Abstract
We introduce the sample asymmetry analysis (SAA) and illustrate its utility for assessment of heart rate characteristics occurring early in the course of neonatal sepsis and systemic inflammatory response syndrome (SIRS). Conceptually, SAA describes changes in the shape of the histogram of RR intervals that are caused by reduced accelerations and/or transient decelerations of heart rate. Unlike other measures of heart rate variability, SAA allows separate quantification of the contribution of accelerations and decelerations. The application of SAA is exemplified by a study comparing 50 infants, who experienced a total of 75 episodes of sepsis and SIRS, with 50 control infants. The two groups were matched by birth weight and gestational age. RR intervals were recorded for all infants throughout their course in the Neonatal Intensive Care Unit. The sample asymmetry of the RR intervals increased in the 3–4 d preceding sepsis and SIRS, with the steepest increase in the last 24 h, from a baseline value of 3.3 (SD = 1.6) to 4.2 (SD = 2.3), p = 0.02. After treatment and recovery, sample asymmetry returned to its baseline value of 3.3 (SD = 1.3). The difference between sample asymmetry in health and before sepsis and SIRS was mainly due to fewer accelerations than to decelerations. Compared with healthy infants, infants who experienced sepsis had similar sample asymmetry in health, and elevated values before sepsis and SIRS (p = 0.002). We conclude that SAA is a useful new mathematical technique for detecting the abnormal heart rate characteristics that precede neonatal sepsis and SIRS.
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Abbreviations
- SAA:
-
sample asymmetry analysis
- HRC:
-
heart rate characteristics
- BW:
-
birth weight
- GA:
-
gestational age
- HR:
-
heart rate
- SIRS:
-
systemic inflammatory response syndrome
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Supported by National Institutes of Health grants R01-DK51562 and GM64640; the American Heart Association, Mid-Atlantic Consortium; Children's Medical Center Research Fund, University of Virginia; W.S. Paley Foundation; Virginia's Center for Innovative Technology; and Medical Decision Networks, Charlottesville, VA.
Potential for conflict of interest: Medical Decision Networks of Charlottesville, VA, which supplied partial funding for this study, has a license to market technology related to heart rate characteristics (HRC) monitoring of newborn infants. As of the submission date of the final version of the article, none of the authors had received consultants' fees or owned equity in Medical Decision Networks or related companies. However, Drs. Griffin and Moorman have been offered an equity share of a new company, Medical Predictive Systems Corporation, that owns the HRC technology license.
APPENDIX: SAMPLE ASYMMETRY OF A RANDOM VARIABLE
APPENDIX: SAMPLE ASYMMETRY OF A RANDOM VARIABLE
To define sample asymmetry of a random variables we first introduce the following:
Weighting functions.
Let ξ be a random variable with values in its sampling space X and unspecified distribution, and let μ ∈X be a point within the sampling space X. For any x ∈X we define a weighting function w (x; α) = (x − μ) α, where α > 0 is a parameter describing the degree of weighting of deviations from the reference point μ. For example, if α = 1, deviations from μ will receive linearly increasing weights, whereas if α = 2, deviations from μ will receive quadratically increasing weights. Note that the weighting parameter α could be selected in various applications to be any positive, including noninteger, number. A number smaller than 1 will result in slower than linear increase of weights, a number greater than 2 will result in a faster than quadratic increase of weights. Further, we define separate weighting for left and right deviations of ξ from its reference point μ as follows: 1) Left-weighting function:w1(x; α) =w (x; α) whenever x < μ and 0 otherwise, and 2) right-weighting function:w2(x; β) =w (x; β) whenever x ≥ μ and 0 otherwise, where the parameter β, similarly to α, describes the degree of weighting of deviation to the right of the reference point. To add flexibility to this model, we allow for different degree of weighting to the left (α) and to the right (β) from the reference point μ. In many applications, the left and right weightings could be equal (see Fig. 1).
Defining sample asymmetry of a random variable.
Let x1, x2, …xn be a sample of n observations on ξ. Given this sample, we define two quantities representing the sum of the weighted deviations to the left and to the right from the reference point μ as follows:
It is now clear that if α = β, and the sample x1, x2, …xn is approximately symmetric with respect to the reference point, then R1 will be approximately equal to R2. If the sample is asymmetric with larger and/or more frequent deviations to the right from the reference point μ, then R2 will be greater than R1. Inversely, if the sample is asymmetric with larger and/or more frequent deviations to the left from the reference point μ, then R1 will be greater than R2.
Definition: The ratio
represents the sample asymmetry of the random variable.
The following properties are pertinent to the applications of sample asymmetry:
(a) If α = β, when the sample x1, x2, …xn is approximately symmetric with respect to the reference point, then R(α, β) will be approximately equal to 1. Values greater than 1 will indicate larger and/or more frequent deviations to the right from the reference point μ, whereas values less than 1 will indicate larger and/or more frequent deviations to the left.
(b) The sensitivity of the ratio R(α, β) to left and right deviations from the reference point can be controlled through separate adjustment of the parameters α and β.
(c) R1(α) and R2(β) can be used separately as estimates of the absolute weighted mass of the distribution of ξ; with respect to its reference point μ.
(d) The reference point μ can be the empirical mean of the random variable ξ, e.g.
the median of ξ, or any other theoretically or practically relevant number. The choice of a reference point could be critical for the subsequent data analyses. The median of the distribution is an obvious initial reference point because the median, as opposed to other statistics such as the mean, is not affected by outliers or large deviations in the data. This is particularly important in the analysis of RR intervals where the goal is to quantify spikes in the data.
(e) A quadratic weighting, that is, α = β = 2, has special properties that set it apart from other parameter configurations. First, the weighted deviations R1(α) and R2(β) are exactly the squares of the classical Euclidean distances of the sample measured to the left and to the right from the reference point. Second, if the reference point μ is the mean (or the median) of the distribution, then, under the null hypothesis that the distribution is normal, the sample asymmetry R(2, 2) will have an F distribution with (n/2–1;n/2–1) degrees of freedom (n/2–1/2;n/2–3/2 if n is an odd number). This property gives a straightforward statistical test for symmetry of a single data sample. Thus, we recommend the use of a quadratic weighting unless a particular data sample proves that another parameter combination is more appropriate.
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Kovatchev, B., Farhy, L., Cao, H. et al. Sample Asymmetry Analysis of Heart Rate Characteristics with Application to Neonatal Sepsis and Systemic Inflammatory Response Syndrome. Pediatr Res 54, 892–898 (2003). https://doi.org/10.1203/01.PDR.0000088074.97781.4F
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DOI: https://doi.org/10.1203/01.PDR.0000088074.97781.4F
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