Multifactorial Correlation Analysis of Nursing Unit Staffing Based on Gray Relation Analysis: A Cross-Sectional Study

The rationalization of nurse staffing is a complex issue that is influenced by a number of factors. The correlation between many different influences and nursing staffing had not yet been clarified.

The aim of this study was to use gray relation analysis to analyze the extent to which factors such as human, material, and financial inputs, nursing services, and nursing quality are associated with nursing human resource allocation from a time series and nursing unit perspective, so as to clarify the priorities of nursing unit staffing.

Based on the previous literature review and expert correspondence, 7 primary and 26 secondary indicators of the factors influencing the staffing of nursing units were identified. Data related to 55 nursing units for the year 2023 were retrospectively collected from the hospital information system and the nursing information system. Gray relation analysis was used to calculate and rank the correlation between each influencing factor and nursing unit staffing in time series and nursing unit series.

Gray relational analysis revealed consistently higher correlation coefficients for primary indicators (time series: 0.72-1.00; nursing unit series: 0.83-1.00) versus secondary indicators (time series: 0.59-1.00; nursing unit series: 0.80-1.00), indicating that the selected manifest variables served as good measures of their underlying latent constructs. Physical/financial inputs and nursing quality/safety-service outputs ranked highest among primary categories. Key secondary indicators showed strong intercorrelations: actual open beds, nurses on duty, nurse-patient ratio, and nursing work hours for inputs; nursing quality assessment results, bed utilization rate, patient satisfaction, and diagnosis-related groups for outputs. The correlation patterns for adverse events differed substantially across dimensions, showing higher correlations in unit comparisons than in time series.

This study demonstrates that a multifactor, value-driven approach using gray relational analysis can effectively identify key inputs and outputs for nursing unit staffing. The findings highlight specific high-impact indicators for management prioritization, including physical and financial inputs alongside nursing quality and safety outputs. When allocating resources and planning staffing, managers should consider that the strength of relationships for key factors varied significantly between the time-series and nursing-unit dimensions. This indicates that the analytical perspective is crucial for identifying critical factors. Future research should focus on developing predictive tools based on these drivers and validating the approach in broader clinical contexts.

The correlation analysis of this study provided managers with a reference for evaluating the efficiency of nursing staffing and constructing a nursing staffing model with the priority of different influencing factors.