Modelling patient movements for hospital outbreaks

Hospital outbreaks

In 2018, a multi-institutional outbreak of CPE highlighted the interlinked nature of healthcare in Victoria.

Since then, CPE is now notifiable, but there is not a centralised surveillance or outbreak response system.

Carbanememase-producing Enterobacterales

• Acquired primarily in hospital
• Resistant to last-line antibiotics
• Mortality, given clinical symptoms, in the order of 30%
• Carriage for >= 12 months

• Testing via rectal swab
• Can carry with no symptoms
• Unknown if asymptomatic people can transmit

Carbanememase-producing Enterobacterales incidence

Notification system

Notifications are required to be sent to the Department of Health within 24 hours of a positive result.

The current surveillance system

Surveillance and outbreak control

End goal is to model outbreak spread, and then surveillance/control methods.

Data

We have line-listed hospital admissions data for all hospitals in Victoria, Australia, from 2016-2021.

The dataset is linked, allowing us to follow individuals through time. Each observation has:

• Admission time,
• Discharge (separation time),
• Hospital of admission,
• Diagnosis codes,
• Handful of demographics

Current state of the field

We need to convert this sort of data into a structure appropriate for modelling.

Different ways to collapse the data

Some notation:

• u, v are locations
• s, t are times, t \geq s
• Hazard for patients returning home, never readmitted: \zeta_u(t)
• w_{uv}(s,t) patients discharged from u at s, then readmitted to v at t

Different ways to collapse the data

Different ways to collapse the data

Then, we have the following set of governing equations:

• Hospital to home: \lambda(u(s) \to \emptyset) = \zeta_u(s)
• Direct transfers: \lambda(u(s) \to v(t)) = d_{uv}(s, t)
• Indirect transfers:
  • Hospital to home: \lambda(u(s) \to z_{uv}(t)) = \eta_{uv}(s, t)
  • Home to hospital: \lambda(z_{uv}(t) \to v(t)) = \rho_{uv}(s, t)

Model 1: Naive Static Method

d_{uv}(s,t) = \frac{\sum_{s,t} w_{uv}(s,t)}{T_\Sigma N_u}

Model 1: Naive Static Method

Transfer patterns change over time

Model 2: Static Method

Choose a threshold value, \omega, to separate direct and indirect transfers

d_{uv}(s,t) = d_{uv} = \frac{\sum_{s,t: (t-s) < \omega} w_{uv}(s,t)}{T_\Sigma N_u} \eta_{uv}(s,t) = \eta_{uv} = \frac{\sum_{s,t: (t-s) \geq \omega} w_{uv}(s,t)}{T_\Sigma N_u} \rho_{uv}(s,t) = \rho_{uv} = \left[ \frac{\sum_{s,t: (t-s) \geq \omega} (t-s) w_{uv}(s,t)}{\sum_{s,t: (t-s) \geq \omega} w_{uv}(s,t)} \right]^{-1}

Model 3: Snapshot Model

Choose a snapshot duration \omega. This defines the threshold duration of an indirect transfer.

\begin{aligned} \lambda(u(s) \to {z'}_{uv}(t)) &= \eta_{uv}(s, t)\\ \lambda({z'}_{uv}(t) \to z_{uv}(t)) &= \delta(t \; \mathrm{ mod } \; \omega)\\ \end{aligned}

Model 4: Temporal Model

Effecitvely, choose a very small snapshot window, \omega. Individuals are not re-admitted to z', instead they are re-admitted to v uniformly between t and t+\omega. This gives,

d_{uv}(s, t) = \frac{\sum_{t: (t-s) < \omega} w_{uv}(s, t)}{\omega N_u} \eta_{uv}(s, t) = \frac{\sum_{t: (t-s) \geq \omega} w_{uv}(s, t)}{\omega N_u} \rho_{uv}(s,t) = \frac{1}{\lceil t \rceil_\omega - t}

Too much maths for 12 minutes!

Too much maths for 12 minutes!

Current state-of-the-art: Patients move instantly, no concept of home, using average return rates over the entire data period

What difference does it make?

What difference does it make?

Takeaway

• Still need to consider surveillance algorithms on these weighted, directed, temporal networks
• Patients going home slows down infection spread
• Most hospital transfer patterns aren’t stationary
• Using the wrong collapsing process means you will probably miss infections
• May declare a hospital “disease-free” when it truly hasn’t arrived yet