Causal risk factors for stroke, delirium, and mortality after elective and urgent open aortic arch surgery for older adults

Mirthe M van Diepen; Ioan Gabriel Bucur; Ralf W J Weijs; Robin H Heijmen; Tom Claassen; Jurgen A H R Claassen

doi:10.1007/s11357-025-01977-z

. 2025 Nov 20;48(5):6577–6606. doi: 10.1007/s11357-025-01977-z

Causal risk factors for stroke, delirium, and mortality after elective and urgent open aortic arch surgery for older adults

Mirthe M van Diepen ^1,^✉, Ioan Gabriel Bucur ¹, Ralf W J Weijs ³, Robin H Heijmen ², Tom Claassen ¹, Jurgen A H R Claassen ³

PMCID: PMC13601408 PMID: 41261339

Abstract

In this exploratory study, we identified causal risk factors in open aortic arch surgery involving antegrade selective cerebral perfusion (ASCP) for postoperative deficits. A retrospective study analyzing open aortic arch surgery involving ASCP data. Causal discovery algorithms can detect how variables in a data set are causally related, and with their aid, we explored whether possible risk factors among preoperative variables, such as renal function and chronic lung disease, are causally related to postoperative deficits such as cerebrovascular accident, delirium, and mortality. Middle cerebral artery velocity (MCAv), a proxy variable for cerebral blood flow, was also included as a risk factor since previous studies have found an association between postoperative neurological deficits and lower MCAv. We found in our study population (n = 142, 46% female, median age 68 [IQR 60,73]) that poor renal function affected mechanical ventilation >24 h with a probability of 0.64 and rethoracotomy with a probability of 0.56, whereas rethoracotomy was causally related to mortality. Moreover, we found evidence that prior cardiac surgery is causally linked to mortality. Age was not found to be directly related to the adverse outcomes in the study population. We identified renal function as a causal risk factor for short-term adverse outcomes, including mortality. For clinical practice, these variables warrant further attention in the decision-making process. Further work could explore whether interventions to improve renal function may positively impact adverse outcomes after aortic arch surgery.

Keywords: Aortic arch surgery, Postoperative complication, Causal risk factors, Causal discovery

Introduction

To reduce mortality and maintain quality of life, aortic arch conditions such as aneurysms and dissections necessitate open thoracic surgery [1, 2]. The number of older adults with aortic aneurysms or dissection is expected to rise in the coming years. Not surprisingly, the highly invasive open aortic arch surgery has risks for the body and brain as the procedure requires circulatory arrest [3]. Brain function is artificially supported with cerebral perfusion strategies such as antegrade selective cerebral perfusion (ASCP) to protect the brain [4] during circulatory arrest by controlling cerebral blood flow [5]. During this procedure, metabolism is slowed by lowering the body temperature with hypothermic circulatory arrest and anesthetic agents [6, 7]. Unfortunately, the risks for mortality and short and long-term neurological deficits, such as ischaemic stroke, embolic stroke, and delirium, remain high [5, 8, 9]. Age is an important risk factor for complications. However, age alone is an unreliable parameter to base life-changing decisions on, because heterogeneity in biological age increases with age. Other risk factors involve intraoperative changes in mean bilateral blood velocity in the middle cerebral arteries, medical history, and other patient characteristics [10, 11] and renal function. Except for age, it is unclear how other possible risk factors are causally related to adverse outcomes of open aortic arch surgery.

Exploring the nature of the relationships between risk factors and postoperative deficits in hazardous open aortic arch surgery is clinically relevant (1) to investigate the relationships of risk factors, other than age, with adverse outcomes for older patients, (2) to understand which patients require more postoperative care, and (3) to think of possibilities to intervene before surgery to limit the adverse outcomes. We do this by distinguishing causal relationships from acausal relationships, where a relationship is acausal when there is an association between two variables explained by something other than a causal relationship (e.g., a hidden confounder). Only if an association between a variable and an adverse outcome is causal could an intervention change the adverse outcome.

Traditional randomized controlled trials (RCTs) to investigate which risk factors cause the adverse outcomes are not feasible for ethical and practical reasons, given the group of sensitive patients who require open aortic arch surgery. Instead, for this exploratory research, we will apply modern statistical causal discovery techniques to search for the causal mechanism from observed data, on variables that are risk factors and adverse outcomes of aortic arch surgery [12]. The state-of-the-art algorithms fast causal inference [13] and Bayesian constraint-based causal discovery [14] were selected, given their flexibility to work in the presence of hidden confounders, which is a realistic setting given the complexity of the human body. Possible causal relationships will then be further analyzed with Bayesian factors of covariance structures [15], a method that computes probabilities for the causal patterns in triplets. We will use multiple causal discovery methods to guarantee robustness by comparing the outputs of these methods, especially since it is challenging to draw causal conclusions from observational real-world data, as the data set in our study is relatively small and contains missing values. Moreover, we use conservative settings and scores to account for the small sample size. We will show how we can draw conclusions in the presence of missing values and how to deal with time-dependent [16, 17] and mixed data [18] when applying causal discovery to aortic arch surgery data. Finally, we will extensively discuss the identified causal and acausal relationships to adverse outcomes.

Materials and methods

Ethics statement

The Medical Research Ethics Committees United (MEC-U) approved this study (W22.187/NO-CASE) on 20 September 2022, where ethical standards of the Helsinki Declaration of 1975 and MEC-U were met in all procedures. Informed consent was not required since this is a retrospective study, and the data was gathered as a routine in medical care.

Study design and population

This retrospective study contains subjects who underwent aortic arch surgery for an aneurysm with bilateral antegrade selective cerebral perfusion (ASCP) between 2017 and 2020 at St. Antonius Hospital in Nieuwegein, The Netherlands. This study is a follow-up of Weijs et al. [19] with results based on the same data set. The selection procedure of the subjects in this study is less restrictive than that of Weijs et al. [19] because we do not exclude patients if the middle cerebral artery velocity (MCAv) had not been measured throughout the surgery, since the main focus of this study is not on the MCAv values. We only selected the first surgical episode when a subject had two aortic arch surgeries between 2017 and 2020. For all subjects, the intervention was scheduled, i.e., elective or urgent aortic arch surgeries are included in this study, where urgent indicates that a subject was hospitalized for other reasons than the aortic arch surgery or not planned to be hospitalized, and that the intervention was necessary during the hospitalization. In total, 142 subjects were selected for the analyses.

Data collection

Selection procedure of patient characteristics

The data set used in this study is from the Netherlands Heart Registration (NHR), which collects all Dutch data on cardiovascular treatments, and is complemented by relevant data from the St. Antonius Hospital, as we will specify below. The selected variables contain patient characteristics variables (such as medical history), variables measured during the screening phase (usually one day before the surgery) or intraoperative phase, and the outcome variables that specify the information from the postoperative phase, such as complications and mortality. We took the following steps in the selection procedure of the variables. We first performed a variable selection step using expert knowledge. Dichotomous variables were only considered if the event’s occurrence of the variable was more than $5 %$ . Further reselection of the variables was based on experiments with the causal discovery algorithms: variables were deselected if the variables were either disconnected from all other variables or had connections that did not impact adverse outcomes, see Appendix D. Following this procedure, we selected fourteen variables for this study. Below, we only describe the 14 variables we included in the final selection.

Risk factors for adverse outcomes after aortic arch surgery

Age (years) is the main risk factor for open aortic arch surgery. Sex (male = 0, female = 1) is included as part of a standard data analysis procedure. Low and high body mass index (BMI) are indicators of poorer health [20, 21]. Chronic lung disease is defined by the long-term use of bronchodilators or steroids because of lung disease, and it can indicate a history of smoking or other health conditions. Coronary vascular health is approximated with a variable that indicates the presence of multivessel disease in the coronary system during the intervention. Multivessel disease is defined by at least 70% stenosis in two or more coronary arteries (RCA, LCC, RCx) or in the first-order side vessels. Coronary artery stenosis counts as a two-vessel disease. Preoperative cerebrovascular accident (CVA) is a proxy variable of cerebral atherosclerosis, which is a hazard, given that CVAs are one of the primary negative effects in the postoperative phase. Preoperative cardiac surgery is a variable that indicates whether a subject had any type of cardiac surgery in their medical history, which can be an indicator of the health status of the heart and aorta. During the screening phase, serum creatinine, a byproduct of muscle metabolism, was measured as a marker of renal function. Age, sex, and serum creatinine are required to compute the creatinine-based estimated glomerular filtration rate (eGFR) based on the 2021 CKD-EPI creatinine equation in Table 2 in Inker et al. [22], which is a proxy variable for the performance of renal function and is related to cardiovascular diseases.

Middle cerebral artery velocity

During the pre- and intraoperative phases of the surgery, transcranial Doppler assessments were done by pulsed Doppler transducers (2 MHz, Delica, type EMS-9UA, Shenzhen Delica Electron) fixed with a headframe on the temporal bone at a focal depth of 45–60 mm to insonate the main stem of the ipsilateral middle cerebral artery (MCA). Performing the assessments by a team with a trained sonographer and clinical neurophysiologist guarantees evaluated values of the mean blood velocities in the left and right MCA, which are estimates of cerebral blood flow (CBF) [3, 23], thus no adjustment on the patient’s systemic blood pressure was needed. Similar to Weijs et al. [19], it is assumed that there are no significant changes in the diameter of the MCA, which implies that changes in MCA velocities (MCAv) are equal to the changes in CBF. Moreover, there was no pressor effect (i.e., no catecholamines or other interventions) at the time of measurement. From the MCAv-specific waveform and flow direction, the MCAv signal was identified.

Weijs et al. [19] investigated if postoperative neurological deficits, such as delirium and CVA, are related to changes in MCAv throughout the surgery. They found an association between postoperative neurological deficits and lower MCAv after the initiation of the ASCP. This finding was the motivation to include MCAv at this stage as an intraoperative variable, and we also include the preoperative MCAv as a baseline measured prior to the surgical procedure. In the supplementary material, Weijs et al. [19] show that there is no evidence that the left and right MCAv are symmetric at baseline at this high-risk moment of the surgery. Therefore, we always take the mean of the left and right MCAv to simplify the problem setting, and the mean is missing if either of the values is missing. The MCAv data considered for this study were analyzed more extensively in Weijs et al. [19].

Adverse outcomes

The aim of this study is to identify new causal risk factors linked to adverse postoperative outcomes in aortic arch surgery, as well as to gain a deeper understanding of the relationships and interactions among all pertinent variables. The most adverse outcome is mortality within 30 days after the surgery. Postoperative CVA, including ischaemic stroke (with or without permanent sequelae) and transient ischaemic attack, is a frequent adverse outcome that can have catastrophic consequences for quality of life after surgery. Neurological dysfunction due to focal ischaemia in the brain, spinal cord, or retina is called ischaemic stroke if it is caused by thrombosis, embolism, systemic hypoperfusion, or systemic hemorrhage leading to acute infarction in brain tissue. Both ischaemic stroke and transient ischaemic attack are diagnosed by a neurologist according to international guidelines [24].

Delirium is a neurological deficit after surgery that can cause immediate complications during the postoperative period (e.g., falls, injury, side effects from medication used to treat delirium) and is associated with poor long-term outcomes such as Alzheimer’s disease. The NHR does not record delirium incidents; thus, the variable is constructed by selecting patients receiving antipsychotic agents (e.g., haloperidol) or benzodiazepines (e.g., oxazepam) after surgery, which are strong clinical indicators for delirium. Afterward, the events were verified by reviewing postoperative notes from patients’ medical files for delirium symptoms, i.e., hallucination, anxiety, restlessness, agitation, or confusion [25] under the supervision of geriatrician Jurgen A.H.R. Claassen, specialized in delirium care.

Other outcome variables we considered were the need for mechanical ventilation for more than 24 h after surgery and rethoracotomy within 30 days, which are both indicators that the patients are not fully recovering or are recovering slowly. These can help to understand causal links to mortality, postoperative CVA, or delirium.

Data processing

The data set contains a mixture of dichotomous and continuous variables, and some values are missing. The data is transferred to a Gaussian copula whose correlation matrix is measured through expectation maximization (EM) with a Gibbs sampling procedure under the missing-at-random (MAR) assumption proposed by Cui et al. [18].1 They also propose a way to estimate an effective sample size for causal discovery. Transferring data to a meaningful Gaussian copula requires the data to be monotonic. In Appendix B, we discuss this assumption (and others) in more detail. The Gibbs sampling procedure outputs a correlation matrix for each iteration. We ran 1000 iterations and estimated the final correlation matrix by taking the mean of the last 500 sampled correlation matrices. See Appendix A.1 for more details on the data processing procedure.

Statistical analyses

The statistical analysis methods described in this section were executed with R (version 4.3.1), and we followed the guidelines and recommendations from the European Journal of Cardio-Thoracic Surgery [26] and STROBE Statement [27]. From Shapiro-Wilk’s test results, we concluded which variable in our selection is normally distributed, and we each of variables with a mean and standard deviation, whereas continuous non-normally distributed variables are represented with a median and interquartile range. We present dichotomous variables with frequency and percentage. We conducted univariate logistic regression on the adverse outcomes (combination of delirium, postoperative CVA, and mortality) to compute the odds ratios with the likelihood ratio test. Moreover, to account for missing values in the data, we performed complete case analysis, and analysis on imputed data found by two imputation methods. The first is multiple imputations by chained equations (MICE)2 [28] with random forest as prediction algorithm [29, 30], 20 iterations [19], and 20 imputed data sets as output [31]. The second method is the Gibbs sampler for mixed data under MAR (GMDM) proposed by Cui et al. [18] by taking the average of the imputed data sets over all iterations.

Causal discovery

In this study, we aim to identify the causal relationships between variables in the data. This way, we can distinguish between direct causal relationships and other types of direct associations.3 Therefore, we apply causal discovery algorithms. Prior studies have already used causal discovery in the healthcare domain [32–36], and even on cardiac surgery data where the causal risk factors for postoperative length are investigated [37].

Three causal discovery algorithms are used to detect the causal mechanism behind open aortic arch surgery. Working with real-world data is tricky, as noise or a small sample size can affect the outcomes; thus, by combining the outputs of multiple algorithms, we can select the relationships that occur most frequently. Each algorithm exploits different statistical methods, so combining the outputs of the three algorithms allows for more reliable conclusions. The first method is the fast causal inference (FCI)4 algorithm [13, 38] which exploits conditional independence information5 and time-dependent information [16, 17]. Outputs of the FCI algorithm on 1000 bootstrapped data sets were combined to compute reliability scores for each connection. The second method, the Bayesian constrained-based causal discovery (BCCD) algorithm [14],6 outputs a causal graph with a reliability score for each connection and exploits time-dependent information. Finally, the Bayes factors of covariance structures (BFCS) [15]7 computes posterior probabilities for all possible causal mechanisms for any triplets of variables. We applied BFCS on triplets with ambiguous causal conclusions from the FCI and BCCD algorithms to get a better understanding of what the actual relationship could be. We only showed triplets that contributed to drawing conclusions about the nature of the ambiguous relationship. We report all relationships with adverse outcomes found by the FCI and BCCD algorithms. On top of that, we report results from additional tests done by BFCS, if it was possible to select a useful triplet for this test. By observing outputs with reliability scores of multiple causal discovery algorithms used in conservative settings, we account for the small size of the data set. In Appendix A, we describe the methods used in this study in more detail.

Results

Study population

The study contains 142 patients, of whom 15 (11%) had postoperative CVA, 38 (27%) had delirium, and 23 (16%) died, see Tables 1 and 2 for the statistics of the other variables. In Appendix D, we showed how we set the final selection of variables. Adverse outcomes, defined by the occurrence of postoperative CVA, a delirium event or mortality, is associated with intraoperative MCAv (after the initiation of the ASCP) in the complete case analysis (OR: $-$ 0.058; CI: [ $-$ 0.100, $-$ 0.022]; p = 0.004), after imputation with MICE (OR: $-$ 0.041; CI: [ $-$ 0.077, $-$ 0.005]; p = 0.027) and GMDM (OR: $-$ 0.113; CI: [ $-$ 0.161, $-$ 0.073]; p = 0.000). Mechanical ventilation and adverse outcomes are also associated (OR: 1.983; CI: [0.600, 3.882]; p = 0.013), as is rethoracotomy (OR: 1.336; CI: [0.363, 2.424]; p = 0.010). Mortality is not associated with whether the surgery was elective (14.4% mortality) or urgent (22.6% mortality) (OR: 0.549; CI: [ $-$ 0.497, 1.518]; p = 0.291).

Table 1.

Perioperative patient characteristics with and without adverse outcomes

	Group (n = 142)	W/o adverse outcomes (n = 79)	W/ adverse outcome (n = 63)
Age, y; median (IQR)	68 (60–73)	66 (58–71)	70 (62–74)
Sex (female), n (%)	65 (46)	41 (52)	24 (38)
Chronic lung disease, n (%)	22 (15)	8 (10)	14 (22)
Multivessel disease, n (%)	5 (4)	1 (1)	4 (6)
Pre-op cerebrovascular	15 (11)	7 (9)	8 (13)
accident, n (%)
Pre-op cardiac surgery, n (%)	59 (42)	28 (36)	31 (50)
BMI, kg/m $^{2}$ ; median (IQR)	25.16 (22.21–29.01)	25.16 (22.56–29.24)	25.05 (22–28.24)
eGFR $^{3}$ , ml/min/1.73m $^{2}$ ;	79.27±18.53	80.09±18.74	78.22±18.34
mean±SD
Pre-op middle cerebral	44.5 (38.25–53.25)	43.5 (38.5–54)	44.75 (38.12–51.75)
artery velocities, cm/s;
median (IQR)
Intra-op middle cerebral	31 (23.5–42)	39.5 (28–47.5)	25.25 (21–33)
artery velocities $^{1}$ , cm/s;
median (IQR)
Mechanical ventilation	12 (8)	2 (3)	10 (16)
>24h, n (%)
Rethoracotomy $^{2}$ , n (%)	21 (15)	6 (8)	15 (24)

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The values are presented as mean ± standard deviation, median (interquartile range), or number of observations and percentage (n (%))

$^{1}$ The intraoperative middle cerebral artery velocity is measured directly after the initiation of the antegrade selective cerebral perfusion in aortic arch surgery

$^{2}$ Rethoracotomy implies rethoracotomy within 30 days

$^{3}$ One subject has a creatinine value of 524 µmol/L, which we considered a data-entry error since it is unlikely that a subject with severe kidney failure will be accepted for cardiac surgery. We set this value to a NaN value to ensure that the outcomes do not bias towards this outlier

Table 2.

Perioperative patient characteristics with and without adverse outcomes

	Group (n = 142)	Missing values, n (%)	Log odds ratio (95% CI)	p-value
Age, y; median (IQR)	68 (60–73)	0 (0)	0.027 (−0.005, 0.061)	0.104
Sex (female), n (%)	65 (46)	0 (0)	−0.561 (−1.243, 0.107)	0.1
Chronic lung disease, n (%)	22 (15)	0 (0)	0.93 (0.008, 1.914)	0.048
Multivessel disease, n (%)	5 (4)	0 (0)	1.665 (−0.277, 4.653)	0.096
Pre-op cerebrovascular	15 (11)	0 (0)	0.403 (−0.678, 1.506)	0.461
accident, n (%)
Pre-op cardiac surgery, n (%)	59 (42)	2 (1)	0.58 (−0.097, 1.266)	0.093
MICE			0.572 (−0.112, 1.256)	0.101
GMDM			0.594 (−0.083, 1.28)	0.085
BMI, kg/m $^{2}$ ; median (IQR)	25.16 (22.21–29.01)	1 (1)	−0.003 (−0.075, 0.068)	0.936
MICE			−0.003 (−0.075, 0.068)	0.924
GMDM			−0.003 (−0.075, 0.068)	0.93
eGFR $^{3}$ , ml/min/1.73m $^{2}$ ;	79.27±18.53	1 (1)	−0.005 (−0.024, 0.013)	0.55
mean±SD
MICE			−0.006 (−0.024, 0.013)	0.545
GMDM			−0.006 (−0.024, 0.012)	0.526
Pre-op middle cerebral	44.5 (38.25–53.25)	47 (33)	−0.01 (−0.046, 0.024)	0.551
artery velocities, cm/s;
median (IQR)
MICE			−0.008 (−0.04, 0.024)	0.605
GMDM			−0.01 (−0.042, 0.021)	0.538
Intra-op middle cerebral	31 (23.5–42)	67 (47)	−0.058 (−0.1, −0.022)	0.001
arter velocities $^{1}$ , cm/s;
median (IQR)
MICE			−0.04 (−0.077, −0.002)	0.037
GMDM			−0.112 (−0.16, −0.071)	0
Mechanical ventilation	12 (8)	0 (0)	1.983 (0.6, 3.882)	0.004
>24 h, n (%)
Rethoracotomy $^{2}$ , n (%)	21 (15)	0 (0)	1.336 (0.363, 2.424)	0.007

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The values are presented as mean ± standard deviation, median (interquartile range), or number of observations and percentage (n (%)). The p-values from univariable logistic regression are given for odds ratios for adverse outcomes. The statistically significant p-values ( $p < 0.05$ ) are in bold. For variables with missing values, results of complete case analyses, imputation with MICE, and imputation with GMDM are given

$^{1}$ The intraoperative middle cerebral artery velocity is measured directly after the initiation of the antegrade selective cerebral perfusion in aortic arch surgery

$^{2}$ Rethoracotomy implies rethoracotomy within 30 days

Outcomes of the causal discovery algorithms

The results of the FCI and the BCCD algorithms suggest some direct associations and even causal relationships, see Fig. 1. Edges in the causal graph are solid when the correlation is positive and dashed when the correlation is negative. In Table 3, we observe the results obtained from BFCS on some triplets of variables that stand out in the outputs of the causal discovery algorithms, see the “Outcomes of the causal discovery algorithms” section. The heatmaps in Fig. 2 visualize the strength of the adjacencies, and in Fig. 3 visualize the strength of the (in)direct causal relationships.

Table 3.

The results of BFCS

	All	Acausal: $A ↛ B$ ,	Acausal: $B ↛ A$ ,	Acausal: $C ↛ A$ ,	Causal: $A \to B$ ,	Causal: $B \to A$ ,	Causal: $C \to A$ ,
	connected	and $A ↛ C$	and $B ↛ C$	and $C ↛ B$	or $A \to C$	or $B \to C$	or $C \to B$
A = renal function	0.11	0.00	0.15	0.01	0.00	0.66	0.03
B = rethoracotomy $^{2}$
C = mortality
A = post-op CVA	0.39	0.01	0.07	0.00	0.05	0.44	0.02
B = pre-op cardiac surgery
C = mortality
A = post-op CVA	0.06	0.00	0.51	0.00	0.00	0.41	0.00
B = pre-op cardiac surgery
C = pre-op CVA
A = delirium	0.10	0.00	0.88	0.00	0.00	0.02	0.00
B = intra-op MCA $^{1}$
C = post-op CVA
A = renal function	0.11	0.00	0.48	0.00	0.00	0.41	0.00
B = mechanical ventilation $^{3}$
C = delirium
A = pre-op CVA	0.19	0.01	0.03	0.00	0.12	0.63	0.00
B = delirium
C = mechanical ventilation $^{3}$
A = age	0.25	0.00	0.74	0.00	0.00	0.00	0.00
B = renal function
C = pre-op cardiac surgery
A = pre-op cardiac surgery	0.17	0.01	0.17	0.00	0.04	0.56	0.01
B = renal function
C = rethoracotomy $^{2}$
A = pre-op cardiac surgery	0.09	0.00	0.25	0.00	0.00	0.64	0.00
B = renal function
C = mechanical ventilation $^{3}$

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The left column shows which triple containing A, B, and C is selected. Then, in the following columns we can read-off with which probability (1) all variables A, B, and C are connected, (2–4) there is an acausal pattern (for example $B ↛ A$ and $B ↛ C$ in (2)), (5–7) there is a causal pattern (for example, $B \to A$ or $B \to C$ in (5)). The probably for the cases when some variables in the triplet have no connection is (almost) zero for all triplets below, see Table 4 in the appendix

$^{1}$ The intraoperative middle cerebral artery velocity is measured directly after the initiation of the antegrade selective cerebral perfusion in aortic arch surgery

$^{2}$ Rethoracotomy implies rethoracotomy within 30 days

$^{3}$ Mechanical ventilation implies mechanical ventilation >24 h

Fig. 2 — The heatmaps of the adjacency matrices from the output of the FCI and BCCD algorithms. The strength of the color visualizes the reliability of the direct relationship. Since an adjacency matrix is symmetric, we only show the lower triangle for clarity. The ratio is either the reliability information on the links found by the BCCD algorithm or the occurrence of the direct relationship in the outcomes of the FCI algorithm on the bootstrapped data sets. We refer to “direct relationship ratio” to avoid ambiguity

Fig. 3 — The heatmaps of the causal relationships from the output of the FCI and BCCD algorithms. The strength of the color visualizes the reliability causal relationship, for example, age (cause) to mechanical ventilation (effect) is strong in both outputs. Here, causes are on the horizontal axis and effects are on the vertical axis. The ratio is either the reliability information on the causal links found by the BCCD algorithm or the occurrence of the (in)direct causal relationship in the outcomes of the FCI algorithm on the bootstrapped data sets. We refer to “cause ratio” to avoid ambiguity

Relationships to mortality

Rethoracotomy is directly related to mortality according to both FCI and BCCD. From BFCS, we find that the triplet with renal function, rethoracotomy, and mortality contains a causal pattern with a probability of 0.66 (see Table 3), implying that rethoracotomy causes mortality since renal function is not an effect of rethoracotomy. On top of that, BCCD suggests that mortality is directly related to preoperative cardiac surgery and chronic lung disease, where preoperative cardiac surgery is also causally related to mortality. The triplet postoperative CVA, preoperative cardiac surgery, and mortality contains a causal pattern with a probability of 0.44. However, postoperative CVA cannot be affected by preoperative cardiac surgery, given that the triplet of postoperative CVA, preoperative cardiac surgery, and preoperative CVA contains an acausal pattern with a probability of 0.51. This implies that there is evidence that preoperative cardiac surgery is not a causal risk factor for postoperative CVA. Thus, preoperative cardiac surgery is a causal risk factor for mortality.

Relationships to post-operative CVA

The FCI and BCCD algorithms find that postoperative CVA is directly related to sex, BMI, preoperative cardiac surgery, and intraoperative MCAv. Moreover, the BCCD algorithm also found a direct connection between postoperative CVA and preoperative MCAv, which is not perceived by the FCI algorithm. There is no evidence that the relationships are causal. The triplet containing delirium, intraoperative MCAv, and postoperative CVA is acausal with a probability of 0.88 according to BFCS, i.e., there is evidence that intraoperative MCAv is not a causal risk factor for delirium and postoperative CVA. Instead, the outcomes of the causal discovery algorithms suggest that hidden confounders are connecting intraoperative MCAv with delirium and postoperative CVA.

Relationships to delirium

Mechanical ventilation >24 h and delirium are directly related, but we obtain contradicting information about the nature of the relationship from the outcomes of the algorithms. In our results, we find the cause ratio of delirium causing mechanical ventilation >24 h is 0.337, and the cause ratio of mechanical ventilation >24 h causing delirium is 0.236, see Fig. 3a. In other words, although this relationship is very robust with a direct relationship ratio of 0.851 by the FCI algorithm in Fig. 2a and a probability of 0.9999987 by the BCCD algorithm in Fig. 2b, it is difficult to determine the direction of the relationship. From the BFCS, we find that the triplet containing renal function, mechanical ventilation >24 h, and delirium might have an acausal patterns with the highest probability of 0.48, and a causal pattern from mechanical ventilation >24 h to delirium with the highest probability of 0.41 given that mechanical ventilation >24 h does not affect the renal function. The triplet with preoperative CVA, delirium, and mechanical ventilation >24 h has a probability of 0.63 for a causal pattern, which implies that delirium causes mechanical ventilation >24 h given the background knowledge that delirium can not be a cause of preoperative CVA. Moreover, we find that delirium is directly related to intraoperative MCAv. According to the output of BCCD, delirium also has a direct link with preoperative CVA and BMI. BFCS discovers that a hidden confounder links intraoperative MCAv to delirium, as mentioned earlier.

Relationships to rethoracotomy

The renal function is associated with rethoracotomy, and BCCD even suggests that renal function is causally linked to rethoracotomy, while FCI established that the relationship is through hidden confounders. The triplet containing age, renal function, and preoperative cardiac surgery is acausal with a probability of 0.74 according to BFCS. We conclude that renal function is not causally related to preoperative cardiac surgery. We find that the triplet containing preoperative cardiac surgery, renal function, and rethoracotomy is causal with the highest probability of 0.56 among the other possible causal patterns according to BFCS. This suggests that renal function is a causal risk factor for rethoracotomy.

Relationships to mechanical ventilation longer than 24 h

Renal function is associated with mechanical ventilation >24 h, and BCCD suggests that renal function causes mechanical ventilation >24 h, while FCI established that the relationship is through hidden confounders. From BFCS, we find that the triplet containing age, renal function, and preoperative cardiac surgery contains an acausal pattern with a probability of 0.74. From this pattern, it follows that preoperative cardiac surgery is not caused by renal function. The triplet with preoperative cardiac surgery, renal function, and mechanical ventilation >24 h contains a causal pattern with a probability of 0.64. Since we found that preoperative cardiac surgery does not affect renal function, the causal pattern suggests that renal function is a causal risk factor for mechanical ventilation >24 h.

Relationships to intraoperative MCAv

In both outputs of the FCI and BCCD algorithms, we find a link between chronic lung disease and intraoperative MCAv, explained by a hidden confounder. From Table 6, we can read that this link is only supported by data imputed via the method proposed by Cui et al. [18].

Table 6.

Perioperative patient characteristics with and without chronic lung disease

	Group (n = 142)	Log odds ratio (95% CI)	p-value
Age, y; median (IQR)	68 (60–73)	0.047 (−0.002, 0.107)	0.061
Sex (female), n (%)	65 (46)	0.636 (−0.278, 1.589)	0.173
Multivessel disease, n (%)	5 (4)	−14.912 (− $\infty$ , 99.843)	0.19
Pre-op cerebrovascular	15 (11)	0.789 (−0.574, 1.983)	0.237
accident, n (%)
Pre-op cardiac	59 (42)	0.595 (−0.322, 1.531)	0.202
surgery, n (%)
MICE		0.593 (−0.332, 1.518)	0.207
GMDM		0.598 (−0.324, 1.539)	0.202
BMI, kg/m $^{2}$ ; median (IQR)	25.16 (22.21–29.01)	0.008 (−0.095, 0.103)	0.88
MICE		0.008 (−0.09, 0.107)	0.865
GMDM		0.007 (−0.093, 0.101)	0.883
eGFR $^{3}$ , ml/min/1.73m $^{2}$ ;	79.27 ± 18.53	−0.026 (−0.052, −0.002)	0.035
mean±SD
MICE		−0.026 (−0.051, −0.001)	0.039
GMDM		−0.026 (−0.052, −0.002)	0.035
Pre-op middle cerebral artery	44.5 (38.25–53.25)	−0.062 (−0.14, 0)	0.051
velocities, cm/s; median (IQR)
MICE		−0.044 (−0.103, 0.015)	0.145
GMDM		−0.074 (−0.138, −0.019)	0.007
Intra-op middle cerebral artery	31 (23.5–42)	−0.044 (−0.107, 0.007)	0.094
velocities $^{1}$ , cm/s; median (IQR)
MICE		−0.032 (−0.078, 0.014)	0.165
GMDM		−0.082 (−0.136, −0.034)	0
Mechanical ventilation	12 (8)	0.666 (−0.904, 1.979)	0.371
>24 h, n (%)
Rethoracotomy $^{2}$ , n (%)	21 (15)	0.648 (−0.567, 1.73)	0.277
Post-op cerebrovascular	15 (11)	0.351 (−1.193, 1.609)	0.621
accident, n (%)
Delirium, n (%)	38 (27)	0.539 (−0.461, 1.486)	0.281
Mortality, n (%)	23 (16)	1.386 (0.336, 2.405)	0.011

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The values are presented as mean ± standard deviation, median (interquartile range), or number of observations and percentage (n (%)). The p-values from univariable logistic regression are given for odds ratios for adverse outcomes. The statistically significant p-values ( $p < 0.05$ ) are in bold. or variables with missing values: results of complete case analyses, imputation with MICE, and imputation with GMDM are given

$^{1}$ The intraoperative middle cerebral artery velocity is measured directly after the initiation of the antegrade selective cerebral perfusion in aortic arch surgery

$^{2}$ Rethoracotomy implies rethoracotomy within 30 days

Effects of including multivessel disease

In Fig. 9 in the appendix, we show the results of including multivessel disease in the analysis. The connection between renal function and mechanical ventilation >24 h disappears since these variables are for many bootstrapped samples independent when conditioning on multivessel disease. BCCD does not detect that delirium is connected with BMI and preoperative CVA when multivessel disease is included. We find that multivessel disease is related to delirium and mechanical ventilation >24 h in Fig. 9, but not significantly, see Table 8. Note that just five subjects have multivessel disease, which makes it less reliable to draw conclusions from the relationship between multivessel disease and other variables in the study.

Table 8.

Perioperative patient characteristics with and without multivessel disease

	Group (n = 142)	Log odds ratio (95% CI)	p-value
Age, y; median (IQR)	68 (60–73)	0.059 (−0.037, 0.193)	0.266
Sex (female), n (%)	65 (46)	−0.245 (−2.295, 1.582)	0.791
Chronic lung disease, n (%)	22 (15)	−16.431 (− $\infty$ , 242.874)	0.19
Pre-op cerebrovascular	15 (11)	−16.371 (− $\infty$ , 297.914)	0.286
accident, n (%)
Pre-op cardiac surgery, n (%)	59 (42)	−0.092 (−2.143, 1.736)	0.921
MICE		−0.08 (−1.917, 1.757)	0.932
GMDM		−0.096 (−2.162, 1.743)	0.918
BMI, kg/m $^{2}$ ; median (IQR)	25.16 (22.21–29.01)	0.045 (−0.15, 0.214)	0.624
MICE		0.045 (−0.133, 0.224)	0.615
GMDM		0.046 (−0.151, 0.214)	0.622
eGFR $^{3}$ , ml/min/1.73m $^{2}$ ;	79.27 ± 18.53	−0.032 (−0.077, 0.014)	0.17
mean±SD
MICE		−0.032 (−0.077, 0.013)	0.165
GMDM		−0.032 (−0.078, 0.014)	0.171
Pre-op middle cerebral artery	44.5 (38.25–53.25)	0.007 (−0.077, 0.073)	0.859
velocities, cm/s; median (IQR)
MICE		0.01 (−0.064, 0.084)	0.789
GMDM		0.011 (−0.079, 0.08)	0.782
Intra-op middle cerebral artery	31 (23.5–42)	−0.085 (−0.206, 0.004)	0.065
velocities $^{1}$ , cm/s; median (IQR)
MICE		−0.063 (−0.166, 0.039)	0.222
GMDM		−0.129 (−0.248, −0.032)	0.007
Mechanical ventilation	12 (8)	2.136 (0.027, 4.046)	0.047
>24 h, n (%)
Rethoracotomy $^{2}$ , n (%)	21 (15)	−16.422 (− $\infty$ , 249.016)	0.201
Post-op cerebrovascular	15 (11)	0.787 (−2.223, 2.785)	0.526
accident, n (%)
Delirium, n (%)	38 (27)	2.495 (0.543, 5.486)	0.011
Mortality, n (%)	23 (16)	0.268 (−2.731, 2.237)	0.819

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$^{1}$ The intraoperative middle cerebral artery velocity is measured directly after the initiation of the antegrade selective cerebral perfusion in aortic arch surgery

$^{2}$ Rethoracotomy implies rethoracotomy within 30 days

Discussion

Renal function as causal risk factor

Figure 1 shows that renal function is directly connected with rethoracotomy via a causal relationship (BCCD) or through a hidden confounder (FCI), and rethoracotomy is a (possible) cause of mortality. Looking more closely with BFCS, we find that renal function is causally related to increased risk of rethoracotomy, and that rethoracotomy is causally related to mortality, i.e., it implies that renal function has an indirect effect on mortality, see Table 3. Poor renal function has been identified as a risk factor for mortality in other studies. Mooney et al. [41] showed that creatinine-based eGFR predicts long-term mortality after cardiac surgery. Other studies show that preoperative creatinine-based eGFR and baseline serum creatinine are associated with short or long-term mortality after cardiac surgery Kolli et al. [42], Dhanani et al. [43], Bernardi et al. [44], but those studies did not investigate causality.

Figure 1b and Table 3 suggest that poor renal function causes mechanical ventilation >24 h, and mechanical ventilation >24 h is directly connected to delirium. This suggests that poor renal function has an indirect relationship to delirium, but the nature of the relationship remains undetermined. Although prior renal disease is not well-known as a risk factor for delirium [45], some studies suggest that preoperative high serum creatinine is related to delirium after cardiac surgery [46, 47]. This is in line with our results showing that pre-operative eGFR is negatively correlated to delirium after surgery. The distributions of eGFR that we obtain when conditioning on delirium seem slightly different; however, the negative correlation can partly be affected by some outliers, as we can see in Appendix F.

For the possible (indirect) effects of renal function on adverse outcomes, it is important to be aware that eGFR is the proxy variable of renal function [22]. Therefore, altering the value of eGFR in a hypothetical intervention does not automatically affect other variables. However, actions targeting renal function may lead to changes in the values of other variables. Surely, there are no simple solutions to improve renal function pre-operatively, but an evaluation of reversible pre-renal and post-renal causes, identifying and stopping nephrotoxic medication, and consulting a nephrologist are feasible clinical strategies. In addition, early advice for maintaining healthy renal function for people at risk of thoracic aneurysms could be a strategy to intervene in renal function. Susanti and Bistara [48] demonstrate that interventions, such as coaching and educating patients and their families about renal function, significantly contribute to raising awareness among chronic kidney disease patients, ultimately helping to prevent the progression of renal function damage.

In Fig. 9, the outputs of the causal discovery algorithms applied to the data extended with the variable multivessel disease are shown. We can see that including multivessel disease leads to the disappearance of the link between mechanical ventilation >24 h and renal function by making the variables independent when including multivessel disease in the conditioning set (or adjustment set). However, multivessel disease can create bias as it only appears in five subjects. Therefore, in future work, it would be interesting to investigate more if the relationship between renal function and mechanical ventilation >24 h remains in a data set with multivessel disease and a larger sample size. In addition, the connection between renal function and rethoracotomy disappears when running the causal discovery algorithms on all variables, including multivessel disease, see Fig. 6a. The disappearance of the relationship can be a consequence of adjusting for too many variables. Moreover, the links between renal function and adverse outcomes are not extremely strong; thus, for future research, it would be interesting to see how these links behave in a data set with a larger sample size and in other populations.

Fig. 6 — The causal graph found by the FCI and BCCD algorithms ran on the data of all variables from the pre-selection. The variables have different color shades to distinguish the types of variables: patient characteristics and medical history are light blue, and postoperative deficits are dark blue. The edge $A \to B$ means A causes B, the $A \leftrightarrow B$ means there is a hidden confounder C causing both A and B, and a circle mark denotes that part of the edge is undetermined. The edge is solid when the correlation is positive and is dashed when the correlation is negative. The thickness of the edge corresponds to the reliability of the existence of the direct relationship. An edge is black when it connects a risk factor with an adverse outcome, and gray otherwise

Preoperative cardiac surgery causes mortality

Similar to renal function, BCCD identifies preoperative cardiac surgery as a cause of mortality, but this is not supported by the outcomes of the FCI algorithm, see Fig. 1. However, our findings with the BFCS algorithm support that the relationship between preoperative cardiac surgery and mortality is causal. In fact, Bianco et al. [49] show that preoperative cardiac surgery is a predictor of both short and long-term mortality. However, we see no realistic strategy to modify this factor, i.e., to prevent cardiac surgery to improve the outcome of future aneurysm repair. On top of that, preoperative cardiac surgery is most likely a proxy variable for other risk factors, such as blood product transfusion [49].

Chronic lung disease and mortality

The results of the causal discovery algorithm BCCD show in Fig. 1b that chronic lung disease and mortality are related, whereas this link is not found with the FCI algorithm. In the literature, a link between short and long-term mortality and chronic lung disease in cardiac surgery is not unfamiliar [50]. In the heatmaps in Fig. 3, the low cause ratios show that this relationship is most probably explained by a hidden confounder.

Sabia et al. [51] searched for explainable factors of poor lung function as risk factors for mortality in general. They showed that chronic lung disease is strongly associated with inflammatory markers. On top of that, it is also related to health behaviors, coronary heart disease, stroke, and diabetes. This implies that chronic lung disease is a proxy variable for various health-related factors, making it a powerful predictor. Nevertheless, chronic lung disease is a challenging variable to interpret from a causal perspective. For example, a hypothetical intervention on chronic lung disease will not change mortality outcomes if the causal relationship is from inflammatory markers to mortality.

Intraoperative MCAv in relationship to patient characteristics and adverse outcomes

Weijs et al. [19] already suggested that intraoperative MCAv is associated with delirium and postoperative CVA. Note that MCAv is a proxy variable of cerebral blood flow (CBF), which makes it an interesting variable to observe in the context of brain performance. With the data we are observing, we cannot conclude that this relationship is causal; see Fig. 1a and Table 3. Thus, intervening in intraoperative MCAv by adjusting the perfusion pump to achieve a higher MCAv may have no effect on adverse outcomes. Instead, a hidden confounder appears to affect both low intraoperative MCAv and adverse outcomes (delirium and postoperative CVA). A hypothetical intervention on this hidden confounder would affect the level of intraoperative MCAv, delirium, and postoperative CVA. For future research, it would be interesting to be able to identify this hidden confounder.

There is a bias towards lower intraoperative MCAv for subjects with chronic lung disease, see Fig. 8 in Appendix G. Note that performing a hypothetical intervention in chronic lung disease will not change the intraoperative MCAv since there is a hidden confounder between chronic lung disease and intraoperative MCAv in the results in Fig. 1. To better understand why there is a relationship between chronic lung disease and intraoperative MCAv, we need to consider that a professional perfusionist controls the level of MCAv during the aortic arch surgery. Here, we do not expect that chronic lung disease plays a role in the perfusionist’s decision-making process. Although the relationship between intraoperative MCAv and chronic lung disease is not trivial, it would be interesting for future work to investigate this relationship, especially because intraoperative MCAv is directly related to delirium and postoperative CVA through a hidden confounder, see Fig. 1 and Table 3. Therefore, it would be very relevant to understand all the factors related to low intraoperative MCAv.

From Table 6 in Appendix G, we understand that chronic lung disease has a significant association with intraoperative MCAv only for imputation via GMDM, making us skeptical about this relationship’s existence. It is important to be critical towards the outcomes as intraoperative MCAv has 47% missing values: while imputing with MICE [28] reduces bias even for a large number of missing values [52], its effect strongly depends on the missingness mechanism in extreme situations where many values are missing [53]. Imputation via GMDM [18] is relatively new and, therefore, not as much analyzed in contrast to MICE. According to D’Angelo et al. [54], EM-algorithm-based estimation of correlation coefficients in the presence of missing values performs similarly to MICE under MAR and up to 50% of missing values. D’Angelo et al. [54] do not compare MICE with GMDM, but we expect similar results.

Strengths and limitations

Deciding if a patient should undergo aortic arch surgery relies on many factors. Age is one of the most important risk factors. Doctors usually look at biological age, but that is not clearly defined, as it describes the age of the state of the body instead of the chronological age. In Table 2 and Fig. 1, we show that age appears to be mediated by other factors that are proxies or indicators of biological age. This could also be a consequence of a well-performing selection procedure for patients for this surgery; namely, after this clinical selection procedure, we can find relationships between independently from age. A consequence is that the age interval is more restricted for patients who undergo this surgery, i.e., there is less variability in age.

Selection bias can create additional edges (or associations) in the outcomes of the causal discovery algorithm. Selection bias appears when the selection procedure is based on the outcomes or when the selection procedure is affected by risk factors. The subjects in this study are invited for the intervention based on the size of the aneurysm in the aortic arch and biological age. Moreover, we only selected the elective and urgent cases for this study, which is a variable defined in the preoperative phase. In this study, there is no risk of selection bias because the selection procedure is not related to the outcome variable. Moreover, by selecting risk factors in such a way that they completely explain the selection procedure according to expert knowledge, it becomes very unlikely that the outcomes are affected by selection bias. Therefore, we carefully selected the preoperative variables describing the health status, which is strongly related to the biological age. From Fig. 6, we conclude that selecting on urgency will not create additional edges due to selection bias.

The nature of the relationship between delirium and prolonged mechanical ventilation remains unknown, as we obtain contradicting results from the FCI, BCCD, and BFCS algorithms. We used the variables eGFR and preoperative CVA to determine the direction of this relationship with BFCS, since these two variables are not directly related and have a direct relationship to eGFR or preoperative CVA according to BCCD. Perhaps there is no single causal mechanism that describes the relationship between delirium and mechanical ventilation >24 h, or there is a cycle or selection bias connecting the two variables. To improve aftercare, it would be interesting to explore this relationship further in future research.

The data set analyzed in this study contains only 142 subjects, and some variables have missing values, which is a limitation. To mitigate the influence of a small sample size, we combined causal conclusions from three causal discovery algorithms in conservative settings. Moreover, we used reliability scores to assess the strength of the existence of the relationships. However, it would be interesting to repeat the analysis on a bigger data set by combining data from different hospitals to examine the robustness of the possible (causal) risk factors for a larger sample size and after a possible population switch.

In our analysis, we did not include acute cases; that is, patients who need aortic arch surgery on the same day as the necessity of the surgery is determined, or cardiopulmonary resuscitation on the way to the surgery room, or before administering anesthesia. We did leave out these patients as they do not follow the standard procedure before the surgery, which can lead to missing values. Moreover, for this group, the risks are higher, but the protective effect of the surgery is also more meaningful. Thus, to ensure that subtypes in the data are not too different, we focus only on elective and urgent cases. We advise investigating separately if the surgery has a protective effect for the acute cases and what extra care this group needs after surgery.

In this study, we did not research the relationship between adverse outcomes and intervention settings such as intraoperative pharmacological indicators or circulatory support. Namely, the main objective of this study was to find preoperative risk factors. Besides that, the subjects had similar intervention settings, and the data were not rich enough for detailed differences in these settings. For future studies, however, it would be interesting to dive deeper into these relationships.

The causal discovery algorithms do not output exactly the same relationships that would be expected in the ideal setting. The reasoning process for the BCCD and the FCI algorithm is different. The reliability score that the BCCD algorithm outputs describes the uncertainty of the existence of an edge or orientation. Here, to infer relationships, decisions are made based on the relationship with the highest reliability score. The FCI algorithm, however, infers relationships by exploiting conditional independence information and logical statements. When sample sizes are small, the FCI algorithm infers fewer relationships due to low power in the conditional independence tests, while the BCCD reacts differently to limited samples. This can explain why the outputs of the FCI and BCCD algorithms are not the same. Another observation is that FCI finds more hidden confounders even though we use an additional test that checks for wrong orientations, called conservative FCI. However, given that the strengths of the relationships found by the FCI algorithm are relatively weak, the orientation of it can also depend on the power of the conditional independence tests.

Conclusion

In this study, we investigate the causality of risk factors, other than age, in open thoracic surgery since this surgery is mostly for geriatric age groups, and age is unreliable to base life-changing decisions on. We showed with causal discovery algorithms that renal function is a causal risk factor for rethoracotomy and mechanical ventilation >24 h, and also that renal function is an indirect cause of mortality and an indirect risk factor for delirium. Moreover, our findings showed that middle cerebral artery velocity (MCAv) after initiating the bilateral antegrade selective cerebral perfusion is a risk factor for postoperative CVA and delirium, and chronic lung disease is a causal risk factor for low MCAv at this risky stage during the surgery. Finally, prior cardiac surgery is a possible causal risk factor for mortality within 30 days.

Supplementary information The code written to pursue the methodology in this research is available at https://github.com/mivadi/AppliedCausalDiscovery.

Acknowledgements

The authors thank the Radboud AI for Health (ICAI lab in Nijmegen, Netherlands) for providing funding for this research. Ioan Gabriel Bucur has been partially funded through the Healthy Data program. The authors thank Kasper F. Beukema (data specialist, Department of Cardiology, St. Antonius Hospital, Nieuwegein, Netherlands) and Marvin Gerritsen (lawyer, FNWI Faculty Office, Radboud University, Nijmegen, Netherlands) for their support in the data sharing collaboration with the St. Antonius Ziekenhuis. The authors also thank Tom Heskes, Joris Mooij, Vanessa Didelez, Daniel Malinsky, and Sara Magliacane for the fruitful discussions.

Appendix A. Detailed methods

A.1. Data processing

Missing values and a mixture of binary and continuous data were two of the challenges, among others; in this section, we illustrate how to tackle them. Causal discovery algorithms are techniques that typically cannot handle missing values and mixed data, so data processing is required. Moreover, in this study, we focused on the causal discovery algorithms that perform best on linear Gaussian data and can take a correlation matrix of the data as input. We transformed a mixture of binary and continuous data into a joint Gaussian distribution by estimating the underlying Gaussian copula. A Gaussian copula is a multivariate cumulative distribution function that describes the dependence between random variables under a Gaussian distribution [55]. Thereafter, the correlation matrix and the Gaussian copula model were (re-)estimated iteratively using expectation maximization to account for the missing values. Expectation maximization is an iterative method to find the maximum-a-posteriori estimate or maximum likelihood of statistical parameters. This procedure is well-studied in combination with causal discovery: see Cui et al. [18], Abegaz and Wit [56], Sokolova et al. [57].8 We obtained the correlation matrix by taking the mean of the last 500 sampled correlation matrices drawn with a Gibbs sampling procedure with 1000 iterations proposed by Cui et al. [18].9 The method works under the assumption of missing at random (MAR), and gives promising results, especially with an effective sample size estimated according to Cui et al. [18]. The effective sample size is equivalent to the number of complete rows in the data set containing missing values for the considered variables in the independence test statement. Another assumption necessary when transforming the data to a Gaussian copula is that the transformation function is invertible or, equivalently, that the data is monotonic. This is similar to the commonly used linearity assumption but less restrictive. We discuss the assumptions further in section B in the appendix.

A.2. Causal discovery

In this study, we are interested in finding the causal relationships between variables in the data. Therefore, we apply causal discovery. There is a growing interest in the use of causal discovery in healthcare [32–37]. However, as these techniques are not well-known in this field, we describe the methods below. In a real-world setting, we face a finite sample size, estimation errors, and missing values. To guarantee more robust conclusions, we apply three causal discovery algorithms that work under similar assumptions but use different techniques. We evaluate the robustness of the inferred relationships by observing if they occur in the outcome of each algorithm. In this section, we first discuss how to interpret the relationships in the causal graph. Then we describe the three causal discovery algorithms we apply in this study and show how to exploit background knowledge and predict reliability scores for all relationships. We will compare the outcomes of the first two algorithms, and focus on particular relationships from the outcomes to get an independent confirmation with the third algorithm. In appendix B, we describe and discuss the required assumptions for these algorithms. Graphics programs used to plot results were ggplot2 in R and TikZ in LaTeX.

A.2.1. How to interpret a causal graph?

The causal discovery algorithms search for a causal graph that models the causal relationships between the variables in the data. An example of a causal graph with partial orientation is shown in Fig. 1. In the causal graph, variables share an edge if no other variables make them independent. There are different types of edges, one of them is $A \to B$ which means “A has a causal effect on B and there is no observed mediator between A and B that accounts for this cause.” By combining adjacent directed edges, we find a directed path, e.g., $A \to B \to C \to D$ is a directed path. Another relationship, $A \leftrightarrow B$ , suggests that there is no causal relationship between A and B, but there is an unobserved confounder C that causes both A and B.

In the search for the causal graph, we can only use statistical information which is unfortunately not as rich as the causal information. Therefore, we cannot infer all causal information, but only a part of it. Instead of a completely inferred causal graph, we obtain an object called a partial ancestral graph (PAG) which encodes the available ancestral causal information [58]. Ancestral causal relationships are direct or indirect causal relationships, e.g., an indirect causal relationship through a directed path. The causal structure contains edges like $\to$ or $\leftrightarrow$ , but it also can contain edges that represent uncertainty. The edges containing a circle mark are variant. The edge $A \circ - \circ B$ means that we do not know if there is a causal relationship ( $A \to B$ or $A \leftarrow B$ ) or a hidden confounder ( $A \leftrightarrow B$ ), and the edge $A \circ \to B$ suggests that there is an edge $A \to B$ or an edge $A \leftrightarrow B$ . Furthermore, besides directed paths, we can identify possible directed paths in this graph, i.e., an ordered list of adjacent edges such that each edge is of the form $A \to B$ , $A \circ \to B$ or $A \circ - \circ B$ , and at least one edge contains a circle mark. For example, $A \circ - \circ B \circ \to C \to D$ is a possible directed path.

A.2.2. Fast causal inference

The fast causal inference (FCI) algorithm10 [13, 38] is a constraint-based causal discovery algorithm that uses conditional independencies between variables to understand which variables are directly linked. Then it applies logical inference rules to decide how the relationships are directed according to the conditional independencies. For more details about all orientation rules, we refer to [13, 38]. Below we elaborate more on the settings we used, such as how we exploit background knowledge and use bootstrapping to handle uncertainty.

The constraint-based causal discovery algorithm, fast causal inference (FCI), depends on conditional independence test results. The conditional independence test selected for this study is the Fisher’s Z transformation of the partial correlation test [39, 40] for which it is assumed that the data is Gaussian distributed. The significance level for these statistical tests is set to 0.05. There are other types of conditional independence tests available, but, as the data is transformed into a Gaussian copula, it satisfies the assumption of Gaussian data, so it is not necessary to focus on other tests. We use a conservative version of the algorithm [59] that runs extra conditional independence tests and can lead to fewer orientations, but the obtained orientations are more robust.

Andrews et al. [16] and Mooij et al. [17] show how FCI can make use of different types of temporal information under the assumption that there is no selection bias. The method of Mooij et al. [17] exploits context information and shows which assumptions are required to directly orient causal relationships from context variables to other variables. In this study, age and sex are such context variables. The method of Andrews et al. [16] works for tiered background knowledge, i.e., the variables can be divided into ordered sets such that each group corresponds to a tier and the order corresponds to the chronological time order. The context and the three phases in the perioperative period are four tiers in the data set observed in this study. Andrews et al. [16] assume that relationships between two variables of different tiers are always explained by a causal relationship, i.e., they assume that there is no unmeasured confounding between tiers. We combine the two methods by orienting relationships from context variables towards other variables and use a version of the method of Andrews et al. [16] that works in a less restrictive setting. For this relaxed version, we assume that there can be hidden confounders between the different tiers. This relaxed version is sound since time-dependent background information is always true, but it is not shown to be complete, that is, it could be that there is more causal information that we could have found based on the statistical information, but the current methods cannot detect it. Moreover, only variables in previous tiers should be selected for the conditioning sets when testing for independence according to [13, p. 93]11

To deal with a small number of observations and uncertainty, we run FCI on 1000 bootstrapped data sets and combine the outputs to obtain a more stable output. We combine the output causal graphs by counting the occurrence of the edges and select an edge if it occurs in more than 50% of the outputs.12 To set the orientation of the edge, we count the positive and negative ancestral information in the outputs. Positive ancestral information is found if there is a directed path $A \to \dots \to B$ between two variables A and B, and there is negative ancestral information if there is an arrowhead in the opposite direction ( $A \leftarrow B$ , $A \leftrightarrow B$ , or $A \leftarrow \circ B$ ) on all possible paths or no (possible) directed path between A and B. We orient the edge as a directed edge $\to$ or the edge mark on the left side of the edge as an arrowhead based on majority voting (>50%) between the positive and negative ancestral information.13 Otherwise, the edge marks stay unoriented (denoted by circle marks).

A.2.3. Bayesian constraint-based causal discovery

The Bayesian constraint-based causal discovery (BCCD) algorithm [14] is a search and inference strategy that combines components from constraint-based and score-based causal discovery algorithms. In the first stage of the BCCD algorithm, a Bayesian score decides which variables are disconnected, and, in the meantime, logical causal statements implied by the outcomes of the score are tracked. Our current implementation14 employs a Gaussian likelihood score and, thus, performs best on Gaussian data. In the second stage, the collection of logical causal statements is used to reconstruct the causal graph that may contain causal relationships and hidden confounders by applying the causal logic rules [61]. To handle uncertainty, the output of the BCCD algorithm gives reliability information for each edge and edge mark based on the Bayesian score. Moreover, it can make use of background knowledge in the second stage as an addition to the logical causal statement.

A.2.4. Bayes factors of covariance structures

Bucur et al. [15]15 propose Bayes factors of covariance structures (BFCS) which is a Bayesian method to locally discover causal relationships in triplets of normally distributed variables. We use this method to examine particular relationships between variables found by the FCI algorithm and/or the BCCD algorithm where we selected them by clinical relevance. The covariance structure of a triplet is how the covariances of variables interact. Bucur et al. [15] show that covariance structures are directly related to causal structures. This implies that causal interactions in triplets can be scored with the posterior probabilities of the corresponding covariance structure. We select variables A, B, C for a triplet in such a way that we are specifically interested if the triplet is causal ( $B \to A$ or $B \to C$ ) or acausal ( $B ↛ A$ and $B ↛ C$ ). BFCS computes the probabilities of all causal patterns. Incorporating the outcomes with background knowledge makes it possible to draw stronger causal conclusions.

Appendix B. Assumptions

Assumptions on the type of data (e.g., missing at random) are used in the “Data processing” and “Statistical analyses” sections. For the causal discovery algorithms, we require the faithfulness assumption, the global Markov condition, acyclicity, and no selection bias.

The faithfulness assumption and the global Markov condition work together and bridge the gap between the statistical information obtained from the data and the graphical information in the causal graph. Under those assumptions, there is no edge between two variables in the causal graph if and only if the variables are (conditionally) independent given a set of other variables (e.g., an adjustment set). The faithfulness assumption and the global Markov condition are standard and reasonable assumptions [13, 62, 63]; however, to handle mistakes in case these assumptions are violated, we use conservative testing for FCI and reliability scores for both FCI and BCCD, see Appendices A.2.2 and A.2.3.

The acyclicity assumption suggests that there are no cycles in the causal graph. For general biological models (e.g., the cell-division cycle), this is an unrealistic assumption. In this study, however, we have clear temporal information and a small set of variables, so cycles are unlikely to occur in the ground truth causal graph.

We can represent selection bias in the causal graph, however, not all algorithms can detect selection bias. Selection bias can create additional edges (or associations) when subjects are selected based on the effects of relevant (hidden) variables. The FCI algorithm is not shown to be sound in the presence of selection bias when background knowledge is used as input [16, 17], whereas the BCCD algorithm can detect selection bias even if background knowledge is used. To make the outputs of the algorithms easier to compare, we assume that the is no selection bias when running both algorithms.

To account for missing values in the data, we used imputation methods that rely on the assumption Missing at Random (MAR). This is a standard assumption, though, it is very challenging to test if MAR is satisfied [64]. For one of the imputation techniques we also need to assume that the data is monotonic. This is true for binary data and easy to check for non-binary data, namely by considering the scatter plots and observing if there is no clear non-monotonic relationship (for example, a parabola). In Appendix C, we show the results of the sensitivity analyses: we test for Gaussianity for the analysis results in the Tables 2, 6, and 8, and we test for monotonicity as explained above.

Appendix C. Test for assumptions

C.1. Test for Gaussianity

Fig. 4 — From Shapiro-Wilk’s test results, we concluded that eGFR is normally distributed (p = 0.0001). At the left the density of eGFR is shown which clearly describes a Gaussian density. At the right, it is visualized with a normal Q-Q plot that the sampled and theoretical quantiles are close enough to conclude that eGFR is normally distributed

C.2. Test for monotonicity

Fig. 5 — In the pairwise scatter plots of the continuous variables age, BMI, eGFR, preoperative MCAv, and intraoperative MCAv, we do not find clear non-monotonic relationships. Here, only the complete cases are considered. The intraoperative middle cerebral artery velocity is measured directly after initiating the antegrade selective cerebral perfusion in aortic arch surgery

Appendix D. Excluded variables

Variables we considered, but did exclude in the final results for clarity, are urgency, Extracardiac arteriopathy (ECA), and New York Heart Association (NYHA). Urgency and ECA were left out of the final results because they were never directly related to outcome variables in the output causal graphs, see Fig. 6. Urgency is a variable that indicates if the aortic arch surgery was elective or urgent, where urgent indicates that a subject was hospitalized for other reasons or unplanned and that the intervention was necessary during the hospitalization. ECA is a known risk factor for cardiac surgery [65], and is diagnosed if one of the following conditions holds: intermittent claudication, carotid stenosis > 50%, amputation as an effect of arterial disease, prior or planned surgery in the abdominal aorta, arteries in the limbs, or carotids. The class of the NYHA indicates the severity of heart failure symptoms in physical activities. It is defined as the highest class measured during the two weeks prior to the surgery. In Fig. 6b, we find that there is a connection between NYHA classes and mechanical ventilation >24 h. However, the 14 patients with mechanical ventilation >24 h had all NYHA class I or II (i.e., very mild symptoms), except for one patient with class IV, which is the only patient in the whole data set with class IV. In other words, the connection between the NYHA classes and mechanical ventilation >24 h in Fig. 6b is possibly found because of the outlier with NYHA class IV. To prevent drawing conclusions based on biased outputs, we decided to exclude NYHA from the final results.

Appendix E. Additional results BFCS

In Table 4 is shown that the chosen triplets to test causality with BFCS, have always at least two connection. In Table 3, the main results are shown.

Table 4.

The results of BFCS as addition to Table 3

	A independent	B independent	C independent	All
	with B and C	with A and C	with A and B	independent
A = renal function	0.00	0.00	0.04	0.00
B = rethoracotomy $^{2}$
C = mortality
A = post-op CVA	0.00	0.01	0.00	0.00
B = pre-op cardiac surgery
C = mortality
A = post-op CVA	0.00	0.01	0.00	0.00
B = pre-op cardiac surgery
C = pre-op CVA
A = delirium	0.00	0.00	0.00	0.00
B = intra-op MCA $^{1}$
C = post-op CVA
A = renal function	0.00	0.00	0.00	0.00
B = mechanical ventilation $^{3}$
C = delirium
A = pre-op CVA	0.00	0.02	0.00	0.00
B = delirium
C = mechanical ventilation $^{3}$
A = age	0.00	0.00	0.00	0.00
B = renal function
C = pre-op cardiac surgery
A = pre-op cardiac surgery	0.00	0.04	0.01	0.00
B = renal function
C = rethoracotomy $^{2}$
A = pre-op cardiac surgery	0.00	0.00	0.01	0.00
B = renal function
C = mechanical ventilation $^{3}$

Open in a new tab

The left column shows which triple containing A, B, and C is selected. Then, in the following columns, we can read-off with which probability some variables in the triplet have no connection

$^{1}$ The intraoperative middle cerebral artery velocity is measured directly after the initiation of the antegrade selective cerebral perfusion in aortic arch surgery

$^{2}$ Rethoracotomy implies rethoracotomy within 30 days

$^{3}$ Mechanical ventilation implies mechanical ventilation >24 h

Appendix F. Estimated GFR under adverse outcomes

Fig. 7 — Histograms that show how eGFR (or renal function) is distributed under all adverse outcomes after open aortic arch surgery

Appendix G. Chronic lung disease

Tables 5 and 6 show how all variables are related to chronic lung disease in pairwise comparison. There is an association found between chronic lung disease and eGFR (OR: $-$ 0.026; 95% CI: [ $-$ 0.052, $-$ 0.002]; p = 0.037), and with mortality (OR: 1.386; 95% CI: [0.336, 2.405]; p = 0.008). In Fig. 8, the histogram with the distributions of intraoperative MCAv with and without chronic lung disease are shown. These distributions show different behavior; the subjects with no chronic lung disease are centered at an intraoperative MCAv of 20–30 cm/s, while chronic lung disease subjects have an intraoperative MCAv of 10–20 cm/s. Moreover, the tail of the distribution for subjects with no chronic lung disease increases more sharply in comparison to subjects with chronic lung disease. There is, however, more data needed to draw stronger conclusions from the comparison of these two distributions.

Table 5.

Perioperative patient characteristics with and without chronic lung disease

	Group (n = 142)	W/o chronic	W/ chronic
		lung disease	lung disease
		(n = 120)	(n = 22)
Age, y; median (IQR)	68 (60–73)	67 (58–72)	68 (66–74)
Sex (female), n (%)	65 (46)	52 (43)	13 (59)
Multivessel disease, n (%)	5 (4)	5 (4)	0 (0)
Pre-op cerebrovascular	15 (11)	11 (9)	4 (18)
accident, n (%)
Pre-op cardiac	59 (42)	47 (40)	12 (55)
surgery, n (%)
BMI, kg/m $^{2}$ ; median (IQR)	25.16 (22.21–29.01)	25.01 (22.13–29.03)	25.38 (23.34–26.96)
eGFR $^{3}$ , ml/min/1.73m $^{2}$ ;	79.27 ± 18.53	80.7 ± 18.22	71.55 ± 18.67
mean±SD
Pre-op middle cerebral artery	44.5 (38.25–53.25)	45 (38.5–53.75)	40 (37.25–43.5)
velocities, cm/s; median (IQR)
Intra-op middle cerebral artery	31 (23.5–42)	32 (24.5–42.5)	19.75 (14–37.88)
velocities $^{1}$ , cm/s; median (IQR)
Mechanical ventilation	12 (8)	9 (8)	3 (14)
>24 h, n (%)
Rethoracotomy $^{2}$ , n (%)	21 (15)	16 (13)	5 (23)
Post-op cerebrovascular	15 (11)	12 (10)	3 (14)
accident, n (%)
Delirium, n (%)	38 (27)	30 (25)	8 (36)
Mortality, n (%)	23 (16)	15 (12)	8 (36)

Open in a new tab

The values are presented as mean ± standard deviation, median (interquartile range), or number of observations and percentage (n (%))

$^{1}$ The intraoperative middle cerebral artery velocity is measured directly after the initiation of the antegrade selective cerebral perfusion in aortic arch surgery

$^{2}$ Rethoracotomy implies rethoracotomy within 30 days

Appendix H. Multivessel disease

Table 7.

Perioperative patient characteristics with and without multivessel disease

	Group (n = 142)	W/o multivessel	W/ multivessel
		disease (n = 137)	disease (n = 5)
Age, y; median (IQR)	68 (60–73)	68 (60–73)	72 (66–76)
Sex (female), n (%)	65 (46)	63 (46)	2 (40)
Chronic lung disease, n (%)	22 (15)	22 (16)	0 (0)
Pre-op cerebrovascular	15 (11)	15 (11)	0 (0)
accident, n (%)
Pre-op cardiac surgery, n (%)	59 (42)	57 (42)	2 (40)
BMI, kg/m $^{2}$ ; median (IQR)	25.16 (22.21–29.01)	25.17 (22.19–29.01)	24.25 (22.59–27.36)
eGFR $^{3}$ , ml/min/1.73m $^{2}$ ;	79.27 ± 18.53	79.69 ± 18.19	67.79 ± 25.87
mean±SD
Pre-op middle cerebral artery	44.5 (38.25–53.25)	44 (38–53.38)	45 (40.5–48.5)
velocities, cm/s; median (IQR)
Intra-op middle cerebral artery	31 (23.5–42)	32 (24–43.75)	22.5 (20.25–24.38)
velocities $^{1}$ , cm/s; median (IQR)
Mechanical ventilation	12 (8)	10 (7)	2 (40)
>24 h, n (%)
Rethoracotomy $^{2}$ , n (%)	21 (15)	21 (15)	0 (0)
Post-op cerebrovascular	15 (11)	14 (10)	1 (20)
accident, n (%)
Delirium, n (%)	38 (27)	34 (25)	4 (80)
Mortality, n (%)	23 (16)	22 (16)	1 (20)

Open in a new tab

The values are presented as mean ± standard deviation, median (interquartile range), or number of observations and percentage (n (%))

$^{1}$ The intraoperative middle cerebral artery velocity is measured directly after the initiation of the antegrade selective cerebral perfusion in aortic arch surgery

$^{2}$ Rethoracotomy implies rethoracotomy within 30 days

Author contribution

All authors contributed to the study conception and design. Mirthe M. van Diepen is the first author, including writing the code, analyzing the data, visualizing the results, and writing the article. The first draft of the manuscript was written by Mirthe van Diepen, and all authors commented on previous versions of the manuscript. Jurgen Claassen (Geriatrics department), and Ioan Gabriel Bucur, and Tom Claassen (Data Science department) contributed by supervising, rewriting, and providing feedback from a geriatrics, medical, mathematical, and data science perspective. Ralf Weijs contributed by helping with setting up this study. Robin Heijmen contributed by providing insights from a cardiovascular surgery perspective. All authors read and approved the final manuscript.

Funding

The Radboud AI for Health (ICAI lab in Nijmegen, Netherlands) provided funding for this research. Ioan Gabriel Bucur has been partially funded through the Healthy Data program. The data is provided by the St. Antonius Hospital in Nieuwegein, Netherlands.

Data availability

Given the retrospective nature of this research, the fact that the data is anonymized, and the patient’s permission for the use of their data for scientific research, it was not needed to request permission from the patients for this study. The data is stored in the management system of the REDCAP server of the St. Antonius Hospital and can only be made available upon request. The code written to pursue the methodology in this research is available at https://github.com/mivadi/AppliedCausalDiscovery.

Declarations

Competing interests

The authors declare no competing interests.

Footnotes

We used the implementation in R from https://github.com/cuiruifei/CausalMissingValues.

We use the R package: https://rdrr.io/cran/mice/man/mice.html with default setting if not stated otherwise.

Here, ‘direct’ means that there are no variables included in the data set that can make the associated variables independent.

⁴

The implementation we used can be found at https://github.com/mivadi/AppliedCausalDiscovery.

⁵

We use Fisher’s Z transformation of the partial correlation test [39, 40] as the conditional independence test, which is a test based on the correlation matrix.

⁶

We used the implementation in R from https://gitlab.science.ru.nl/gbucur/RUcausal.

⁷

We used the implementation from https://github.com/igbucur/BFCS.

⁸

Although the imputation technique MICE [28] is widely spread and well-understood, it is not always the best choice for causal discovery algorithms. Causal discovery algorithms are sensitive to the type of input data. Depending on the score function or type of test, the data must satisfy some modeling assumption, e.g., linear Gaussianity. Especially for mixed data, a property of the data analyzed in this study, such a modeling assumption is difficult to guarantee. Cui et al. [18] propose a method that transfers the data to a Gaussian copula to handle this problem. After imputing with MICE, however, it is unclear which score function or independence test in a causal discovery algorithm will perform well on the mixed data without getting errors due to violations of the modeling assumption.

⁹

We used the implementation in R from https://github.com/cuiruifei/CausalMissingValues.

¹⁰

The implementation of this algorithm we used for our analyses can be found at https://github.com/mivadi/AppliedCausalDiscovery.

¹¹

Spirtes et al. [13] claim that only variables from previous tiers should be selected for the conditioning sets when testing for independence under the causal sufficiency assumption. Note that the order of the tiers is closed under marginalization (i.e., the time-dependent order does not change if we do not include some variables in the data set) which implies that the same statement holds for causal models in the presence of unmeasured confounding.

¹²

The threshold is an adjustable parameter that we set such that the output of the FCI algorithm has a similar edge degree as the output of the BCCD algorithm which makes the outputs easier to compare.

¹³

In theory, we can obtain (almost) directed cycles which contradicts an assumption made on the underlying causal graph [60]. For clarity, this graph shows uncertainty, therefore, edges or edge marks that are not in the ground truth are possibly shown with a reliability score in the output graph. This implies that (almost) directed cycles in the output graph suggest that at least one of the edges or edge marks in the (almost) directed cycle is not in the ground truth.

¹⁴

We used the implementation from https://gitlab.science.ru.nl/gbucur/RUcausal.

¹⁵

We used the implementation from https://github.com/igbucur/BFCS.

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PERMALINK

Causal risk factors for stroke, delirium, and mortality after elective and urgent open aortic arch surgery for older adults

Mirthe M van Diepen

Ioan Gabriel Bucur

Ralf W J Weijs

Robin H Heijmen

Tom Claassen

Jurgen A H R Claassen

Abstract

Introduction

Materials and methods

Ethics statement

Study design and population

Data collection

Selection procedure of patient characteristics

Risk factors for adverse outcomes after aortic arch surgery

Middle cerebral artery velocity

Adverse outcomes

Data processing

Statistical analyses

Causal discovery

Results

Study population

Table 1.

Table 2.

Outcomes of the causal discovery algorithms

Fig. 1.

Table 3.

Fig. 2.

Fig. 3.

Relationships to mortality

Relationships to post-operative CVA

Relationships to delirium

Relationships to rethoracotomy

Relationships to mechanical ventilation longer than 24 h

Relationships to intraoperative MCAv

Table 6.

Effects of including multivessel disease

Fig. 9.

Table 8.

Discussion

Renal function as causal risk factor

Fig. 6.

Preoperative cardiac surgery causes mortality

Chronic lung disease and mortality

Intraoperative MCAv in relationship to patient characteristics and adverse outcomes

Fig. 8.

Strengths and limitations

Conclusion

Acknowledgements

Appendix A. Detailed methods

A.1. Data processing

A.2. Causal discovery

A.2.1. How to interpret a causal graph?

A.2.2. Fast causal inference

A.2.3. Bayesian constraint-based causal discovery

A.2.4. Bayes factors of covariance structures

Appendix B. Assumptions

Appendix C. Test for assumptions

C.1. Test for Gaussianity

Fig. 4.

C.2. Test for monotonicity

Fig. 5.

Appendix D. Excluded variables

Appendix E. Additional results BFCS

Table 4.

Appendix F. Estimated GFR under adverse outcomes

Fig. 7.

Appendix G. Chronic lung disease

Table 5.

Appendix H. Multivessel disease

Table 7.

Author contribution

Funding

Data availability

Declarations

Competing interests

Footnotes

References

Associated Data