Using telephone call rates and nurse-to-patient ratios as measures of resilient performance under high patient flow conditions

Abstract

Patient admissions, discharges, and transfers are high work demand activities that have been associated with 30-day readmissions and increased patient mortality. Most mitigation strategies target peak demand, but variable demand may be more significant. Self-organizing holarchic open systems (SOHOs) and resilience engineering frameworks may explain system behavior, but a few quantitative studies of resilient organizational performance have been published. We used three measures to explore SOHO and resilience engineering constructs. We collected hourly data over 2 years, from five inter-related units in a cardiovascular disease division of a metropolitan teaching hospital. Our results show that information flows (inbound, outbound, answered, and unanswered telephone calls) representing anticipatory management are related to patient flows (patient admissions discharges and transfers) and nurse-staffing levels (nurse-to-patient ratios). We also found overall system stability despite high patient flow effects in lower level units. Unexpectedly, the time to recovery from high patient flow events lasted up to 7 days. We conclude that constructs proposed by resilience engineering can be quantified using simple measures collated within routine operations. The application of nonlinear statistical analyses can uncover important insights about resilient performance that may assist managers in better preparing for managing and recovering from unexpected variation in patient flow.

Appendices

Appendix 1: Glossary of abbreviations

ADT::

Admissions, discharges, and transfers

CVICU::

Cardiovascular intensive care unit

GDP::

Gross domestic product

LoS::

Length of stay

NPR::

Nurse-to-patient ratio

SD::

Standard deviation

SOHO::

Self-organizing holarchic open system

VHVI::

Vanderbilt Heart and Vascular Institute

Appendix 2: Elastic net modeling

We apply optimization techniques to observe the interdependent relations between variables. The variables included in the model are NPR, ADTs, to inbound, outbound, answered, and unanswered calls for each unit, adding up to a total of 36 variables.

We defined a vector with the 30 variables denoted as y and let y_t denote the vector values at time t (so y_t e.g., 34-by-1). We then solved for the coefficient matrix A (34-by-34) in the following optimization problem:

$${\text{Minimize}}_{A,b} \|y\_t-A\times{\text{ }}y\_{(t-1)}-b{\text{ }}\|^2,$$

where b is a 30-by-1 constant vector, and e_t is a time-invariant 30-by-1 vector of error terms with mean zero and a positive semi-definite contemporaneous covariance matrix. With this error term, we expect A to have many nonzero elements. This can make it hard to interpret. Therefore, instead of solving this naïve formulation, we improved the objective function, so that the solution for A has a limited number of nonzero elements. A penalty term is thus added to the naïve formulation to provide the following elastic net formulation:

$$\begin{aligned}&{\text{Minimize }}_{A,b}\|y\_t{\text{ }}-{\text{ }}A\times y\_(t - 1)-{\text{ }}b{\text{ }}\|^2+{\text{ }}alpha{\text{ }} \times {\text{ }}lambda{\text{ }} \\&\quad\times {\text{ }}\|\text{vec}(A)\|_1{\text{ }}+{\text{ }}\left( {1 - alpha} \right){\text{ }} \times {\text{ }}gamma{\text{ }} \times {\text{ }}\|\text{vec}(A)\|^2,\end{aligned}$$

where the parameter alpha adjusts for the trade-off between penalties on the L-1 loss and the L-2 loss. Lambda and gamma are the two parameters that control the penalties of the two losses, respectively.