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

Appendix 2. The target papers for the systematic review on approximate optimisation methods

	Author	Year	Optimisation problem	Optimisation	Method	Disease	CEA model
1	Rauner ^[192]	2010	To identify mitigation strategies that minimize the total costs.	o	The Pareto ant colony optimisation	Breast cancer	o
2	Zhao ^[190]	2011	To discover optimal individualized treatment regimens in clinical trial that maximize the overall survival time	o	Adaptive reinforcement learning approach (Q-learning)	Lung Cancer	x
3	van Gerven ^[60]	2007	To approximate the optimal treatment strategy, which maximizes the global utility defined as a discounted additive combination of the quality of life and the cost.	o	Single policy updating, single rule updating and simulated annealing algorithms	Oncology	o
4	Vahedi ^[187]	2009	To find a control strategy that minimizes the expected total discounted cost in the long run.	o	Probabilistic Boolean networks (PBNs)	Cancer	x
5	Tse ^[188]	2007	To optimise the multidrug cancer chemotherapy schedule, which minimizes the tumour size under a set of constraints.	o	Memetic algorithm	Cancer	x
6	Chi ^[429]	2008	To describe a data mining model for constructing an optimal diagnostic sequence that assists cost-effective sequential decisions.	o	Hill climbing and genetic algorithms	?
7	Martín-Guerrero ^[430]	2009	To individualize Erythropoietin dosages to optimise Hb levels in the long-term.	o	Reinforcement learning	Hemodialysis	x
8	Lee ^[129]	2008	To derive approximately optimal strategies (dialysis dose per week and hours) that maximize patient welfare.	o	Reinforcement learning	Dialysis (chronic kidney failure)	o
9	He ^[132]	2010	To identify the optimal dosage policy, which minimizes the total costs.	o	Dynamic programming	Controlled ovarian hyperstimulation	o

Appendix 3. Full search strategies of the systematic review on approximate optimisation methods

A3.1 Web of Science

Set	Search history	Results
A	((TI=("NP hard” or “nondeterministic polynomial-time hard” or sequen* or dynamic or "time-dependent" or Marov* or multistage* or multi-stage*) OR TS=("NP hard” or “nondeterministic polynomial-time hard” or sequen* or dynamic or "time-dependent" or Marov* or multistage* or multi-stage*)))	2,040,041
A'	(TI=(("NP hard” or “nondeterministic polynomial-time hard” or sequen* or dynamic or "time-dependent" or Marov* or multistage* or multi-stage*) near/5 (decision* or problem* or pathway* or polic* or strateg*)) OR TS=(("NP hard” or “nondeterministic polynomial-time hard” or sequen* or dynamic or "time-dependent" or Marov* or multistage* or multi-stage*) near/5 (decision* or problem* or pathway* or polic* or strateg*)))	53,400
A''	(TI=(("NP hard” or “nondeterministic polynomial-time hard” or sequen* or dynamic or "time-dependent" or Marov* or multistage* or multi-stage* or multidrug* or multi-drug* or individualiz*) near/5 (decision* or problem* or pathway* or polic* or strateg* or treatment* or regimen* or therap*)) OR TS=(("NP hard” or “nondeterministic polynomial-time hard” or sequen* or dynamic or "time-dependent" or Marov* or multistage* or multi-stage* or multidrug* or multi-drug* or individualiz*) near/5 (decision* or problem* or pathway* or polic* or strateg* or treatment* or regimen* or therap*)))	77,965
B	(TI=(heuristic* or metaheuristic* or algorithm* or (approximat* near/5 (approach* or method* or function* or search*))) OR TS=(heuristic* or metaheuristic* or algorithm* or (approximat* near/5 (approach* or method* or function* or search*))))	585,439
B'	(TI=((heuristic* or metaheuristic* or approximat* or iterative or cyclic or adaptive or backward) near/5 (algorithm* or approach* or method* or function* or search*)) OR TS=((heuristic* or metaheuristic* or approximat* or iterative or cyclic or adaptive or backward) near/5 (algorithm* or approach* or method* or function* or search*)))	172,268
C	(TI=(optim* or minim* or maxim*) OR TS=(optim* or minim* or maxim*))	2,064,178
A∩B	#1 AND #4	125,449
A'∩B'	#2 AND #5	6,011
A''∩B'	#3 AND #5	6,170
A∩B∩C	#1 AND #4 AND #6	51,068
A'∩B'∩C	#2 AND #5 AND #6	4,339
A''∩B'∩C	#3 AND #5 AND #6	4,342
A∩(B∪C)	#1 AND (#4 OR #6)	378,184
A'∩(B'∪C)	#2 AND (#5 OR #6)	21,771
A''∩(B'∪C)	#3 AND (#5 OR #6)	26,339

1) The row in grey is the final search result used for the systematic review.

A3.2. Scopus

Set	Search history	Results
A	TITLE-ABS-KEY("NP hard" OR "nondeterministic polynomial-time hard" OR sequen* OR dynamic OR "time-dependent" OR marov* OR multistage* OR multi-stage*)	1,948,450
A'	TITLE-ABS-KEY(("NP hard" OR "nondeterministic polynomial-time hard" OR sequen* OR dynamic OR "time-dependent" OR marov* OR multistage* OR multi-stage*) W/5 (decision* OR problem* OR pathway* OR polic* OR strateg*))	50,124
A''	TITLE-ABS-KEY(("NP hard" OR "nondeterministic polynomial-time hard" OR sequen* OR dynamic OR "time-dependent" OR marov* OR multistage* OR multi-stage* OR multidrug* OR multi-drug* OR individualiz*) W/5 (decision* OR problem* OR pathway* OR polic* OR strateg* OR treatment* OR regimen* OR therap*))	80,102
B	TITLE-ABS-KEY(heuristic* OR metaheuristic* OR algorithm* OR (approximat* W/5 (approach* OR method* OR function* OR search*)))	684,764
B'	TITLE-ABS-KEY((heuristic* OR metaheuristic* OR approximat* OR iterative OR cyclic OR adaptive OR backward) W/5 (algorithm* OR approach* OR method* OR function* OR search*))	233,930
C	TITLE-ABS-KEY(optim* OR minim* OR maxim*)	2,222,123
A∩B	#1 AND #4	119,961
A'∩B'	#2 AND #5	7,653
A''∩B'	#3 AND #5	7,817
A∩B∩C	#1 AND #4 AND #6	47,774
A'∩B'∩C	#2 AND #5 AND #6	5,394
A''∩B'∩C	#3 AND #5 AND #6	5,834
A∩(B∪C)	#1 AND (#4 OR #6)	338,674
A'∩(B'∪C)	#2 AND (#5 OR #6)	23,102
A''∩(B'∪C)	#3 AND (#5 OR #6)	28,578

1) The row in grey is the final search result used for the systematic review.

9.1

A3.3. Ovid

Set	Search history	Results
A	("NP hard" or "nondeterministic polynomial-time hard" or sequen$ or dynamic or "time-dependent" or Markov$ or multistage$ or multi-stage$).ab,kw,ti.	858,663
A'	(("NP hard" or "nondeterministic polynomial-time hard" or sequen$ or dynamic or "time-dependent" or Markov$ or multistage$ or multi-stage$) adj5 (decision$ or problem$ or pathway$ or polic$ or strateg$)).ab,kw,ti.	9,409
A''	(("NP hard" or "nondeterministic polynomial-time hard" or sequen$ or dynamic or "time-dependent" or Markov$ or multistage$ or multi-stage$ or multidrug$ or multi-drug$ or individualiz$) adj5 (decision$ or problem$ or pathway$ or polic$ or strateg$ or treatment$ or regimen$ or therap$)).ab,kw,ti.	30,134
B	(heuristic$ or metaheuristic$ or algorithm$ or (approximat$ adj5 (approach$ or method$ or function$ or search$))).ab,kw,ti.	109,279
B'	((heuristic$ or metaheuristic$ or approximat$ or iterative or cyclic or adaptive or backward) adj5 (algorithm$ or approach$ or method$ or function$ or search$)).ab,kw,ti.	25,113
C	(optim$ or minim$ or maxim$).ab,kw,ti.	961,438
A∩B	#1 AND #4	20,703
A'∩B'	#2 AND #5	248
A''∩B'	#3 AND #5	307
A∩B∩C	#1 AND #4 AND #6	6,414
A'∩B'∩C	#2 AND #5 AND #6	158
A''∩B'∩C	#3 AND #5 AND #6	182
A∩(B∪C)	#1 AND (#4 OR #6)	111,976
A'∩(B'∪C)	#2 AND (#5 OR #6)	1,990
A''∩(B'∪C)	#3 AND (#5 OR #6)	6,141

1) The row in grey is the final search result used for the systematic review.