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

4.5Implication for the hypertension SDDP modelling

This chapter conceptualised the hypertension SDDP using 1) the topography of the sequential drug decision process in primary hypertension as in Figure ‎4., and 2) the elements of the mathematical description of the SDDP as per section 2.4. Modelling the hypertension SDDP can be overwhelmingly complex because of 1) the long-term follow-up period, 2) the large number of potential combinations of health state transitions, 3) the large number of potential alternative treatment sequences, and 4) the interaction between the treatment sequences and the health state transitions. Therefore, the conceptualisation focused on how to define the scope of the hypertension SDDP and how to reduce the size and computational complexity of the problem.

Firstly, the hypertension SDDP model restricts the maximum number of drug switches to three, as per the treatment algorithm recommend by NICE. As the hypertension is a long-term health condition, it is common to follow-up for lifetime in economic evaluation. However, it is practically impossible to consider all possible drug switches in the long-term because of the huge number of possible combinations of health state and treatment sequences. Setting a limit on the number of drug switches, based on clinical grounds, leads to a reduction in the size of the health state space (see Equation 2.1); this also reduces the size of the search space linearly (see Equation 2.2).

As it is assumed that the drug switching is only allowed in the first four time periods, the hypertension SDDP model is structured in a successive decision tree, which is called the short-term drug switching model, with an add-on Markov model, which is called the long-term CVD model. Drug switching only happens in the short-term drug switching model, whereas the add-on model calculates the long-term impact of sequential drug use on cost and effectiveness. Most of the issues related to the size and computational complexity of this hypertension SDDP model occur within the short-term drug switching model.

Secondly, the size of the health state space is reduced by combining several states that share similarities in terms of transition probability to an aggregate state^[58]. Failure is an aggregate state that includes the patients who fail to achieve the treatment goal or have a CVD, DM, or other AE. This further reduces the size of the health state space and the computation of matrices for transition probabilities and rewards. To consider the (potentially) higher risk of subsequent CVDs for the patients who have a history of CVD or DM, a proportion of patients who have either a CVD or DM move from the short-term drug switching model to the long-term CVD model in the next period (see 1) d1-d4 represents the drug used for the specific health state in each period, given a policy π=(d1,d2,d3,d4).). The drug decision rules are also different for those patients who have never had a CVD or DM and those who have, or have previously had, a CVD or DM - this will be further explained in Chapter 5.

Thirdly, excluding drugs or treatment sequences that are not in accordance with the recommendations from major clinical guideline, also reduces the size of search space. For example, the traditionally recommended treatment algorithm for primary hypertension is a stepped-care approach, which starts with a single low-dose drug (usually Ds) and then adds a second-line drug to the current treatment regimen if the initial treatment fails to achieve the treatment goals^{[9, 63]}. The hypertension SDDP model assumes decision rules that follow this stepped-care approach. The hypertension SDDP model does not consider drug switching within the same class and dose-titration. The patients are assumed to take the equivalent dosages of the drugs included in the same class. Due to a sparsity of available data, dose titration is also considered as a single treatment option, where it is assumed that the patients take the average dose of each drug. For the patients currently have, or have had, a CVD or DM, it can be assumed that one of the recommended drugs from major guidelines is used. For those patients with DM, for example, it is well-known that the use of ACEIs is ideal. In the case of stroke, the algorithm can only allow selecting one drug between Ds and ACEIs.

The interaction between the treatment sequences and the health state transitions in the short-term drug switching model is assumed to be semi-Markovian. The main factors in determining the transition probability between health states are the average SBP lowering effect and the average risk of CVD, DM and AEs, which are time and drug dependent for a group of patients in a specific health state at time t. Every time disease history and treatment results are saved in memory variables and used for the calculation of transition probabilities and the decision-making in the next period. The reduced computational complexity facilitates the use of the semi-Markov assumption in the hypertension SDDP model.