Technical considerations on the use of Granger causality in neuromonitoring

Neuromonitoring-derived indices play an important role in implementing personalised medicine for traumatic brain injury patients. A well-established example is the pressure reactivity index (PRx), calculated from spontaneous fluctuations of arterial blood pressure (ABP) and intracranial pressure (ICP). PRx assumes causal relationship between ABP and ICP but lacks the check for this assumption. Granger causality (GC) — a method of assessing causal interactions between time series data — is gaining popularity in neurosciences. In our work, we used ABP and ICP data recorded at the frequency of 100 Hz or higher from 235 traumatic brain injury patients. We focused on time domain GC. Analysis was first performed directly on high-resolution data, which included pulse waves. We showed that due to the measurement delay in high-resolution ABP data, GC analysis may erroneously indicate strong ICP→ABP causal relation. Subsequently, the data were downsampled to 0.1 Hz, effectively removing pulse and respiratory waves. We aimed to investigate how different ways of calculating GC influence results and which way should be recommended for ABP-ICP recordings. We considered aspects like selecting autoregressive model order and dealing with data non-stationarity. In addition, we generated simulated signals to investigate the influence of gaps and different procedures of missing data imputation on GC estimation. We showed that unlike methods which interpolate missing data, replacing missing data by white Gaussian noise did not increase the rate of false GC detection. Python source code used in this study is available at: https://github.com/m-m-placek/python-icmplus-granger-causality.

Statement of significance

Assessing causality between time series data is of particular interest when neuromonitoring indices are derived from those time series and causal interaction between them is assumed. Causality assessment can improve reliability of such indices and open pathways for their safe clinical implementation. Granger Causality (GC) has recently been investigated in data collected from traumatic brain injury patients. However, there are two main issues related to applications suggested in these studies. Firstly, they considered GC for entire multi-day data recordings or for 24-h long episodes. There is interest in considering causal relationships in finer granularity, also in terms of their potential real-time applications at the bedside. Secondly, GC calculation requires selecting some parameters and there is no unique nor standardised way of doing that. Many papers often provide very brief description of data pre-processing and GC calculation. For this reason, it can be harder to reproduce and compare results derived from GC application. Different ways of obtaining GC may potentially lead to inconsistent results. Here, we attempted to explore possibility of time-varying GC of finer granularity and to provide general guidelines for application of GC to neurocritical care time series affected by periods of missing values.