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

Hospital outbreaks

The immediate question:

When an outbreak is detected, what other hospitals could be affected?

Natural to consider patients in a hospital as a network, that has the nodes as the hospitals and edges between them related to the probability of transfer.

Current methods can grossly over-estimate the rate of spread of disease between hospitals

Current state of the field

Most methods are based on line-listed admissions data:

patient_id admission_date separation_date location diagnosis_codes
1 2020-01-01 2020-01-02 H1 A B C
2 2020-01-01 2020-01-02 H2 A B C
1 2020-01-03 2020-01-04 H2 A B C

This is interpreted as one transfer from H1 to H2, with a one-day gap.

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

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)

Different ways to collapse the data

Model 1: Naive Static Method

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

Tip

All movements are instanteous, and the rate of movement is the mean over the entire observation period.

Model 2: Improved 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}

z' contains the individuals that would enter z within the duration of a given snapshot [t, t+\omega], so that they do not immediately readmit to their next hospital.

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!

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

Our models: from least to most ‘accurate’

  1. State-of-the-art
  2. State-of-the-art + patients return home
  3. Return rates change over time, patients held at home in “blocks”
  4. Return rates change over time, patients held at home for actual time

What difference does it make?

What difference does it make?

Takeaway

Time is critical when considering an outbreak

  • 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

Hospital outbreaks

The immediate question:

When an outbreak is detected, what other hospitals could be affected?

Changes over time, but it’s not as fast as you think it is