Data were collected by the respective emergency medical services in an observational prospective study of out-of-hospital cardiac arrest patients in Akershus (Norway), Stockholm (Sweden) and London (UK) in the period March 2002 to September 2004 [1, 18]. The appropriate ethical boards at each site approved the study, and the need for informed consent from each patient was waived as decided by these boards in accordance with paragraph 26 of the Helsinki declaration for human medical research. The study is registered as a clinical trial at http://www.clinicaltrials.gov/, (NCT00138996). Continuous ECG, transthoracic impedance, and chest compression depth measurements were collected using a modified Heartstart 4000 (Phillips Medical Systems, Andover, MA, USA) (Heartstart 4000SP (Laerdal Medical, Stavanger, Norway)) and patient records registered according to the Utstein template [19]. The ECG was obtained through the defibrillator's self-adhesive defibrillation pads positioned in lead II equivalent positions and the same types of electrodes were used throughout the data collection. The signal was digitally recorded with a sampling rate of 500 samples per second and 16 bits resolution. Before digital sampling the analogue ECG signal was filtered with a second order bandpass filter with passband of 0.9–50 Hz and before analysis a 48 tap lowpass digital filter with an upper passband edge of 30 Hz was applied to the digitised ECG to remove any 50 Hz power line noise. Regarding the mapping-dataset (described below) ROSC was indicated either by a clinically detected pulse or by changes in the transthoracic impedance >50 mΩ coincident with QRS complexes [1]. Compression depth measurements were used to identify the presence and absence of chest compressions. Further details about registrations and methodology have been given elsewhere [1].
Intervals without chest compressions
We extracted ECG segments from intervals without chest compressions following an interval with compressions. Only segments with VF or VT during both intervals were included. The ECG segments were then divided into 2-second analysis windows centred at 3, 5, 7 and so on up to 27 seconds into the pause, depending on the length of the pause. The first and last 2 seconds of each interval were left out to ensure that the signals were uncorrupted by compression artefacts. We will refer to this dataset as the interval-dataset. ECG segments were manually checked for noise and noisy parts of ECG segments were censored from further analysis. The definition of noise was influence from a pacemaker (regular spikes on the ECG) or short bursts of high frequency signal that visually differ substantially from the surrounding VF or VT. The source of the latter noise form might be electrode noise or muscle artefacts.
Outline of analysis
The ECG from the analysis windows in the interval-dataset was characterised by computing the logarithm of the mean-slope (logslope), one of the most accurate indicators of P
ROSC [11]. Mean-slope can be viewed as a measurement of the coarseness of the ECG. High amplitude and frequency of the ECG give high mean-slope values, indicating a high P
ROSC. If ecg(n) is the digitised ECG signal, logslope is defined as
(1)
Logslope values have the desirable property of having an approximate Gaussian distribution, and we thus expected an approximately linear decay with time in untreated VF/VT. A linear mixed-effects model was therefore fitted to logslope versus time. Then a mapping from logslope to P
ROSC scale, obtained from a second clinical dataset (described below), was applied to the fitted linear mixed-effects model for easier interpretation.
Mapping logslope to P
ROSC
The mapping from logslope to P
ROSC was found from a dataset (mapping-dataset) of pre-shock logslope values and corresponding defibrillation outcomes (ROSC or no-ROSC) that has previously been described [20]. The mapping-dataset was collected during cases of out-of-hospital cardiac arrest and ROSC was defined as circulating rhythm for a minimum 10% of the post-shock interval. A marginal logistic regression model for longitudinal data, accounting for correlation between samples from the same patient [21], was fitted to the mapping-dataset using the add-on package 'geepack' to the statistical software R (R Development Core Team, R Foundation for Statistical Computing). The mapping function has the following form:
(2)
α
0 and α
0 are parameters of the logistic regression estimated during model fitting. The interval-dataset and the mapping-dataset were extracted from the same cardiac arrest episodes. However, since the last 2 seconds of ECG in an interval without chest compressions were not included in the interval-dataset, and we only used the last 2 seconds of ECG before a shock in the mapping-dataset, there is in this respect no overlap of data between the datasets.
Describing logslope development
Using the statistical software S-plus (Insightful Corporation, Seattle, WA, USA), we fitted a linear mixed-effects model to the interval-dataset [17]. The linear mixed-effects model takes into account the fact that the general level of logslope varies between intervals by allowing individual variation in the regression parameters from interval to interval. The logslope values are the response variable in the model, and the development of this described with a polynomial in t, where t is time (seconds) after chest compressions stopped minus 10 seconds (t = t
org-10). The subtraction is performed in order to decorrelate the covariates of the model (t, t
2, etc). If i identifies the interval (cluster), the model for the development of logslope with time is given by:
(3)
K is the polynomial degree for the fixed-effects part of the model and M the degree for the random-effects part (accounting for variations between intervals) and K ≥ M. Gaussian model residuals ε
it
are assumed and also a multivariate Gaussian distribution of the random terms U
ik
, k ∈ 1, ..., M
The S-plus function used to fit the model, lme, has several different possible ways of modelling correlation between residuals within each interval (cluster), and possible heteroschedasticity in the data [17]. We chose the optimal correlation model, variance model (for heteroschedastic data) and the necessary polynomial degree (K and M), in that order, by comparing Akaike information criterion (AIC) values. Polynomial degrees up to four were tested and among possible models with similar AIC values the model of lowest polynomial degrees was chosen. We did not experiment with other variance covariates than the fitted-model value (software default). For mathematical details about the modelling of correlation between residuals and heteroschedastic data we refer to Pinheiro and Bates [17]. After choosing our final model it was validated by plotting normal probability plots for the model residuals and the random terms, the distribution of residuals against time and fitted-model value and the response against fitted values.
Calculating P
ROSCdevelopment
The linear mixed-effects model was fitted to logslope values due to the statistical properties mentioned above, but we wanted to interpret the implications on the P
ROSC scale. More specifically we wanted to find the expected development of P
ROSC for intervals with different starting values. To avoid the random short time variation in logslope (and P
ROSC) from influencing the development, we relate each expected development to the starting value of the regression, representing the true underlying behaviour. The results are derived from the fitted linear mixed-effects model (not from specific regression lines for each interval) and the obtained mapping from logslope to P
ROSC. Further descriptions of these procedures are given in Appendix 2.
We present the estimated parameters of the chosen linear mixed-effects model and of the logistic regression model for the logslope to P
ROSC mapping, along with 95% confidence intervals (CI) or standard deviation (Std) of estimates for all parameters. Further we present estimates of the expected development with time (into the intervals without compressions) of P
ROSC for intervals with different starting values. Approximate 95% CIs for the P
ROSC developments are derived by drawing 1000 simulated parameter values from the model parameters asymptotic distributions, and then recalculating the resulting P
ROSC values for each simulation. The 95% CI for the estimated expected P
ROSC developments are defined as the 95% CI of P
ROSC at a given time into an interval, given a chosen P
ROSC value at the first point of analysis (3 seconds into the intervals).