Vector Autoregressive Models and Granger Causality in Time Series Analysis in Nursing Research: Dynamic Changes Among...

Patients undergoing continuous vital sign monitoring (heart rate [HR], respiratory rate [RR], pulse oximetry [SpO2]) in real time display interrelated vital sign changes during situations of physiological stress. Patterns in this physiological cross-talk could portend impending cardiorespiratory instability (CRI). Vector autoregressive (VAR) modeling with Granger causality tests is one of the most flexible ways to elucidate underlying causal mechanisms in time series data.

The purpose of this article is to illustrate the development of patient-specific VAR models using vital sign time series data in a sample of acutely ill, monitored, step-down unit patients and determine their Granger causal dynamics prior to onset of an incident CRI.

CRI was defined as vital signs beyond stipulated normality thresholds (HR = 40-140/minute, RR = 8-36/minute, SpO2 < 85%) and persisting for 3 minutes within a 5-minute moving window (60% of the duration of the window). A 6-hour time segment prior to onset of first CRI was chosen for time series modeling in 20 patients using a six-step procedure: (a) the uniform time series for each vital sign was assessed for stationarity, (b) appropriate lag was determined using a lag-length selection criteria, (c) the VAR model was constructed, (d) residual autocorrelation was assessed with the Lagrange Multiplier test, (e) stability of the VAR system was checked, and (f) Granger causality was evaluated in the final stable model.

The primary cause of incident CRI was low SpO2 (60% of cases), followed by out-of-range RR (30%) and HR (10%). Granger causality testing revealed that change in RR caused change in HR (21%; i.e., RR changed before HR changed) more often than change in HR causing change in RR (15%). Similarly, changes in RR caused changes in SpO2 (15%) more often than changes in SpO2 caused changes in RR (9%). For HR and SpO2, changes in HR causing changes in SpO2 and changes in SpO2 causing changes in HR occurred with equal frequency (18%).

Within this sample of acutely ill patients who experienced a CRI event, VAR modeling indicated that RR changes tend to occur before changes in HR and SpO2. These findings suggest that contextual assessment of RR changes as the earliest sign of CRI is warranted. Use of VAR modeling may be helpful in other nursing research applications based on time series data.