Comparison of linear–stochastic and nonlinear–deterministic algorithms in the analysis of 15-minute clinical ECGs to predict risk of arrhythmic death

Figures & data

Table 1 Comparison of linear and nonlinear algorithms in 312 low-to-high-risk patients presenting in the emergency department with chest pain and assessed risk of AMI > 7%. All subjects had ECGs recorded, follow-up completed, and no paced rhythms. The defined arrhythmic death outcomes are expressed as true or false predictions (T or F) by positive or negative algorithmic tests (P or N). The same edited N-N data set was used for the comparative algorithmic analyses

Nonlinear deterministic algorithmsa–d
PD2i ≤ 1.4	PD2i > 1.4	DFA-OUT	DFA-IN	1/fS ≤ − 1.07	1/fS > − 1.07	ApEn ≤ 1.0	ApEn > 1.0
TP = 20	TN = 130	TP = 6	TN = 52	TP = 6	TN = 149	TP = 4	TN = 161
FP = 96	FN = 1e	FP = 218	TN = 4	FP = 75	TN = 14	FP = 57	FN = 16
SEN = 95**	SUR = 65	SEN = 30	SUR = 17	SEN = 30	SUR = 65	SEN = 20	SUR = 65
SPE = 58**	OUT = 0	SPE = 19	OUT = 6	SPE = 67	OUT = 3	SPE = 74	OUT = 9
REL ≫ 23**	N = 312	REL = 0.13	N = 312	REL = 0.86	N = 312	REL = 0.80	N = 312

Linear stochastic algorithmsf–i
SDNN ≤ 65	SDNN >65	MNN ≤ 750	MNN > 750	LF/HF ≤ 1.6	LF/HF > 1.6	LF(ln) ≤ 5.5	LF(ln) >5.5
TP = 19	TN = 55	TP = 19	TN = 154	TP = 7	TN = 188	TP = 19	TN = 90
FP = 197	FN = 6	FP = 98	FN = 6	FP = 62	FN = 18	FP = 160	FN = 6
SEN = 76	AF = 29	SEN = 76	AF = 29	SEN = 28	AF = 29	SEN = 76	AF = 29
SPE = 23	OUT = 6	SPE = 61	OUT = 6	SPE = 76	OUT = 8	SPE = 36	OUT = 8
REL = 0.93	N = 312	REL = 4.33*	N = 312	REL = 1.16	N = 312	REL = 1.69	N = 312

Notes:

** p ≤ 0.001; binomial probability test; with multiple-test alpha-protection (alpha level required is 8-fold smaller); expansion of (P + Q)ⁿ × eightfold protection implies p = 0.00016; also p ≤ 0.001 by Fisher’s exact test for row vs column associations in a 2 × 2 contingency table; all others in Table 1 are not significant by binomial probability test or Fisher’s exact test.

a PD2i, point correlation dimension (positive if minimum PD2i ≤ 1.4 dimensions, with a systematic low-dimensional excursion of more than 1 PD2i value); cases of randomized-phase SUR were identical to the cases of %N < 30%.

b DFA-OUT, detrended fluctuation analysis (α₁ [short-term] is positive, if outside normal range of 0.85 to 1.15); randomized-sequence surrogate rejections (SUR).

c 1/f S, 1/f Slope (positive, if ≤ −1.075 for slope of log[microvolts²/Hz] vs log [Hz] integrated over 0.04 Hz to 0.4 Hz). SUR = randomized phase.

d ApEn, approximate entropy (positive with cut-point ≤ 1.0 units, slope distance). SUR = randomized phase.

e This single AD patient died at 79 days and may not be a true FN; the ECG was recorded prior to two normal clinical ECGs, followed by a third positive one (ie, the patient could be classifiedas an “evolving acute MI” who may have been TN at the time the ECG was recorded).

f SDNN, standard deviation of normal beats (positive, if ≤ 65 msec; for positive, if ≤ 50 msec, TP = 17).

g MNN, mean of normal R-R intervals (positive, if ≤750 msec).

h LF/HF, low frequency power (0.04 to 0.15 Hz)/high frequency power (0.15 to 0.4 Hz) (positive, ≤ 1.6).

i LF(ln), low frequency power (0.04 to 0.15 Hz), normalized by natural logarithm (positive, ≤ 5.5).

Abbreviations: AF, atrial fibrillation-rejection (required for linear stochastic algorithms);AMI, acute myocardial infarction; ECG, electrocardiography; OUT, outlier-rejection; REL, relative risk; SEN, sensitivity (%); SPE, specificity (%); SUR, surrogate-rejection; N, total number of subjects.

Table 2 Subgroup comparison of algorithms using the relative risk (REL) statistic. All subjects had ECGs recorded and follow-up completed (N = 312). Rejections of noisy N-N data were the same as in Table 1, and these rejections included all cases of atrial fibrillation and high arrhythmia rate a. The arrhythmic death outcomes were expressed as true or false predictions (T or F) by positive or negative tests (P or N), and then the REL was determinedb

	AMI	non-AMI	post-MI	nonpost-MI
PD2i	7.39**	>12.17**	>4.51*	>16.85**
DFA	0.70	0.44	0.63	0.48
1/f Slope	1.67	0.56	0.87	0.90
ApEn	0.50	1.44	0.00	0.72
SDNN	0.68	1.75	0.83	1.34
MNN	1.94	>20.82**	3.00	3.61*
LF/HF	1.08	0.66	2.52	0.61
LF(ln)	1.08	>5.13*	0.73	2.09

Notes:

a Atrial fibrillation, high sinus arrhythmia and high ventricular ectopy tend to randomize the heartbeats, with or without movement artifacts removed; rejection occurs when the edited normally-conducted beats are not statistically different from their surrogate. The randomized phase surrogate rejections were used for all algorithms, except DFA, which used the randomized sequence surrogate (ie, it is not sensitive to phase).

b REL = TP/FN × [TN + FN/TP +FP].

* p ≤ 0.05, Fisher exact Test for row vs column association in 2 × 2 contingency table; the > sign means that REL went to infinity because FN = 0; the values shown used FN = 1;

** p ≤ 0.001.

Abbreviations: PD2i, point correlation dimensions; DFA, detrended fluctuation analysis; 1/f S, 1/f Slope; ApEn, approximate entropy; SDNN, standard deviation of normal beats; MNN, mean of normal R-R intervals; LF/HF, low frequency power/high frequency power; LF(ln), normalized by natural logarithm; AMI, documented acute myocardial infarction; non-AMI, documented no AMI; post-MI, documented history of myocardial infarction; nonpost-MI, no history of myocardial infarction.

Figure 1 Power spectra, R-R intervals, and associated PD2is of three representative patients. A) The power apectra of the edited heartbeats (N-N) is shown for a normal patient with gastroesophageal reflex disorder (GERD), a patient with an acute myocardial infarction (AMI) who lived for at least the one year of follow-up (LIVED) and a patient with a matched AMI who died of arrhythmic death (AD) after discharge. B) The R-Rs (unedited) and the corresponding PD2is of the GERD patient. C) The R-Rs (unedited) and corresponding PD2is of the AMI, LIVED patient. D) The R-Rs (unedited) and corresponding PD2is of the AMI, AD patient.

Notes: R-R values are in milliseconds, PD2is are in dimensions (degrees of freedom); the horizontal bar in B through D is at PD2i = 1.4.
Abbreviations: AD, arrhythmic death; AMI, acute myocardial infarction; GERD, gastroesophageal reflux disorder; LIVED, lived for at least one year of follow-up; NORM, normal patient; PD2i, point correlation dimensions.