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

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% Average the sampled total net benefits and determine the optimal solution.

[OptV,OptSol] = max(mean(TNB(:)));

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Figure ‎6.. Pseudo-code of the enumeration used for the hypertension SDDP model
Given a specific scenario defined by the variables in Table ‎6., the underlying evaluation model ‘EvModel’ calculated the total net benefit of the policy generated by enumeration, SA or GA (see Figure ‎6.). The decision tree as in Table ‎6. was generated by ‘TreeGenerator’ (i.e., dTree). The matrices indexing the actual drug use of a specific sequential treatment policy, DrugIdx, and the maintenance therapy, Maintenance, were also generated as in Table ‎6. and Table ‎6.. Memory variables defined by time t and health state h were used to store treatment success rate, SBP and the variation of SBP, the probabilities of AEs, CVDs, HF and DM for each health state h at t (i.e., pTrtSux, SBP, SBPSD, pAE, pCVD, pHF and pDM) .

The transition probabilities between the health states included in the decision tree were saved in pDizPath. As the patients who had a CVD or DM moved to the long-term CVD model straight away, pDizPath only included the patients who have never had a CVD or DM during the drug switching period. The state transition probabilities for the patients who moved to the long-term model were saved in the long-term state transition matrix called CumLTProb.

The outer loop t is the time period and the inner loop h is the possible health states in each time period. For each health state h at t, the baseline SBP and the SD of SBP were updated based on the information saved in SBP and SBPSD. The cohort of patients was initialized to use the first-line drug of the given sequential treatment policy for the initial health state. Treatment failure invoked change from the first-line drug to the second, third, and fourth-line drugs according to DrugIdx, which is the matrix generated by ‘VasGenerator’. If a patient used all four drugs in the sequential treatment policy, where the selected drug switching period was longer than four time periods, the next drug was selected randomly among the drugs, which were not previously used. If treatment was successful, the same drug was continued in the next period. The period of maintenance therapy was considered by Maintenance.

Given the information about SBP, drug and maintenance therapy, ‘SBPmodelling’ returned the treatment success rate, the level of SBPs after treatment (separately for the controlled and uncontrolled patients) and the risk of CVDs, HF, DM and AEs (see Figure ‎6. for the pseudo-code). The outputs of ‘SBPmodelling’ were used to calculate the transition probabilities to the health states in the next period. The SBPs after treatment and the variations for the controlled and the uncontrolled patients were also saved separately for the use in the next period. The short-term costs included the costs for the regular GP check-up and drug use for the time period. The short-term QALYs were calculated based on the age-dependent utility assuming there was no disutility from hypertension or antihypertensive treatment.

‘CVDmodelling’ calculates the long-term costs and QALYs for a group of patients who have a CVD or DM during the drug switching period; and for all patients alive after the drug switching period (see Figure ‎6. for the pseudo-code). 23 cohorts were defined by when they moved to the long-term CVD model. For each cohort including the patients who move to the long-term CVD model from h at t, the outputs are the matrices including the state transition probabilities from the time they had a CVD or DM to 100 years old (i.e., LTProb) and the long-term costs and QALYs occurred with the state transitions (i.e., LTCost and LTQaly). Those matrices were added up into the cumulated long-term transition matrices (i.e., CumLTProb, CumLTCost and CumLTQaly), which included the transition probabilities and the long-term costs and QALYs from all patients who had a CVD or DM until t, and updated as a new cohort of patients moved into the long-term CVD model.

Total costs and QALYs for h at t are the sum of the costs and QALYs from the short-term drug switching model and the long-term CVD model. The long-term costs and QALYs only referred to the costs and QALYs occurred from h at t during the drug switching period. At the last stage of the drug switching period (i.e., t=4), the long-term costs and QALYs included all the costs from the end of the drug switching period to 100 years old.

% For the selected scenario, the function ‘EvModel’ provides the total net benefit of the inputted policy.