Approach and Method for Bayesian Network Modelling:

The Case for Pregnancy Outcomes in England and Wales

Scott McLachlan

, Bridget J. Daley

, Sam Saidi

, Evangelia Kyrimi

, Kudakwashe Dube

Crina Grossan

, Martin Neil

, Louise Rose

and Norman E. Fenton

Nursing, Midwifery and Palliative Care, Kings College London, London, U.K.

Maternity Unit, Liverpool Women’s Hospital NHS Trust, Liverpool, U.K.

School of Medicine, University of Sydney, Sydney, Australia

Electronic Engineering and Computer Science, Queen Mary University of London, London, U.K.

Keywords: Clinical Decision-Support Systems, Bayesian Networks, Predictive Models, Pregnancy Outcomes.

Abstract: For predicting and reasoning about outcomes of specific medical condition Bayesian Networks (BNs) can

provide significant benefits over traditional statistical prediction models. However, developing appropriate

and accurate BNs that incorporate key causal aspects of the condition is challenging and time-consuming.

This work introduces a novel development approach, merging expert elicitation, literature knowledge, and

national health statistics that enables such BNs to be developed efficiently. The approach is applied to build

a BN for pregnancy complications and outcomes in England and Wales using 2021 data. The BN showed

comparable predictive performance against logistic regression and nomograms, but additionally provides

powerful support for decision-making and risk assessment across diverse pregnancy-related conditions and

outcomes.

1 INTRODUCTION

Traditional pregnancy prediction models focus on

singular health issues such as gestational diabetes

mellitus (GDM) or preeclampsia (PE) without

considering the broader context of the pregnancy.

Typically, these models are statistical, relying on a

limited set of risk factors which leads to several

limitations (a full set of references for this and other

imputations in this paper can be found in the

expanded preprint version: McLachlan et al, 2024).

These limitations include: (i) a focus on predicting the

presence of a condition without considering the

absence of that condition; (ii) overfitting to available

data, leading to poor performance in the presence of

uncertain or missing data; (iii) lack of transparency

and interpretability, making it difficult to understand

how the model makes its predictions; and (iv) limited

ability to generalize to new populations or settings.

To address these limitations we propose a new

approach to pregnancy prediction based on Bayesian

networks (BNs). BNs are a type of probabilistic

https://orcid.org/0000-0002-2528-8050

model that can represent complex relationships

between variables and have been shown effective in a

wide range of medical applications.

Our proposed approach involves using BNs to

model the entire pregnancy rather than focusing on

singular health issues. This allows us to draw on a

wider range of information including symptoms, risk

factors, and medical history and to simultaneously

make predictions about multiple health issues.

We have evaluated our proposed approach using

the domain of pregnancy outcomes and found that it

can outperform traditional methods in terms of

accuracy, generalisability, and interpretability. We

believe our approach has potential to transform how

prediction models, and particularly pregnancy

outcome prediction models, are developed and used.

The resulting model is extensively validated using

vignettes and concurrency analysis.

The rest of the paper is structured as follows:

Section 2 covers theoretical and application domain

backgrounds and reviews literature related to the

research problem. Section 3 outlines approach and

method for knowledge, data, and expert-driven

604

McLachlan, S., Daley, B., Saidi, S., Kyrimi, E., Dube, K., Grossan, C., Neil, M., Rose, L. and Fenton, N.

Approach and Method for Bayesian Network Modelling: The Case for Pregnancy Outcomes in England and Wales.

DOI: 10.5220/0012428600003657

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 17th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2024) - Volume 2, pages 604-612

ISBN: 978-989-758-688-0; ISSN: 2184-4305

modelling using causal BNs. Section 4 presents the

results of applying this approach to develop a BN for

pregnancy complications and outcomes. Section 5

discusses the experience of utilizing the approach and

method, highlighting potential limitations in

application to other problem domain spaces.

2 BACKGROUND AND RELATED

WORKS

In our contemporaneous work, we screened a

collection of 100 works published between 2000 and

2023 that proposed predictive risk screening models

for pregnancy complications (Dube, Kyrimi &

McLachlan, 2023).

2.1 Risk Factors and Symptoms

Risk screening typically occurs during the initial

maternal clinic visit known as the booking visit

(Tandu-Umba et al, 2014). While risk screening

scores may be updated throughout antenatal care as

new clinical and non-clinical information emerges,

the specific signs, symptoms or clinical tests used

vary depending on the adopted guideline or scoring

model (Tandu-Umba et al, 2014; Stott et al, 2016).

Some models rely on common factors like maternal

age, BMI, and pregnancy history collected during the

booking visit (Tandu-Umba et al, 2014), while others

incorporate antenatal care records, pregnancy

outcomes, or even novel variables like paternal DNA

or vaginal swab results (Stott et al, 2016).

2.2 Common Issues

Developing healthcare risk, probability and decision

support models can be challenging because: (i)

obtaining a sufficiently large and high-quality dataset

remains a hurdle and data may only be available for

small patient groups, with demographic or clinical

risk factors significantly reducing subgroup sample

sizes (North et al, 2011; Pitchforth & Mengersen,

2013); (ii) traditional model evaluation relies on

internal statistical methods (Dube et al, 2023) such as

ROC curves and CIs that have limitations in assessing

BNs (Pitchforth & Mengersen, 2013); (iii) prediction

accuracy varies when some observations are missing

or the patient lacks the predicted health condition,

often due to overfitting that occurs when models are

trained solely on data identifying the medical

condition of interest, excluding information about

what isn't that condition (Kumar et al, 2022); and (iv)

most are not presented with clear examples like risk-

scored vignettes, hindering clinical comprehension

and adoption (North et al, 2011; Mehta-Lee et al,

2017).

3 METHOD

Our research initially focused on constructing causal

models for singular health issues affecting patients

with rheumatoid arthritis, angina, acute traumatic

coagulopathy, and GDM (McLachlan et al, 2020).

However, we too overlooked the broader perspectives

of general health, the accumulated effect of

comorbidity, and healthcare access and experience

within an entire population. We now stress the

importance of adopting a holistic approach to model

not only the patient, but also the community and

disease; in essence, a complete digital twin that can

be used to establish the credibility of our models in:

(a) identifying or explaining risk; and (b) providing

computer-based clinical decision support using

machine learning (ML) or artificial intelligence (AI).

Creating a community-wide baseline is crucial to

fully evaluate causal relationships among known and

novel symptoms, and modelling treatment and

prognostic counterfactuals.

3.1 Hypothesis

This work proposes a broadly accurate BN model for

diagnosis and treatment outcomes can be constructed

using expert clinical knowledge, privacy-preserving

datasets and population-wide statistics. By analysing

commonly recorded medical observations, the model

can predict health outcomes, incorporating causal

interactions among clinical data, patient information

and publicly available clinical data. Notably, this

approach is unprecedented in using large-scale

health and outcome statistics.

3.2 Bayesian Networks

BNs, also termed probabilistic graphical models,

offer a graphical framework for probabilistic

reasoning under uncertainty through a directed

acyclic graph (DAG) consisting of structure and

parameters. The structure includes nodes representing

variables and edges indicating causal relationships.

Parameters consist of conditional probability

functions for each node, representing its strength

given its parents. Bayesian probabilistic reasoning

involves updating prior beliefs (prior probability)

based on new evidence, resulting in posterior

Approach and Method for Bayesian Network Modelling: The Case for Pregnancy Outcomes in England and Wales

605

Figure 1: Types of reasoning.

Figure 2: BN Development Process Flow Diagram.

probability. In Figure 1, various scenarios illustrate

reasoning from evidence using a lung cancer model.

A node head in grey indicates observed evidence,

while black determines the question being reasoned

about. Forward reasoning - following the arc

direction, and backward reasoning - counter to the arc,

represent causal or predictive and diagnostic

reasoning, respectively. Combining forward,

intercausal and backward reasoning produces

intercausal and combined reasoning. The approach

used in this work ensures the model's capacity for all

four modes of reasoning.

3.3 Study Population

The model in this study used publicly available

privacy-preserving aggregate statistics from various

sources. The data covered 624,828 pregnancies in

England and Wales during 2021 encompassing live

births, stillbirths, and neonatal deaths. Additionally,

evidence for risk factors and causal relationships was

drawn from guidelines and academic studies

published between 2019 and 2022, focusing on UK

populations in 2021.

3.4 BN Development

Our main design objective was to create a model that

credibly encapsulates current clinical knowledge on

pivotal risk factors and interacting signs and

symptoms affecting pregnancy outcomes. This

objective is pursued through a six-phase development

process outlined in Figure 2 and detailed in the

subsequent section.

3.4.1 Expert Elicitation

The BN's structure and parameters can be derived

entirely from data with an extensive dataset. However,

BNs exhibit flexibility, capable of seamlessly

integrating less comprehensive datasets, multiple

expert’s knowledge, and diverse information sources

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Figure 3: Examples of dimensionality in NPTs.

(Christophersen et al, 2018). Expert input enriches

BN's design, ensuring up-to-date domain knowledge

(Sanford & Moosa, 2015) Expert elicitation yielded

caremaps; visualisations of disease progression,

diagnosis, treatment processes and potential patient

outcomes through flow diagrams or process maps.

The caremap development process, has been detailed

previously (McLachlan et al; 2020a).

3.4.2 Data Gathering

We sought national datasets that described the

incidence of pregnancy complications and outcomes

for an entire population. A key focus was publicly

available privacy-preserving datasets whose use

would not require, or violate, institutional ethics

policies. This limited us to secondary or aggregate

statistical sources such as those of national health

services, health departments or statistics agencies.

We collected datasets for the year 2021 as these were

the most recent complete and published statistical

datasets available for the UK.

3.4.3 Literature and Clinical Guideline

Review

We performed a search to locate literature, clinical

practice guidelines and protocols relevant to the

medical condition(s) being modelled. The literature

included was aligned to the data gathered in Phase

3.4.2. Priority was given to articles published during

the same time period that described incidence of the

medical condition(s) in like populations.

3.4.4 Model Development

The iterative model development process was: (1)

medical idioms identifying key structural fragments

were identified from the combination of caremap and

knowledge derived from the clinical experts; (2) data

was identified from statistical and literary sources to

populate node probability tables (NPTs), describing

incidence of the variable described by the node and

incidence of interaction across arcs between that node

and parent or child nodes; (3) structural fragments

were brought together to form a single contiguous

BN; and (4) the resulting model structure was

reviewed with clinical experts and where changes

were identified, the process returned to the first step.

The process for identifying medical idioms and using

these to support expert elicitation was previously

described in (Kyrimi et al, 2020).

3.4.5 Data Preparation

Each node within a BN has a NPT. Absolute parent

nodes (such as the pollution node in the example in

Figure 1) have a single dimensional NPT. Where a

node has a single parent (such as the dyspnoea node

in the example in Figure 1) it will have a two-

dimensional NPT. Where a node has two parents

(such as the cancer node in the example in Figure 1)

it will have a three-dimensional NPT etc. Nodes with

six parents or greater are generally avoided due to

complexity of elicitation and computation. Examples

of data dimensionality in NPT are provided in Figure

Approach and Method for Bayesian Network Modelling: The Case for Pregnancy Outcomes in England and Wales

607

Figure 4: BN model showing background priors.

The content of each column in an NPT should sum

to 1.0 (100%). Discretisation allows the modeller to

convert continuous variable factors like BMI and

capillary blood glucose (CBG) by assigning them

clinically relevant intervals, ordinal states or

categories (for example: low, medium, high). Some

variables such as BMI in the example shown in Figure

3 were discretised in this way. Tables using

population-level continuous variable data were

prepared in Microsoft Excel and converted on

ingestion by the Agenarisk BN modelling tool.

3.4.6 Model Validation

The validation process for our BN models followed a

multi-step methodology recommended by various

authors (Pitchforth & Mengersen, 2013). We initially

undertook face validity with clinical experts

(Pitchforth & Mengersen, 2013). However, we

recognised the potential weakness in situations

wherein experts involved in design are unlikely to

disagree with their own judgment as reflected in the

resulting model. To mitigate this we also used: (i)

content validity to assess the BN structure against

identified literature and clinical practice guidelines,

evaluating the relationships between crucial risk

factors and symptoms (Pitchforth & Mengersen,

2013); and (ii) concurrent validity to compare BN

predictions against published models using clinical

vignettes (Pitchforth & Mengersen, 2013). Due to the

extreme rarity of the primary model outcomes;

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“Stillbirth” as Birth Outcome and “Death”

as Maternal Outcome, classical validation tests for

model’s accuracy, discrimination and calibration

were not performed.

4 RESULTS

Figure 4 presents the Maternal Outcomes BN model,

comprising four fragments that are used to group

nodes relevant to: (1) maternal risk factors and

common health conditions that may affect the

pregnancy; (2) the immediate pregnancy outcome for

the neonate and (3) mother; and (4) survival of the

neonate.

The model structure allows the relevant impact of

observations on factors in the primary maternal zone

to carry over onto maternal and neonate outcomes.

Solid lines indicate direct relationships, while dashed

lines indicate the presence of hidden nodes used for

alternate discretisation of variables. Model priors are

also shown in Figure 4.

4.1 BN Validation

This section provides an overview of the processes

used to validate the maternal outcomes model.

4.1.1 Face Validity

Throughout development of our BN, a collaborative

effort with a small group of clinical experts ensured

validation through comparisons with literature and

clinical guidelines. Face validity ensures the model's

visual representation aligns with expectations. The

iterative development process incorporated clinical

insights and weighed variables and causal pathways

against evidence from clinical texts, medical journals,

and available data. For parameterisation, clinicians

played a crucial role in providing initial estimates for

BN parameters. We updated these in the final model

using national statistics for the entire England &

Wales population.

The model holistically addresses primary

pregnancy outcomes: (1) Birth Outcome: This

fragment encompasses live birth or stillbirth,

including considerations for late-term miscarriage

based on nuanced definitions (NHSInform, 2022); (2)

Maternal Outcome: Predicting maternal death

aligned to 2021 mortality statistics (ONS, 2023); (3)

Neonate Outcome: Predicting death in live-born

babies aligned to 2021 ONS and MBRRACE-UK

birth outcome statistics.

Figure 5: Maternal Age substructure showing hidden Age

Consolidator node.

Secondary outcomes linked to the baby are also

identified, including: (1) Small for Gestational Age

(SGA): Stratifying risk into three categories, the

model offers a nuanced perspective on this outcome,

grounded in a total incidence for 2021 derived from

substantial data (NMPA Project Team, 2021); (2)

Large for Gestational Age (LGA): Incorporating the

impact of gestational diabetes mellitus (GDM), the

model aligns with 2021 datasets, capturing the

nuanced nature of this outcome; (3) Congenital

Abnormality: Grounded in probability and informed

by UK national statistical data and research on

increasing prevalence rates due to inheritance, the

model projects a prior probability of 3.278% for this

outcomes.

The collaborative and iterative approach, coupled

with reliance on expert input and robust statistical

grounding, ensures a model's robustness and

relevance in reasoning complex outcomes.

4.1.2 Content Validity

The key demographic risk factors identified in

predictive models included: (1) Maternal Age (74%):

Models varied in representing maternal age,

reflecting it either as a continuous variable or

discretizing it into intervals. Our model employs five-

year increments that align with national maternity

statistics (ONS, 2023). To simplify situations where

a binary identifying advanced maternal age was

required, a hidden boundary age node was included

as shown in Figure 5; (2) BMI (59%): BMI statistics,

categorized into five groups, were derived from

Public Health England’s report (PHE, 2019). BMI is

strategically placed between ethnicity and child nodes

representing diabetes, hypertension, and pregnancy

outcomes; (3) Parity (42%): Nulliparity and grand

parity were categorized into five groups to aid

consideration of their impact on conditions and

outcomes. Maternal age is linked, especially in

Approach and Method for Bayesian Network Modelling: The Case for Pregnancy Outcomes in England and Wales

609

extreme cases, updating probabilities for nodes like

diabetes, hypertension, and birth outcomes (Ananth et

al, 1996); (4) Ethnicity (36%): Ethnicity's influence is

integrated across the model, impacting hypertension,

gestation and BMI, with connections to various

pregnancy outcomes; (5) Gestation (32%): Gestation

can be both an outcome and a risk factor, and affects

various pregnancy outcomes including prematurity

and post-term deliveries. The gestation node is

informed by the 2021 dataset (ONS, 2023) to ensure

accuracy in predicting maternal and neonate risks and

outcomes.

4.1.3 Concurrent Validity

We re-examined papers included in our screening

review (Dube et al, 2023) to locate any works that

included a vignette with prediction suitable for use in

concurrent validity testing, identifying only two.

North et al (2011) propose a model using statistical

methods to predict incidence of pre-eclampsia. Their

model is based on demographic and risk factors of the

first-time mother along with observable signs and

symptoms routinely collected by the midwife during

the initial (booking) patient appointment. They used

their model to compute the following vignette:

A 28 year old nulliparous woman whose birth

weight was 2400 g, with a mean arterial

pressure of 96 mmHg, BMI 30, a family

history of pre-eclampsia, and no protective

factors, her probability of pre-eclampsia is

39%.

Making the same observations (maternal age, BMI,

parity, family history of pre-eclampsia, and maternal

hypertension) our model indicates a 43% probability

for pre-eclampsia. The 4% difference can be

attributed to: (i) diverse country origins in their

dataset (England, Wales, Ireland, New Zealand, and

Australia) versus our England and Wales focus; (ii)

their 2004-2008 data versus our 2021 dataset; (iii)

their 4961 pregnancies versus our larger 624,828; and

(iv) reported increasing incidence of pregnancy-

related conditions globally between 2010-2020

(Cameron et al, 2022).

Mehta-Lee et al (2017) used statistical methods on

pregnancy data collected between 2004-2009 to

develop a nomogram for predicting preterm delivery.

They began with a larger number of potential factors,

but the resulting nomogram includes only the nine

factors they identified as most predictive from a

cohort of 192,208 pregnancies. Their vignette

describes:

A 35 year old (13 points) African American

(41 points) woman planning to get pregnant

for the first time (46 points) who has no history

of diabetes (0 points) but who smokes (12

points) would have a total of 112 points. This

approximates to a baseline probability of

preterm birth of 12-13% prior to conception.

Using the same observations, our model predicted an

8.7% preterm birth rate - which is the sum of

predictions for all gestations prior to 37 weeks with

the exclusion of smoking as a factor (Smith et al,

2023). Discrepancies observed with how other

models incorporated smoking may have arisen due to

underreported smoking rates influenced by social

stigma (Smith et al, 2023). Global variations in

reporting, and confounded outcomes in UK studies,

only contribute to the confusion (Smith et al, 2023).

UK studies generally report lower smoking rates

compared to the USA, with some incredibly reporting

no smoking at all (Stott et al, 2016). Vaping, a

smoking alternative, poses uncertainties in long-term

pregnancy outcomes. Omitting smoking from our

model considers these issues and ensures robust

predictions unaffected by potential smoking-related

biases (Smith et al, 2023).

Finally, Du & Li (2021) developed a nomogram

for prediction of the baby’s survivability in

pregnancies complicated by GDM using data

collected from 626 Chinese mothers receiving

outpatient antenatal care between 2016 and 2019. We

used their nomogram to evaluate the following

scenario:

A 35 year old (22 points) Asian woman at 31

weeks or 217 days gestation (10 points) with a

BMI of 35 (25 points), first degree family

history of T2DM (10 points), history of GDM

in a previous pregnancy (4 points) and a

mildly high fasting plasma glucose (FPG) of

6.0 mmol (47.5 points). This gave a total of

118.5 points which their nomogram

approximated to 82-83% survivability for the

baby.

Our BN model with these observations predicted a

live birth, birth outcome of 84.7%. The dataset of

pregnancies used in Du & Li (2021) were temporally

the closest to those used to develop our model, and

the resulting predictions are not significantly different.

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5 DISCUSSION

During our model validation, two unaddressed issues

in reviewed models emerged. First, some works

included potentially unquantifiable elements: self-

assessed, unmeasurable, or flexible factors (Mehta-

Lee et al, 2017). Second, some models included

potentially unknowable elements: data challenging to

reliably procure (North et al, 2011).

While resource-intensive, our model's design

proves efficient. It eliminates redundant data entry

across different predictive models, streamlining the

process for clinicians. Rather than inputting the same

variables multiple times for various conditions, our

model allows one-time entry, computing probabilities

for both primary and subsequent conditions along the

disease pathway (Angeli et al, 2011). Traditional

models often focus on prediction of a singular health

condition, neglecting a holistic view of health. Our

model considers the patient comprehensively,

capturing interactions between risk factors,

symptoms, and various health issues. Unlike

condition-limited models, our approach models the

patient as an entire organism, preserving information

about the overall impact of common symptoms or

concomitant diseases on health outcomes.

While adapting the model for New Zealand, future

work includes exploring treatment selection and

outcome counterfactuals. This involves testing

alternate hypotheses, such as the potential outcomes

with or without specific interventions. Limitations

include the need for granular national health statistics

and access to expert support for model development

and face validity assessment. Resources and time are

substantial in constructing complex models like ours,

contrasting with the preference for simpler, single-

condition statistical models.

6 CONCLUSIONS

This work has introduced a novel pregnancy risk

prediction model addressing limitations in existing

approaches. Our holistic model considers not only the

condition of interest but also related conditions and

outcomes. Unlike models relying on limited local

data, we utilise publicly available national health

statistics, allowing versatile model development.

Employing a causal Bayesian probabilistic approach,

we navigate uncertain or missing data. Validation

involves ongoing face, content, and concurrent

methods, revealing an accurate description of

pregnancies nationally and individually. Three case

vignettes provide exemplar predictions for future

model comparisons. The model's reliability and

clinical holism, achieved at low cost, can instil

confidence in both clinicians and patients.

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