We collected data from all patients who had larger artery occlusion stroke who underwent EVT treatment at the Karolinska University hospital during 12 February 2018–11 February 2020. Data were collected retrospectively through the electronic patient charts at the hospital. Baseline and demographic characteristics were recorded, in addition to radiological examinations, blood test results, and data on EVT procedural outcomes. Outcomes from 3-month follow-up visits were recorded for all patients who were included during the study period. The data that support the findings of this study are available from the corresponding author on reasonable request.
Blood pressure
SBP and diastolic BP were recorded at baseline, end of EVT procedure, and during the first 24 hours after EVT treatment. BP was measured according to the local monitoring protocol, which included 21 measurements during the first 24 hours after EVT treatment with measurements every 30 min from 0 hour to 4 hours, measurements every hour from 4 hours to 8 hours, and measurements every 2 hours from 8 hours to 24 hours. Additional eight optional measurements were possible every 2 hours from 9 hours to 23 hours, and these data were collected if they were available. The method for measuring BP was through non-invasive cuffs.
The local guidelines at Karolinska University Hospital recommend using SBP thresholds that are set by the physician performing the EVT procedure. Although individually chosen SBP thresholds were allowed, they largely follow current guidelines,15 with a commonly used SBP interval being 100–160 mm Hg for the first 24 hours after thrombectomy.
Statistical analysis
Baseline and demographic characteristics were presented for the entire study population and stratified by primary outcome. For group comparisons, Student’s t-test and Pearson’s χ2 tests were used for continuous and categorical variables, respectively. We included patients in our analyses if they had at least 10 SBP measurements during the first 24 hours after EVT treatment.
To investigate if deviating from a specific SBP course was associated with outcomes, we created models of SBP measurements over the first 24 hours after EVT treatment for every individual patient, allowing for a linear, quadratic or cubic shape of the SBP course. The initial step for creating each model was to consider the SBP course of patients with favourable outcomes as a reference SBP course, applying the differently shaped curves to their SBP measurements. This SBP course was then compared with patients with unfavourable outcomes. As the shape of the curve of SBP measurements over 24 hours will not match every patient’s SBP measurement exactly, we could test if deviating from the SBP course could itself be associated with outcomes.
Each predictive model was created in three steps, which are summarised as follows and explained in more details further: (1) estimation of the SBP course for patients with favourable outcome using a linear mixed effects model; (2) calculating the random effects for each patient in the entire study population with empirical best linear unbiased predictors (EBLUPs), which provides a value for how much any patient is deviating from the SBP course of patients with favourable outcome; and (3) prediction of the outcome through logistic regression models using the random effects of each patient as the predictor. These steps were based on the previous work by Sandström et al.16
Step 1 of the prediction model
In the first step, we estimated, for each outcome, a linear mixed effects model for the association of SBP over the first 24 hours after EVT in patients who had favourable outcomes. We included random effects for each coefficient of the model, including the intercept, producing the following linear mixed models:
for linear, quadratic and cubic versions, respectively, where time was measured in hours. Subscript i was for the ith patient, and j was for the jth SBP measurement, as each patient could have a different number of total SBP measurements. The fixed effects a, b, c and d were the SBP course parameters for the fixed effect coefficients for the functions’ level, trend, curvature and twist, respectively, where applicable, and differed for each version. The random effects vectors u=(u0, u1)′, v=(v0, v1, v2)′, and w=(w0, w1, w2, w3)′ for the linear, quadratic and cubic versions, respectively, were patient specific. They represented the individual deviation for each patient from the fixed effects of the linear mixed effects model. The residual term ei,j was assumed to follow a zero-mean normal distribution with variance equal to the SD of the residuals squared (σe2).
The random effects vectors for each patient were assumed to follow a multivariate normal distribution with mean equal to the n-dimensional vector of zeros and covariance matrix (G matrix), where n was the length of the random vector, that is, the number of coefficients, in that version of the predictive model:
The diagonal γ1,1 to γn,n was constrained to be positive, while the remaining values were left unconstrained. The random vectors and the residual ei,j were assumed to be independent of each other and the time after the EVT procedure.
Step 2 of the prediction model
The second step of the predictive models was to obtain the random effects for both patients with favourable and unfavourable outcome, by using the fixed effects found in step 1 as a reference point. Essentially, this was to numerically quantify the deviation of each patient from the fixed effects in step 1. For each patient, we used the EBLUP to estimate the random effects vectors u, v and w, separately, with
where G was the G matrix, σe2 was the variance of the residuals; α was the vector of fixed effects for the predictive model version; Ii was the identity matrix for a specific patient; qi was the vector of SBP measurements for a specific patient; and Zi was a matrix of (time0, …, timen) with n being the number of coefficients in that version of the prediction model. While G, σe2 and α were the same for all patients within a prediction model version, Zi and Ii differed in he number of rows for each patient based on the number of SBP measurements for that patient.
Using the EBLUP to acquire the random effects for the entire population has several advantages.17 The EBLUP optimally merges the observed SBP values for each patient to the observed values for the population as a whole in order to predict a patient’s trajectory over time. The EBLUP uses shrinkage of the observed residual (qi−Ziα) by a factor of GZi′(ZiGZi′+σe2Ii)−1 to predict by how much the patient differs from the population trajectory. When the shrinkage factor is large, the predicted trajectory nears the population trajectory. When the shrinkage factor is small, the predicted trajectory nears the observed values for the patient. There are two quantities on which the shrinkage depends: the number of SBP measurements, and the relative magnitude of the variability between patients and within a patient’s measurements. Therefore, the shrinkage factor varies from patient to patient.
Step 3 prediction model
The third step of the prediction models involved using values of the random vectors obtained in step 2 in logistic regression models for the outcomes. For each version of the prediction models, all random effects were used in the logistic regression models at the same time. Variables that were deemed clinically relevant according to a directed acyclic graph approach18 were also added into the logistic regression models. These covariates were age, sex, baseline NIHSS score, history of hypertension and recanalisation grade by Modified Treatment in Cerebral Infarction (mTICI) score dichotomised as mTICI 2b-3 vs mTICI 0 to 2a.19
The three steps described previously are inherently prone to produce possibly underestimated results in step 3, as the steps do not consider any uncertainty in the results from steps 1 and 2. To address this issue, we performed bootstrapping of all the steps for each prediction model version using 1000 iterations per bootstrap. The 95% CIs produced by bootstrapping were presented with the point estimates of step 3.
These three steps were used to compare the SBP courses of two populations, in our case patients with favourable outcomes and patients with unfavourable outcomes. The patients with favourable outcomes were used as a reference SBP course. The reference SBP courses were the fixed effects calculated in step 1, where the SBP course could be modelled from time 0 hour to 24 hours after EVT treatment following the linear, quadratic or cubic shapes for each model. However, even patients with favourable outcome do not necessarily have values that exactly matched the reference SBP course. Therefore, it was necessary to calculate how far from the SBP course an individual may deviate while still predicting favourable outcome. This is measured through the individual random effects of each patient. However, the fixed and random effects from step 1 are known only for the patients with favourable outcomes, meaning that there are no values for patients with unfavourable outcomes. To solve this, we used the EBLUP. The EBLUP uses the fixed effects, in other words, reference SBP course, of the original population to apply the observed values of the patients in the new population as if they were part of the original population using the G matrix and the variance of the residuals of the original population (which represent the variation of the random effects in the original population). This creates random effects for the new population that are essentially the quantified deviation from the reference SBP course of the original population. Because we now have the deviation from the reference SBP course for both patients with favourable and unfavourable outcomes, we can test to see if the deviation itself can be used to predict favourable outcome in logistic regression models.
To compare the prediction models and their predictive stability, we used the area under the curve (AUC) from the receiver operating characteristic curves. In addition to all the SBP measurements that were collected during 24 hours after EVT treatment, we tested the predictive stability of the reference SBP course in different scenarios by using data which contained SBP measurements for only 18, 12 or 6 hours after EVT treatment. Due to fewer SBP measurements in these time scenarios, we included patients with a minimum of 8, 6 and 3 SBP measurements during the time scenarios of 18, 12 and 6 hours, respectively. For these scenarios, the fixed effects, the G matrices and the variance of the residuals remained the same. Due to the different number of SBP measurements within the shorter time scenarios, the random vectors changed for each patient for each scenario.
All statistical analyses were performed with the software R V.4.0.4 (cran.r-project.org).
