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

2.2.3Individual-based models

Rather than a cohort of patients moving through the model simultaneously, a large number of individual patients can move through the model consecutively in IBMs. In the context of healthcare modelling, IBMs, such as DES, explicitly model the disease progression and other relevant characteristics (either static such as gender or dynamic such as age and drug uses) of sampled individual patients over time. Entities represent patients assigned with attributes such as age, gender and other risk factors. These attributes are updated while the patients go through the events that can happen to an entity during simulation. The updated information is stored in a variable and used to determine the transition to the subsequent disease pathway, as well as the associated costs and effectiveness. As the whole history of an individual is tracked and used to determine the transition to the subsequent disease pathway, IBMs do not have the constraints incurred by the memoryless property of Markov models. The method to handle time is flexible for IBMs where time can either be modelled by fixed interval time slices/cycles (as for Markov models) or handled by discrete events where the system clock jumps from event to event only when system state changes.

Due to the flexibility of IBMs, they may be considered when the SDDPs have a large number of health states and/or potential drugs with patient heterogeneity, and when it is essential to model non-Markovian relationships in the model. The “curse of dimensionality” does not affect IBMs as the complexity of IBMs only increase linearly, rather than exponentially, when more drug choices, health states, or time periods are modelled. A time-to-event approach potentially reduces the computational time for modelling SDDPs because the model is only updated when relevant event (e.g., change of health states, change of drugs) happens. Figure ‎2. illustrates an example using a DES structure.

Nevertheless, there are certain limitations to DES. Firstly, they require more data than other models, such as input parameters conditional on various individual patients’ history. Secondly, DES models take a relatively long time to calibrate and validate because they may require sampling a large number of patients to increase the accuracy of mean effects. This is also associated with less flexibility of DES models to assess uncertainty due to computational burden. A full sensitivity analysis of DES requires two levels of simulation: one is based on fixed parameters to estimate a single expected value and the other is to sample from a distribution of possible input values^[74]. If the DES model runs for 10,000 patients to get the reasonable average costs and effectiveness, for example, conducting the full sensitivity analysis may result in 100 million individual simulations. This may be only feasible for a small proportion of DES models implemented in a fast programming language or by extended computing resources that facilitate parallel runs across multiple processors^[75].

FOR individual i 1: Sample relevant initial patient attributes (e.g., gender, age, whether or not smoking, etc.). 2: Assign initial drug. 3: Decide the outcome (success/failure) and timing of next health state, and accrue costs and QALYs. 4: Assign the next drug. 5: Decide the outcome (success/failure) and timing of next health state, and accrue costs and QALYs. 6: Repeat step 4-5 until the patient dies or the pre-set simulation time is reached. NEXT individual i+1

Figure ‎2.. An example IBM model of SDDPs