dutch-TIA.

Regardless of the class of antihypertensive drugs, combining two drugs from different classes of antihypertensive drugs has shown an additive effect. Law et al’s review showed that the blood pressure lowering effects of different classes of antihypertensive drugs were independent and additive based on the observed average reductions of two different drugs on blood pressure separately and in combination^{[282, 319]}. Wald et al reconfirmed the additive effect with the ratio of observed to estimated additive SBP lowering effect from combining antihypertensive drugs, which was 1.01 (0.90-1.12) across all classes of antihypertensive drugs^[315]. The additive effects between BBs and Ds^[320], between CCBs and Ds^[321], between CCBs and BBs^[322], and between CCBs and ACEIs^[116] have been also proved in RCTs. Although there was no clear evidence on the additive effect of three-drug combinations, Law et al suggested that the effect of three-drugs in combination would be not much different with two-drug combinations^{[282, 319]}. This study assumed that the SBP lowering effect of both two and three-drug combinations was additive as following:
, for two-drug combinations

for three-drug combinations Equation 5.6.

Figure ‎5. shows the SBP lowering effect over time where the additive effect of two or three-drug combinations was assumed.

Figure ‎5.. The absolute SBP lowering effect of single drugs and two or three drug combinations over time
The SBP lowering effect may be different depending on the baseline SBP before treatment. In order to consider the population variation of each treatment effect depending on the baseline SBP, the absolute SBP lowering effect was converted to the relative SBP lowering effect based on pre-treatment SBP as following: