Utilizing Bayesian Networks to forecast ancillary service quantity in hospitals | by Gabe Verzino | Aug, 2023

A Python instance utilizing diagnostic enter variables

Photograph from Unsplash, by EJ Strat

Since I’ve been working with healthcare knowledge (nearly 10 years now), forecasting future affected person quantity has been a troublesome nut to crack. There are such a lot of dependencies to contemplate — affected person requests and severity, administrative wants, examination room constraints, a supplier simply known as out sick, a nasty snow storm. Plus, unanticipated eventualities can have cascading impacts on scheduling and useful resource allocation that contradict even one of the best Excel projections.

These sorts of issues are actually attention-grabbing to try to remedy from a knowledge perspective, one as a result of they’re powerful and you may chew on it for awhile, but in addition as a result of even slight enhancements can result in main wins (e.g., enhance affected person throughput, decrease wait instances, happier suppliers, decrease prices).

How you can remedy it then? Properly, Epic gives us with a number of knowledge, together with precise information of when sufferers arrived for his or her appointments. With historic outputs identified, we’re primarily within the area of supervised studying, and Bayesian Networks (BNs) are good probabilistic graphical fashions.

Whereas most choices will be made on a single enter (e.g., “ought to I deliver a raincoat?”, if the enter is “it’s raining”, then the choice is “sure”), BNs can simply deal with extra advanced decision-making — ones involving a number of inputs, of various chance and dependencies. On this article, I’m going to “scratch pad” in python an excellent easy BN that may output a chance rating for a affected person arriving in 2 months primarily based on identified possibilities for 3 components: signs, most cancers stage, and therapy purpose.

Understanding Bayesian Networks:

At its core, a Bayesian Community is a graphical illustration of a joint chance distribution utilizing a directed acyclic graph (DAG). Nodes within the DAG symbolize random variables, and directed edges denote causal relationships or conditional dependencies between these variables. As is true for all knowledge science initiatives, spending a number of time with the stakeholder to start with to correctly map the workflows (e.g., variables) concerned in decision-making is important for high-quality predictions.

So, I’ll invent a state of affairs that we meet our Breast oncology companions they usually clarify that three variables are important for figuring out whether or not a affected person will want an appointment in 2 months: their signs, most cancers stage, and therapy purpose. I’m making this up as I kind, however let’s go along with it.

(In actuality there will probably be dozens of things that affect future affected person volumes, a few of singular or a number of dependencies, others fully impartial however nonetheless influencing).

I’ll say the workflow appears to be like just like the above: Stage is dependent upon their symptom, however therapy kind is impartial of these and likewise influences the appointment occurring in 2 months.

Based mostly on this, we might the fetch knowledge for these variables from our knowledge supply (for us, Epic), which once more, would include identified values for our rating node (Appointment_2months), labeled “sure” or “no”.

# set up the packages
import pandas as pd # for knowledge manipulation
import networkx as nx # for drawing graphs
import matplotlib.pyplot as plt # for drawing graphs

!pip set up pybbn
# for creating Bayesian Perception Networks (BBN)
from pybbn.graph.dag import Bbn
from pybbn.graph.edge import Edge, EdgeType
from pybbn.graph.jointree import EvidenceBuilder
from pybbn.graph.node import BbnNode
from pybbn.graph.variable import Variable
from pybbn.pptc.inferencecontroller import InferenceController

# Create nodes by manually typing in possibilities
Symptom = BbnNode(Variable(0, 'Symptom', ['Non-Malignant', 'Malignant']), [0.30658, 0.69342])
Stage = BbnNode(Variable(1, 'Stage', ['Stage_III_IV', 'Stage_I_II']), [0.92827, 0.07173,
0.55760, 0.44240])
TreatmentTypeCat = BbnNode(Variable(2, 'TreatmentTypeCat', ['Adjuvant/Neoadjuvant', 'Treatment', 'Therapy']), [0.58660, 0.24040, 0.17300])
Appointment_2weeks = BbnNode(Variable(3, 'Appointment_2weeks', ['No', 'Yes']), [0.92314, 0.07686,
0.89072, 0.10928,
0.76008, 0.23992,
0.64250, 0.35750,
0.49168, 0.50832,
0.32182, 0.67818])

Above, let’s manually enter some chance scores for ranges in every variable (node). In observe, you’d use a crosstab to realize this.

For instance, for the symptom variable, I’ll get frequencies of their 2-levels, about 31% are non-malignant and 69% are malignant.

Photograph by creator

Then, we contemplate the following variable, Stage, and crosstab that with Symptom to get these freqeuncies.

Photograph by creator

And, so on and so forth, till all crosstabs between parent-child pairs are outlined.

Now, most BNs embody many parent-child relationships, so calculating possibilities can get tedious (and majorly error inclined), so the perform beneath can calculate the chance matrix for any youngster node corresponding with 0, 1 or 2 mother and father.

# This perform helps to calculate chance distribution, which fits into BBN (word, can deal with as much as 2 mother and father)
def probs(knowledge, youngster, parent1=None, parent2=None):
if parent1==None:
# Calculate possibilities
prob=pd.crosstab(knowledge[child], 'Empty', margins=False, normalize='columns').sort_index().to_numpy().reshape(-1).tolist()
elif parent1!=None:
# Test if youngster node has 1 mum or dad or 2 mother and father
if parent2==None:
# Caclucate possibilities
prob=pd.crosstab(knowledge[parent1],knowledge[child], margins=False, normalize='index').sort_index().to_numpy().reshape(-1).tolist()
# Caclucate possibilities
prob=pd.crosstab([data[parent1],knowledge[parent2]],knowledge[child], margins=False, normalize='index').sort_index().to_numpy().reshape(-1).tolist()
else: print("Error in Chance Frequency Calculations")
return prob

Then we create the precise BN nodes and the community itself:

# Create nodes by utilizing our earlier perform to mechanically calculate possibilities
Symptom = BbnNode(Variable(0, 'Symptom', ['Non-Malignant', 'Malignant']), probs(df, youngster='SymptomCat'))
Stage = BbnNode(Variable(1, 'Stage', ['Stage_I_II', 'Stage_III_IV']), probs(df, youngster='StagingCat', parent1='SymptomCat'))
TreatmentTypeCat = BbnNode(Variable(2, 'TreatmentTypeCat', ['Adjuvant/Neoadjuvant', 'Treatment', 'Therapy']), probs(df, youngster='TreatmentTypeCat'))
Appointment_2months = BbnNode(Variable(3, 'Appointment_2months', ['No', 'Yes']), probs(df, youngster='Appointment_2months', parent1='StagingCat', parent2='TreatmentTypeCat'))

# Create Community
bbn = Bbn()
.add_edge(Edge(Symptom, Stage, EdgeType.DIRECTED))
.add_edge(Edge(Stage, Appointment_2months, EdgeType.DIRECTED))
.add_edge(Edge(TreatmentTypeCat, Appointment_2months, EdgeType.DIRECTED))

# Convert the BBN to a be part of tree
join_tree = InferenceController.apply(bbn)

And we’re all set. Now let’s run some hypotheticals via our BN and consider the outputs.

Evaluating the BN outputs

First, let’s check out the chance of every node because it stands, with out particularly declaring any situations.

# Outline a perform for printing marginal possibilities
# Possibilities for every node
def print_probs():
for node in join_tree.get_bbn_nodes():
potential = join_tree.get_bbn_potential(node)
print("Node:", node)

# Use the above perform to print marginal possibilities

Node: 1|Stage|Stage_I_II,Stage_III_IV
Node: 0|Symptom|Non-Malignant,Malignant
Node: 2|TreatmentTypeCat|Adjuvant/Neoadjuvant,Therapy,Remedy
Node: 3|Appointment_2weeks|No,Sure

That means, all of the sufferers on this dataset have a 67% chance of being Stage_I_II, a 69% chance of being Non-Malignant, a 58% chance of requiring Adjuvant/Neoadjuvant therapy, and solely 22% of them required an appointment 2 months from now.

We might simply get that from easy frequency tables with out a BN.

However now, let’s ask a extra conditional query: What’s the chance a affected person would require care in 2 months provided that they’ve Stage = Stage_I_II and have a TreatmentTypeCat = Remedy. Additionally, contemplate the truth that the supplier is aware of nothing about their signs but (possibly they haven’t seen the affected person but).

We’ll run what we all know to be true within the nodes:

# So as to add proof of occasions that occurred so chance distribution will be recalculated
def proof(ev, nod, cat, val):
ev = EvidenceBuilder()
.with_evidence(cat, val)

# Add extra proof
proof('ev1', 'Stage', 'Stage_I_II', 1.0)
proof('ev2', 'TreatmentTypeCat', 'Remedy', 1.0)
# Print marginal possibilities

Which returns:

Node: 1|Stage|Stage_I_II,Stage_III_IV
Node: 0|Symptom|Non-Malignant,Malignant
Node: 2|TreatmentTypeCat|Adjuvant/Neoadjuvant,Therapy,Remedy
Node: 3|Appointment_2months|No,Sure

That affected person solely has an 11% likelihood of arriving in 2 months.

A word in regards to the significance of high quality enter variables:

The success of a BN in offering a dependable future go to estimate relies upon closely on an correct mapping of workflows for affected person care. Sufferers presenting equally, in related situations, will sometimes require related providers. The permutation of these inputs, whose traits can span from the medical to administrative, finally correspond to a considerably deterministic path for service wants. However the extra difficult or farther out the time projection, the upper the necessity for extra particular, intricate BNs with high-quality inputs.

Right here’s why:

  1. Correct Illustration: The construction of the Bayesian Community should replicate the precise relationships between variables. Poorly chosen variables or misunderstood dependencies can result in inaccurate predictions and insights.
  2. Efficient Inference: High quality enter variables improve the mannequin’s capacity to carry out probabilistic inference. When variables are precisely related primarily based on their conditional dependence, the community can present extra dependable insights.
  3. Lowered Complexity: Together with irrelevant or redundant variables can unnecessarily complicate the mannequin and enhance computational necessities. High quality inputs streamline the community, making it extra environment friendly.

Thanks for studying. Completely satisfied to attach with anybody on LinkedIn! In case you are within the intersection of information science and healthcare or when you have attention-grabbing challenges to share, please depart a remark or DM.

Try a few of my different articles:

Why Balancing Classes is Over-Hyped

Feature Engineering CPT Codes

7 Steps to Design a Basic Neural Network

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