Patient-to-nurse ratios: Balancing quality, nurse turnover, and cost

Abstract

We consider the problem of setting appropriate patient-to-nurse ratios in a hospital, an issue that is both complex and widely debated. There has been only limited effort to take advantage of the extensive empirical results from the medical literature to help construct analytical decision models for developing upper limits on patient-to-nurse ratios that are more patient- and nurse-oriented. For example, empirical studies have shown that each additional patient assigned per nurse in a hospital is associated with increases in mortality rates, length-of-stay, and nurse burnout. Failure to consider these effects leads to disregarded potential cost savings resulting from providing higher quality of care and fewer nurse turnovers. Thus, we present a nurse staffing model that incorporates patient length-of-stay, nurse turnover, and costs related to patient-to-nurse ratios. We present results based on data collected from three participating hospitals, the American Hospital Association (AHA), and the California Office of Statewide Health Planning and Development (OSHPD). By incorporating patient and nurse outcomes, we show that lower patient-to-nurse ratios can potentially provide hospitals with financial benefits in addition to improving the quality of care. Furthermore, our results show that higher policy patient-to-nurse ratio upper limits may not be as harmful in smaller hospitals, but lower policy patient-to-nurse ratios may be necessary for larger hospitals. These results suggest that a “one ratio fits all” patient-to-nurse ratio is not optimal. A preferable policy would be to allow the ratio to be hospital-dependent.

Appendices

Appendix A

1.1 Three case study hospitals

We collected nursing data from three hospitals in the United States. One is located in California and two are located in Indiana. They range in size from 350 to 550 beds. We obtained information on nurse wages, shift types, staff size and mix, shift preferences and availability, patient-to-nurse ratios, and limited bed demand data. Note that detailed and extensive historical patient flow and demand data were not available. Due to the limited bed demand data, we also use data from the American Hospital Association and California Office of Statewide Health Planning and Development to estimate inpatient demand and create hospital size categories, as described in the next subsection. The three hospitals differ in size and nurse wages. Table 5 summarizes the data.

Table 5 Summary of hospital data

1.2 American hospital association (AHA) data

In addition to the three case study hospitals, we acquired 2015 AHA Annual Survey data from California, New York, and Texas for our numerical experiments. From the dataset, we consider hospitals with the primary service code of “general medical and surgical” and that are coded as either “nongovernment, not-for-profit” or “corporation-owned, for-profit”. We exclude hospitals that do not have any general medical and surgical adult beds. After filtering, the data set contains information on 493 hospitals across the three states of California, New York, and Texas.

Based on the 2015 AHA Annual Survey data, we created four hospital size categories, as shown in Table 6. While the range of total facility inpatient days for category 3 is relatively wide, the impact of hospital size on the policy patient-to-nurse ratio is still captured effectively with the four categories, as shown by the results in Section 5.1.

Table 6 Distribution of total annual facility inpatient days for hospitals in AHA data set

Figure 11 reports the proportion of general medical and surgical beds in the included hospitals according to the AHA data. The AHA data provides total hospital-wide inpatient days, but not unit-specific inpatient days, which is what we need. Therefore, based on Fig. 11, we estimate that the inpatient days for med/surg units are around 50–80% of the total hospital-wide inpatient days.

Fig. 11

Distribution of medical and surgical bed proportion for hospitals in AHA data set

1.3 California office of statewide health planning and development (OSHPD) data

To further support our estimate of med/surg inpatient days, we also acquired data from the “2014–2015 Fiscal Year Hospital Annual Financial Disclosure Report” provided by California’s Office of Statewide Health Planning and Development (OSHPD). While this data set is limited to hospitals in California, it includes unit-specific information regarding beds and patient (census) days. After applying the identical filter as used for the AHA data set, the OSHPD data set provides information on 198 hospitals in California. Figure 12 shows that our assumption of inpatient days for the med/surg unit being around 50–80% of the total hospital-wide inpatient days is reasonable.

Fig. 12

Distribution of medical and surgical patient days proportion for California hospitals in OSHPD data set

Appendix B. Limiting undesirable shifts for each nurse

In Section 5.3, we minimize the total number of undesirable shifts without incurring any additional schedule costs, but we do not limit the number of undesirable shifts for each nurse. Thus, it is theoretically possible for the remaining undesirable shifts to be assigned disproportionately to a small number of nurses. While this was not a major issue for our numerical experiments in Section 5.3 due to the very low number of remaining undesirable shifts with the second objective function, we can also add constraints (27) and (28) that limit the number of undesirable shifts along with second objective function (23).

$$\begin{array}{cc}\sum\limits_{j\in S{U}^{i}}\sum\limits_{d\in D{U}^{i}}{a}_{ij}{x}_{ijd}\le {\overline{US} }_{i}^{UN}&,\quad i\in UN\end{array}$$

(27)

$$\begin{array}{cc}\sum\limits_{j\in S{F}^{i}}{b}_{ij}{u}_{ij}\le {\overline{US} }_{i}^{FN}&,\quad i\in FN\end{array}$$

(28)

where ${\overline{US} }_{i}^{UN}$ and ${\overline{US} }_{i}^{FN}$ are upper limits on the number of undesirable shifts assigned to unit and float nurse $i$, respectively.

Because we still do not allow additional schedule costs, our optimal costs do not change in this case. Furthermore, we also do not observe any meaningful differences in total number of undesirable shifts compared to the results presented in Section 5.3 as long as ${\overline{US} }_{i}^{UN}$ and ${\overline{US} }_{i}^{FN}$ are not too low. We note that when the limit is too low (for example, 0 or 1 undesirable shift per nurse), the problem sometimes becomes unsolvable for policy PTN ratio of 4:1 due to the insufficient number of available and desirable shifts to stay under the policy PTN for every shift since we do not allow any increase in costs.