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\begin{document}
\title{Markov models in cardiac surgery}
\author[1]{Marco Moscarelli}%
\author[2]{Giuseppe Nasso}%
\author[1]{Giuseppe Speziale}%
\affil[1]{GVM Care and Research}%
\affil[2]{GVM Care \& Research}%
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\date{\today}
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\begin{abstract}
Spinal cord ischemia remains a dreadful complication after
thoracoabdominal aortic aneurysm repair. The role of cerebrospinal fluid
drain in such patients needs further clarifications. Tam and colleagues
carried out an interesting decision analysis study that supports the
routine use of the cerebrospinal fluid drain after thoracoabdominal
aneurysm repair. They also demonstrated that the use of the
cerebrospinal drain was safe. Here, we firstly discuss the paper's
finding and methodology and, secondly, we try to simply explain what a
decision analysis study is and, broadly, and how to construct a Markov
model.%
\end{abstract}%
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\par\null
There is still uncertainty whether the use of cerebrospinal fluid (CSF)
drain is associated with a reduction in the incidence of post-operative
spinal cord ischemia (SCI) in patients undergoing repair of
thoracoabdominal aortic aneurysm (TAAA)\textsuperscript{1-2}.
Tam and colleagues\textsuperscript{3} utilized a Markov state-transition
cohort model that compared TAAA repair with adjunctive CSF drain
insertion to TAAA repair without drain insertion. They demonstrated that
the use of CSF drain was associated with improved 5-year life expectancy
and also it reduced the incidence of SCI related mortality and morbidity
without complication from the CSF drain itself.
Authors have to be commended for this interesting study for two main
reasons: first, they contributed to further explore and clarify the role
of CSF in the setting of TAAA surgery; second, they shed light to a
specific tool analysis model (Markov process) that not very often is
encountered in cardiac surgery, yet it can be a powerful mathematical
model for decision making in complex scenarios.
What are Markov processes? How can they be simply explained? Why are
they useful?
The Markov processes and/or models are named after Andrey Markov
(1856-1922), a Russian mathematician. A Markov process is a series or,
betters, a chain of events, that is `memory-less'; in simple words the
next event that will happen depends only on what is happening `now'
(current event) and not on what has happened before (previous event).
In the simulation study, Tam and colleagues considered three states: a)
`alive and well'; b) `alive with SCI' and c) `death'. In the two alive
states, patients can either remain in that state of the end of a
specified observation period or transition to the dead state (absorbing
state). Transition probabilities (from one state to the other) tell us
which state the patients is likely to move to, given where he is. Every
time we observe the outcome of interest and the patients `travels' from
one state to the other, we call that a transition event. After TAAA with
or without CSF, the patient has a certain probability to move to state
`a' or `b', or `c'. All the transition probabilities summed together are
equal to 1 (or 100\%) and all the transition probabilities going out
from a state should always sum to 1.
How can we choose the transition probabilities? Rather the observing in
prospective way the events and their frequency, we can inform the system
with numbers already available in literature.
In the Tam's decision analysis study, the model inputs were obtained
from relevant meta-analyses that have pooled observational data and
randomized trials data on morbidity and mortality associated with TAAA
repair with or without the use of CSF drain. Once all the probabilities
are obtained, the model can be constructed. The transition probabilities
are entered in a matrix where the columns represent the state where the
patient `came from' and the rows represent the state the patient is
`moving to'. By using the matrix it is possible to compute different
sorts of calculation. In order to use the matrix we need a starting
probability vector (that represents what we know about patients'
starting state in terms of probability); if we multiply our transition
matrix by the probability vector we obtain a new vector that represents
the prediction for the next level (one event in the future); if we keep
multiply the transition matrices we can make reasonable prediction which
state the patient will be at any time in the future (theoretically even
if the time approaches infinity).
Nevertheless, Markov process accounts for different models (chain /
decision process / hidden model / partially observable model) that can
be used situationally.
Are the Markov model used frequently in cardiac surgery context?
Regrettably, besides the Tam's example, only few solid studies have been
published. A noteworthy micro-simulation / state-transition study, for
example, was conducted by Ferket and colleagues; they used data from the
Cardiothoracic Surgical Trials Network to estimate long-term predictions
of costs and QALYs\textsuperscript{4}.
Other relevant studies on Markov simulation are also from Tam et
all\textsuperscript{5,6}.
Nevertheless, the newest decision analysis study from the Tam and
colleagues has some limitations.
As already underscored by the Authors, some of the crucial and pivotal
parameters (transition probabilities) were informed by meta-analyses of
observational studies that can be undermined by biases inherent to the
study design. The three states considered (`a', `b', `c') where perhaps
very simplified, since patients may be alive but in many various other
states. Lastly, the model time horizon was only 60 months and that was
because of the limited follow-up of the studies included; hence this
study cannot predict complication beyond the 60 months time horizon.
Nevertheless, Markov models are valid and useful scientific and
mathematical tools that can definitively help physicians and surgeons
during the decision making process.
\textbf{Abbreviation}
CSF= cerebrospinal fluid
SCI= spinal cord ischemia
TAAA= thoraco-abdominal aneurysm
\textbf{References}
1. Coselli JS, LeMaire SA, K\selectlanguage{ngerman}öksoy C, Schmittling ZC, Curling PE.
Cerebrospinal fluid drainage reduces paraplegia after thoracoabdominal
aortic aneurysm repair: results of a randomized clinical trial. J Vasc
Surg. 2002 Apr;35(4):631--9.
2. Rong LQ, Kamel MK, Rahouma M, White RS, Lichtman AD, Pryor KO, et al.
Cerebrospinal-fluid drain-related complications in patients undergoing
open and endovascular repairs of thoracic and thoraco-abdominal aortic
pathologies: a systematic review and meta-analysis. Br J Anaesth. 2018
May;120(5):904--13.
3. Tam D, Khan FM, Robinson B, Hameed I, Rong LQ, Fremes S, Girardi L,
Gaudino M. A decision analysis and personalized clinical tool for
cerebrospinal fluid drains in thoracoabdominal aortic aneurysms repair.
JOCS 202. In press.
4. Ferket BS, Thourani VH, Voisine P, Hohmann SF, Chang HL, Smith PK,
Michler RE, Ailawadi G, Perrault LP, Miller MA, O'Sullivan K, Mick SL,
Bagiella E, Acker MA, Moquete E, Hung JW, Overbey JR, Lala A, Iraola M,
Gammie JS, Gelijns AC, O'Gara PT, Moskowitz AJ; Cardiothoracic Surgical
Trials Network Investigators. Cost-effectiveness of coronary artery
bypass grafting plus mitral valve repair versus coronary artery bypass
grafting alone for moderate ischemic mitral regurgitation. J Thorac
Cardiovasc Surg. 2020 Jun;159(6):2230-2240.e15.
5. Tam DY, Wijeysundera HC, Ouzounian M, Fremes SE. The Ross procedure
versus mechanical aortic valve replacement in young patients: a decision
analysis. Eur J CardioThorac Surg Off J Eur Assoc Cardio-Thorac Surg.
2019 Jun 1;55(6):1180--6.
6. Tam DY, Hughes A, Fremes SE, Youn S, Hancock-Howard RL, Coyte PC, et
al. A costutility analysis of transcatheter versus surgical aortic valve
replacement for the treatment of aortic stenosis in the population with
intermediate surgical risk. J Thorac Cardiovasc
Surg.2018;155(5):1978-1988.e1.
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