Pools versus Queues: The Variable Dynamics of Stochastic "Steady States"

Healthcare Worker Staffing Ratios Affect Methicillin-Resistant Staphylococcus aureus Acquisition

Importance

This study addresses the pressing clinical question of how variations in physician and nursing staffing levels influence methicillin-resistant Staphylococcus aureus (MRSA) rates, providing essential insights for optimizing staff allocation and improving patient outcomes in critical care settings.

Objective

The main objective is to assess whether variations in staffing ratios and workload conceptualization significantly alter the rates of MRSA acquisitions in the ICU setting.

Design

This simulation-based study utilizes stochastic compartmental mathematical modeling to explore the impact of staffing ratios and workload conceptualization on MRSA acquisitions in ICUs. Derived from a previously published model, the analysis involves running year-long stochastic simulations for each scenario 1000 times, varying nurse-to-patient ratios and intensivist staffing levels under infinite and finite workload conceptualizations. Our baseline model was a 3:1 nurse ratio with one intensivist.

Main Outcome

MRSA acquisitions in ICUs, measured as median acquisitions per 1000 person-years.

Results

Under baseline conditions, our model had a median of 8.2 MRSA acquisitions per 1000 person-years. Varying patient-to-nurse ratios and intensivist numbers showed substantial impacts. For infinite models, a 2:1 nurse ratio resulted in a 21% decrease, while a 1:1 nurse ratio led to a 65% reduction. Finite models demonstrated even larger effects, with a 48% decrease when having a 2:1 ratio, and an 83% reduction with a 1:1 nurse ratio. Reducing patient-to-nurse ratios in finite models increased acquisitions exponentially with a 348% increase for a 6:1 ratio. Intensivist variations had modest impacts.

Conclusions and Relevance

Our study highlights the crucial role of optimizing staffing levels in ICUs for effective MRSA infection control. While intensivist variations have modest effects, bolstering nursing ratios significantly reduces MRSA acquisitions, underscoring the need for tailored staffing strategies, and recognizing the nuanced impact of workload conceptualization. Our findings offer practical insights for refining staffing protocols, emphasizing the dynamic nature of healthcare-associated infection outcomes.

Examining the impact of ICU population interaction structure on modeled colonization dynamics of Staphylococcus aureus

Background

Complex transmission models of healthcare-associated infections provide insight for hospital epidemiology and infection control efforts, but they are difficult to implement and come at high computational costs. Structuring more simplified models to incorporate the heterogeneity of the intensive care unit (ICU) patient-provider interactions, we explore how methicillin-resistant Staphylococcus aureus (MRSA) dynamics and acquisitions may be better represented and approximated.

Methods

Using a stochastic compartmental model of an 18-bed ICU, we compared the rates of MRSA acquisition across three ICU population interaction structures: a model with nurses and physicians as a single staff type (SST), a model with separate staff types for nurses and physicians (Nurse-MD model), and a Metapopulation model where each nurse was assigned a group of patients. The proportion of time spent with the assigned patient group (γ) within the Metapopulation model was also varied.

Results

The SST, Nurse-MD, and Metapopulation models had a mean of 40.6, 32.2 and 19.6 annual MRSA acquisitions respectively. All models were sensitive to the same parameters in the same direction, although the Metapopulation model was less sensitive. The number of acquisitions varied non-linearly by values of γ, with values below 0.40 resembling the Nurse-MD model, while values above that converged toward the Metapopulation structure.

Discussion

Inclusion of complex population interactions within a modeled hospital ICU has considerable impact on model results, with the SST model having more than double the acquisition rate of the more structured metapopulation model. While the direction of parameter sensitivity remained the same, the magnitude of these differences varied, producing different colonization rates across relatively similar populations. The non-linearity of the model’s response to differing values of a parameter gamma (γ) suggests simple model approximations are appropriate in only a narrow space of relatively dispersed nursing assignments.

Conclusion

Simplifying assumptions around how a hospital population is modeled, especially assuming random mixing, may overestimate infection rates and the impact of interventions. In many, if not most, cases more complex models that represent population mixing with higher granularity are justified.

Estimating the impact post randomization changes in staff behavior in infection prevention trials: a mathematical modeling approach

BACKGROUND

Randomized controlled trials (RCTs) of behavior-based interventions are particularly vulnerable to post-randomization changes between study arms. We assess the impact of such a change in a large, multicenter study of universal contact precautions to prevent infection transmission in intensive care units.

METHODS

We construct a stochastic mathematical model of methicillin-resistant Staphylococcus aureus (MRSA) acquisition in a simulated 18-bed intensive care unit (ICU). Using parameters from a recent study of contact precautions that reported a post-randomization change in contact rates, with fewer visits observed in the treatment arm, we explore the impact of several possible interpretations of this change on MRSA acquisition rates.

RESULTS

Scenarios where contact precautions resulted in less patient visitation resulted in a mean decrease in MRSA acquisition rate of 37%, accounting for much of the effect reported in the trial.

CONCLUSIONS

Behavior changes that impact the contact rate have the potential to drastically alter the results of RCTs in infection control settings. Careful monitoring for these changes, and an assessment of which changes will likely have the greatest impact on the study before the study begins are both recommended.