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

2.2Classification of evaluation models for sequential drug decision problems

Several studies have categorised modelling techniques by the key issues, which should be considered to select an appropriate method in economic evaluation in healthcare^{[14, 64-66]}. Brennan et al developed guidance on choosing a modelling technique using a range of model structure criteria, which include time and interaction between individuals, the heterogeneity of entities, the role of expected values, randomness and the degree of non-Markovian structure^[64]. This thesis uses the taxonomy proposed by Brennan et al as the basis to develop a specific classification for economic evaluation of SDDPs (see ).

Firstly, similar to the taxonomy proposed by Brennan et al^[64], the models are classified according to whether it is cohort/aggregate level (column A and B) or individual level (column C and D), and then by whether the model is Markovian (column A and C), semi-Markovian (column B and C) or non-Markovian (column D). From another perspective, the models are classified as decision-tree (row 1), Markov models (row 2), and non-Markovian IBMs (row 3) according to the underlying type of models commonly known in the discipline of healthcare modelling and operational research. Regarding the specific models included in the proposed classification for SDDPs, decision-tree models, where the Markovian assumption is difficult to be relaxed, are classified as classic cohort-level decision-tree models (column A, row 1) and simulated patient-level decision-tree (SPLDT) (column C, row 1). Markov models are classified as classic cohort-level Markov models where the Markovian assumption is strictly applied (column A, row 1), and cohort-level semi-Markov models (column B, row 1) and simulated patient-level Markov model (SPLMM) (column C, row 1) where the Markovian assumption is relaxed. This study broadly defines non-Markovian IBMs as individual level models where the changes of individual states do not necessarily need to follow the Markovian assumption. According to this definition, non-Markovian IBMs include individual event history model (IEH) (column C and D, row 3), which includes two commonly known specific IBMs: DES and agent-based simulation (ABS).

Table ‎2.. Classification of evaluation models for SDDPs

		A	B	C	D
		Cohort/aggregate level		Individual level
		Markov	Semi-Markov	Markov or semi-Markov	Non-Markov
1	Decision-tree	Decision-tree	n/a	Simulated patient-level decision-tree (SPLDT)	n/a
2	Markov models	Markov model	Semi-Markov model	Simulated patient-level Markov model (SPLMM)	n/a
3	Non-Markov individual-based models (IBM)	n/a	n/a	Individual event history model (IEH), including discrete event simulation (DES), agent-based simulation (ABS)

Compared to the taxonomy proposed by Brennan et al, the classification proposed for SDDPs makes no distinction between timed vs. untimed models and between continuous vs. discrete state models, because considering time is essential for modelling SDDPs (i.e., all timed) and in most cases, discrete, rather than continuous, health states would be used for SDDPs. No distinction between discrete vs. continuous time was made in the proposed classification because Markov-based models and various non-Markovian IBMs could potentially handle both discrete and continuous time (this feature is less relevant to decision-tree models). There is also no distinction between deterministic vs. stochastic models, because all the models within the proposed classification could be evaluated both deterministically and stochastically. Finally, the proposed classification makes no distinction between models allowing or not allowing for interaction, because interactions among patient cohorts or individual patients are not necessary for SDDPs, especially in long-term medical conditions assuming unconstrained-resource.

In practice, SPLDT and SPLMM are not as common as the classic cohort-level decision-tree and Markov models. It is also straightforward to adapt IEH models such as DES or ABS to develop SPLDT or SPLMM models. Therefore, this study will focus on three types of models for the evaluation of SDDPs: cohort-level decision-tree models, cohort-level Markov models (Markovian or semi-Markovian) and IEH including DES and ABS. These models are simply referred to as decision-tree, Markov models and IBMs hereafter.