Live Health Short-term Baseline Preliminary User Guide

Transcription

1 Live Health Short-term Baseline Preliminary User Guide Create Date: February 28, 27 Last Modified Date: April 4, 27 Version. Copyright 27 Computer Associates International, Inc. Staples Drive Framingham, MA 72 All Rights Reserved

2 Overview The short-term baseline rule for Live Health described herein is designed to detect variations from the normal behavior of a time-series variable, where the normal value is determined over a relatively short period. This period can be anywhere between five minutes and one day; 3 minutes is expected to be typical. The short-term baseline rule is closely related to the entire-baseline rule; the main difference is that the averaging window can be much shorter, but the same basic calculation is performed, saving average (α) and standard deviation (σ), from which triggering thresholds can be defined based on absolute value, relative value, or a multiplier of σ. Due to the fact that many more data points may be involved, implying a greater number of calculations than were a straightforward averaging window employed, these rules approximate average and standard deviation using digital filter technology. Not only is the error from the approximation very small, but the smoothing properties are much better than those of a direct averaging window, resulting in more accurate measurement and detection of problems. The theory of operation is described in Appendix A Use of Digital Filters. A graphical depiction of its operation is shown in Figure. An additional factor, again due to the high computational cost involved, is that the short-term baseline calculations are not saved in the ehealth database. Hence, they will not appear in reports such as the Alarm Detail Report. Due to these considerations, use of the short-term baseline rule is governed by a specific selection in the rule editor, as shown in Figure 2. Data value Measured data Smoothed data (baseline) Alarm can be generated by sufficient deviation from baseline (before adding the measured point into the baseline). Standard deviation current poll time rolling baseline window Figure Graphical depiction of the short-term baseline operation

3 2 User-visible Functionality 2. Rule Controls The new rule control is shown below in Figure 2. New control The control has the following properties: Figure 2 Short-term Baseline option in the Live Health Rule Editor Choosing the short-term baseline prevents the baseline from being calculated/accumulated in the database. Should the user switch from short-term baseline to either entire baseline or same hour and day, baseline accumulation will begin anew. The control also applies to the And clause if a second conditional is used with the same condition types specified here. The short-term baseline window is expressed in minutes, whereas the longer-term baselines are expressed in weeks. The averaging window must be greater than zero and less than or equal to 44 (one day expressed in minutes). Values not in this range result in an error pop-up window upon pressing OK or Apply. The number of polled samples used in the averaging calculation is determined by dividing the averaging window by the poll interval and rounding to the nearest integer (with a minimum value of one). So, for example, for a polling interval of five minutes, if a 3 minute window is specified, six points will be used in the average. If 28 minutes is specified, six points will also be used. If 26 minutes is specified, five points will be used. If one minute is specified, the resulting zero will be raised to one; of course, this is not a very useful average.

4 2.2 Rule Behavior Note the following behavioral characteristics of a rule defined by the control: Processing of the short-term averaging window begins immediately; there is no need to wait for baseline samples to accumulate in the database. When a short-term baseline rule processing on an element is initiated start a (e.g., when the element has just begun polling, or the rule has just been applied), checking against the baseline will not begin until at least one complete averaging window has been processed. This is to avoid creating alarms based on too few averaging points. When determining whether the current polled sample should generate an alarm with respect to a short-term baseline rule, the sample is first compared against the baseline and is then used to update the baseline average. In this way, the current sample does not dilute the average before checking whether an alarm should be generated (this is noted in Figure ). 2.3 Control of Digital Filter Parameters See Appendix A Use of Digital Filters for the digital filter controls. Generally, these should not need to be changed by the user. 2.4 DCI Support To specify use of the short-term baseline via DCI files, the symbol shorttermaverage should be used. The baseline type appears in the ThresholdConditions section of a Live Health DCI file, the format of which is specified in $NH_HOME/sys/stdHdrLiveEx.dci. Here is an excerpt from the field definition section of this file: FN, ThresholdConditions, thresholdconditionid, alarmtype, \ variable, thresholdoperator, threshold, \ deviationoperator, deviationmodifier, \ baselineweeks, baselinemethod The full set of baseline method specifiers in Live Health DCI files is thus: Symbol Meaning Units asdayandhour Same day and hour baseline periodic averaging weeks entirebaseline Entire baseline long-term, continuous, sliding averaging window weeks shorttermaverage Short-term baseline short-term, continuous, sliding averaging window minutes

5 3 Appendix A Use of Digital Filters Calculation of average (α ) and standard deviation (σ) presents problems from two major fronts. First, over small intervals, accuracy will be poor, and the baselines questionable. Second, over long intervals, computation effort becomes too large to support. Both of these problems are resolved by employing a lowpass recursive digital filter, rather than an averaging window. This results in much better smoothing over short intervals, and maintains smoothing properties up to a large number of average-equivalent points, using the same small number of filter points. In addition, the same smoothing filter can be applied to a calculation of σ. It must be emphasized, however, that windows which are too short will still have questionable accuracy, regardless of the smoothing technique used. 3. Approximating Average A basic first-order linear lowpass digital filter is given by: k y ( n) = ky( n ) + ( x( n) + x( n )) () 2 This filter, adopted from Mitra [], has the advantage of a unity gain in the passband and a simple formula for k at the 3-db cutoff frequency ω : k sinω c c c = (2) cosω When cascaded, a lowpass filter with a greater cutoff slope results, and generally the calculation of the current value is based on an expression of previous x and y values. A four-stage filter results in an expression in the following form: y ( n) = E[ y( n ), y( n 2), y( n 3), y( n 4), x( n), x( n ), x( n 3), x( n 4)] (3) Where E[] indicates a linear expression derived from eqn. (). An averaging filter is of the form: y ( n) = ( x( n) + x( n ) x( n ( m ))) (4) m where m is the number of points in the average. In the frequency domain, this filter has a lowpass comb response (as in the red traces of the right-hand graphs below). The initial zero is given by: ω = a 2πm (5) We can approximate the averaging filter by using this cutoff point as the cutoff point for the lowpass filter in eqn. (), so that: sin k = 2πm (6) cos 2πm The basic thesis is that the digital filter form is (a) a close approximation to average, (b) a better smoothing function than average (hence gaining more value from shorter baselines), and (c) much more efficient than computing average directly. The figures below show that a four-stage filter of this type tracks average quite well, with better smoothing, up to the equivalent of at least 5 points, and with far fewer operations and points which need to be saved.

6 A four stage filter was chosen empirically, by examining the shapes of the step and frequency responses. Note that in each frequency graph, the curves match well down to the 3-db point (.77). Thereafter, the filter attenuates high frequencies (i.e., fast changes) much better than the averaging filter. The number of stages is adjustable in the delivered system, so that the user may apply a degree of smoothing as appropriate.

7 point average point average point average point average point average point average point average point average Figure 3 Step and Frequency responses for averaging-window filters and their equivalent 4-stage recursive filter.

8 2 8 input 5-point averaging window smoothing filter equivalent Figure 4 Example of an averaging filter (5 points) and an equivalent recursive filter (4 stages) on simulated data. The input data is unity except for the spikes shown. 3.2 Approximating Standard Deviation Standard deviation, σ, is the root-mean-square deviation from the mean: σ = N N = i ( x x i ) 2 From this definition is derived the standard formula, the square root of the mean of the squares minus the square of the mean: σ = 2 2 x x In this case, x represents the set of points in the averaging window, x ( n)... x( n ( m )). 2 Since we approximate x with the filtering function to good accuracy, approximating x by use of the same filter on the squared x samples should also provide a good approximation toσ. If we let the filter transformation above be represented by F, then 2 2 σ ( n) ( F[ x ( n)] ( F[ x( n)]) ) N This is also computationally efficient, as in the average approximation. 3.3 Control of Digital Filter Parameters There are many forms of digital filter; the one chosen here conforms well to the need to approximate a moving average. The only parameter applicable here is the number of stages (also referred to as the number of pole-zero pairs, in filter parlance). The need to vary this should be very infrequent, so this parameter is exposed via an environment variable:

9 NH_LEX_BASELINE_FILTER_STAGES Default = 4 Requires ehealth restart if changed.

10 4 References. Mitra, S.K, Digital Filter Presentation,