A Network Theoretical Analysis of Admission, Discharge, and Transfer Data Clinical Data Mining and Machine Learning (Part 2) S46

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1 A Network Theoretical Analysis of Admission, Discharge, and Transfer Data Clinical Data Mining and Machine Learning (Part 2) S46 Joe Klobusicky Rensselaer Polytechnic Institute

2 Disclosure All authors of this presentation have no relevant relationships with commercial interests to disclose. 2

3 Learning Objectives After attending this conference the learner should be better able to understand similarities and differences between various network metrics used for importance ranking of hospital rooms and departments. 3

4 Geisinger Medical Center and Bucknell University From 2014 to 2016, I worked as a data scientist at Geisinger Medical Center, a hospital in central Pennsylvania. Geisinger is one of the pioneers in electronic data collection, going back to the mid 90 s. In 2015/2016, I was also an adjunct at Bucknell University, located about 20 miles from Geisinger. Currently, I m a postdoc at Rensselaer Polytechnic Institute. 4

5 Collaborators and the BGRI grant With Nathan Ryan (Bucknell Mathematics Department), we obtained funding from the BGRI grant (Bucknell Geisinger Research Initiative) to conduct research on the development of sepsis with two undergraduates. Nathan Ryan Maria Cioffi Naba Mukhtar (not shown) 5

6 A Warm Up Question While the main motivation for the grant was sepsis, a first question was to understand the transfer of patients from one event to another. We wanted a warm up dataset where the events were Discrete in space. Continuous in time. Relatively free of errors The main motivation was to track all events associated with patients who identified sepsis as a sequence of events, and assign importance of certain events (or collections of events)- possibly for building a predictive algorithm. 6

7 The ADT dataset The ADT dataset is a good candidate dataset. It consists of patient admission and discharge time from various rooms at GMC. We re keeping things simple here: no diagnoses, no vital signs- this dataset only keeps track of population flow. Patient Room Admission Time Description (not part of original dataset) :51 03/03/07 Patient A enters OR prep :48 03/03/07 Patient A enters operating room :11 03/03/07 Patient A in bed :24 03/05/07 Patient A discharged :21 02/28/07 Patient B in Emergency Medicine :33 02/28/07 Patient B in maternity ward

8 Networks: motivation Network models appear in all major fields of science. Nodes include possible states, and edges represent transitions between states. On the right is an example of pathways of selffolding polyhedra. Here, very small flattened nets are heated, and curl up into different shapes. What do the intermediate stages look like, and which are most prevalent? 8

9 Some basic questions about traffic Some basic questions involving population dynamics are 1. What are the most populated rooms? 2. Which rooms are most visited? Note: This is not this same question as 1! 3. Which rooms are the hubs of the hospital? In other words, which nodes are common to patients, regardless of the type of care needed? To answer these types of questions, we will represent rooms as a network. 9

10 The Hospital Graph We represent rooms by a hospital graph G =(V,E) Here, V is the set of rooms in the hospital, and E is the set of possible transfers between two rooms in the hospital. In some instances, edges on a graph can be weighted. For our purposes, weights will be the average rate of transfer. 10

11 Continuous Time Markov Chains To answer questions about population, we can use continuous time Markov chains. For an initial distribution of rooms p(0) = (p 1 (0),...,p N (0)), and a state transition matrix A given by state transitions, rooms may grow or shrink in population with the following set of birth-death equations dp i dt = X X a ki p k a ik p i k k!i k i!k All patients are eventually discharged, so we need to include a cemetery state S. Also, we can include patient influx c(t). The equations take a compact form dp dt = Ãp + c(t) 11

12 Exact solution to birth-death equations From Duhamel s formula, a solution formula for inhomogeneous differential equations, we can find the distribution at time t>0 as p(t) =eãt p(0) + Z t 0 eã(t s) c(s)ds, t > 0, p(0) = p 0 The initial condition can be adjusted for multiple different scenarios, including simulating a crisis scenario (large proportion at the emergency room). For our purposes, we consider 0 initial conditions, and see how the hospital populates over time. 12

13 Results For Markov models, population densities tend to stabilize. Popular departments: 1. Neonatal ICU 2. Nursery 3. Geriatric Psychology The last two reflect items reflect that departments may with large populations may not have high transmission rates. 13

14 Network metrics: closeness centrality The simplest graph metric is closeness centrality, which measures which nodes have the greatest 1 step cost CC(n) = 1 P n6=m2e c(m, n) Here, cost is defined as the inverse of the number of patients who travel from m to n. Thus, rooms with the smallest closeness centrality are those with the most patients entering the room. The top performers for closeness centrality. 1. Emergency rooms 2. Pre-operating holding areas Note that these results are for departments, and may depend on number of rooms. Thus one pre operating holding area may be used for several operating rooms, and may thus have a higher ranking. 14

15 Network metrics: betweenness centrality For a, b 2 V, let (a, b) denote the number of shortest paths from a to b, with (a, b n) be the number of shortest paths that pass through n. Then BC(n) = X a,b2n (a, b n) (a, b) is a measure for how many shortest paths cross through n. Betweenness centrality measures hubs in a network. The top performers for betweenness centrality. Pre-operating holding areas Telemetry beds (critical care) (?!) How could the shortest path include patients in critical condition? One interpretation: to get from one unrelated area to another, it might take a critical event to occur in between. 15

16 Network metrics: eigenvalue centrality Eigenvalue centrality is the hardest to explain, but arguably the most profitable (PageRank). The main idea: rank each room as important if it is connected with many other important rooms. This can be shown to satisfy an eigenvalue problem Ax = where A is the adjacency matrix, x is a vector of rankings for rooms, and is some eigenvalue. Some theory is needed to show that the largest possible corresponds to the correction weighting of x. x The top performers for eigenvalue centrality. Pre-operation Intra-operation Post-operation This makes sense: we d expect these departments to be individually important, and certainly related to each other. 16

17 Conclusion: what we have done We have analyzed a dataset (admissions, discharges, and transfers) that is amenable to a network theoretic analysis. Specifically, We analyzed the network according to a continuous time Markov chain. This gives an idea of the most populated departments. We also studied what happens when looking at network metrics that are commonly applied to social media algorithms. These metrics produced different rankings of importance, suggesting that certain departments may be central in some ways, but not others. This analysis could be done either by looking at individual rooms, or by coarsening the graph to include departments as individual nodes. 17

18 What we have not done (and should eventually do) Metrics are a good way of laying groundwork for helpful datatypes. However, the ultimate goal is improved efficiency of a hospital, and health of patients. Some helpful suggestions from the editors: Use domain knowledge: which departments are most dependent on these types of metrics and why? (e.g. ER for total population, hospital beds for rate of transmission of infections like C. Diff.) Recall the original goal of the grant: sepsis detection. How can we apply these metrics to get better sense of categorical patient histories? This might require linking to more traditional time series analyses. 18

19 Thank you! me at: [optional]