Cardiac output (CO) is a key variable when describing and treating the cardiovascular system. Thermodilution via a pulmonary artery catheter is the most frequently used method, but it lacks accuracy, has a significant associated morbidity, and its clinical value when used to improve patient outcomes has been recently questioned.1,2 In recent years, new technology has emerged that can continuously monitor CO, such as esophageal Doppler, electrical velocimetry (modified bioimpedance),3 and arterial pulse contour analysis. There have been a number of published reports describing investigation of the utility of these measurement methods. The most frequently used analytical method of evaluating CO monitoring devices is the Bland and Altman method of plotting the bias against the mean CO and determining limits of agreement.4 However, the Bland and Altman method only addresses how well the method being evaluated agrees with the reference method and fails to show whether the new method reliably detects changes in CO, or trending, an important feature of these new monitoring technologies. A common assertion when evaluating CO monitoring devices is that when the device fails to provide a reliable measure of the absolute value of CO, it may still be useful as a trend monitor. At the time of this writing, the most appropriate experimental design and method of data analysis for showing clinical utility as a trend monitor are not clearly defined in the literature. The number of publications in which CO technology is evaluated has recently increased from <10 per year in early 2000, to >30 per year in 2009, and this increase in interest has led to calls for a consensus on how trend data should be analyzed and presented.5,6 Therefore, we have reviewed the CO measurement literature published over the past 12 years, provide an up-to-date perspective on the statistical methods in current use, and suggest how CO trend data might be collected and presented in the future.
Medline and EMBASE searches of the English medical literature were performed using the keywords cardiac output, thermodilution, comparative, trending/trend analysis, and Bland and Altman. All publications in the last 12 years (1997–2009) in which ≥2 CO devices were compared were selected. This time period was chosen because 1 of the authors had published a report that already reviewed the CO literature before 1997.7 In the current literature review, we identified those articles in which ability to trend CO had been evaluated (Table 1). Statistical methods for analyzing the data were categorized and selected articles were classified according to the statistical method used.
The 2 main manufacturers of pulmonary artery catheters, Edwards Lifesciences, Irvine, CA (i.e., Baxter catheters) and Arrow International, Inc., Reading, PA (now a subsidiary of Teleflex Medical), both produce an electrical filament wire version of the thermodilution catheter that provides continuous CO readings, the CCO series and Opti-Q, respectively. Hospira also produces electric filament wire cardiac catheters that measure continuous CO in their Q2 system (Hospira Inc., Lake Forest, IL). The continuous CO method has been shown in the 1990s to be as accurate as the single bolus method in most validation studies,8 – 10 but its accuracy is limited during periods of hypothermia, such as coming off bypass during cardiac surgery and during liver transplantation.11,12 Another problem when using a continuous CO thermodilution catheter is the significant time delay when performing readings. The electric filament wire heater is cycled every 40 to 60 seconds, depending on the manufacturer. Because of averaging aimed at reducing noise and improving reliability, it can take up to 12 minutes for a change in CO to be fully registered by the monitor.8 Therefore, although continuous CO catheters can be used as trend monitors, they should not be used when rapid changes in CO need to be detected.
Transpulmonary thermodilution CO measurement has become popular in recent years. It avoids the need for a pulmonary artery catheter placement and its associated risks, including arrhythmias, catheter knotting, and pulmonary artery rupture and thrombosis. CO is measured using a thermodilution catheter placed retrograde in the femoral artery via the groin. The cold saline injectate is given via a central venous line. The best known of these systems is the PiCCO (Pulsion Medical Systems, Munich, Germany). Transpulmonary thermodilution CO has been shown to have an accuracy comparable to single bolus CO, although there are slight differences between the measurements, the pulmonary artery method reflecting right heart CO, and the transpulmonary method reflecting left heart CO, which is less affected by ventilation.8 When used in conjunction with an arterial pulse contour method, such as the PiCCO, the transpulmonary method can be used as part of a system to provide continuous CO readings and trend monitoring.
The detection of electrical resistance changes across the thorax during the cardiac cycle as a method of measuring CO dates back to the original 1970s description by Kubicek et al.13 and the development of the BoMed NCCOM3 in the 1980s by Bo Sramek.14 The BoMed was the first commercially produced minimally invasive continuous CO or trend monitor and made use of the emerging microprocessor technology available at that time. Like all of its successors, the BoMed was never shown to be sufficiently accurate or reliable to be widely accepted clinically.15 – 17 It is even questionable whether bioimpedance devices actually measure blood flowing out from the heart. They probably detect dimensional changes of the aorta, which is closely related.18,19 There are 2 significant problems when using bioimpedance technology: the effects of excessive lung water (pulmonary edema), and changes in peripheral resistance. Both affect the reliability of CO measurements.19 – 22 These negative influences help to explain the repeatedly poor results from validation studies in critically ill and septic patients.23
Persistence in marketing the bioimpedance method probably reflects its low cost, ease of application, and simplicity of use. However, despite all the misgivings about its reliability, bioimpedance has experienced something of a renaissance during the last few years. In addition to the BioZ (CardioDynamics, San Diego, CA [now a subsidiary of SonoSite]), a digitalized version of the BoMed, a number of newly launched bioimpedance devices were identified by the review, such as the PhysioFlow (NeuMeDx, Inc., Bristol, PA), the NICOMON (Larsen and Toubro Ltd., Mumbai, India), the NICCOMO (Medis, Ilmenau, Germany), and the CSM3000 (Cheers Sails Medical, Shenzhen, China).24,25 Yet another bioimpedance device, the ECOM (ConMed, Utica, NY), uses a novel approach to detect the bioimpedance signal by placing the electrodes on the distal end of an endotracheal tube, rather than using the conventional neck and thorax electrode configuration.26 There are not much data on the reliability of these new devices, but those that exist are not very supportive of their use, with limits of agreement of ≥30%. Neither are there good data on their ability to follow trends.
Electrical Velocimetry and Bioreactance Devices
Newer methods of processing the impedance signal were also identified. The AESCULON (Osypka Medical Services, Berlin, Germany) uses the second derivative (d2Z/dt2) rather than the slope (dZ/dt[max]) of the impedance wave to measure aortic blood flow, a method the Osypka company calls electrical velocimetry or cardiometry.3 The AESCULON has been validated on several occasions in both adults and children. Data from adults suggest it may be better than classical bioimpedance with limits of agreement at approximately the ±30% acceptance mark. In children, it seems less accurate. There are no reliable published data on the trending abilities of the AESCULON.
Another newly marketed bioimpedance device is the NICOM (Cheetah Medical, Portland, OR), which measures the bioreactance, or the phase shift in voltage, across the thorax.27,28 Bioreactance is thought to improve the signal-to-noise ratio of the bioimpedance signal thus improving impedance signal quality and reliability. Early reports of the NICOM's performance against thermodilution do not support a greater accuracy compared with thermodilution, but currently available data do not exclude an ability to track changes in CO reliably.27,28 Previous attempts to improve the reliability of the bioimpedance method by using advanced signal processing technology, such as spectral power in the IQ System (Renaissance Technologies, Newton, PA), never resulted in a successfully marketed monitor.29
Doppler Ultrasound Devices
Transesophageal echocardiography (TEE), developed in 1990, is now well accepted as a clinical tool for assessing cardiac function. To measure CO using Doppler, the cross-sectional area of the descending aorta and angle of the ultrasound beam to aortic blood flow need to be measured for calibration. The TEE probe can measure the diameter of the vessel using its ultrasound imaging function. A number of smaller, more portable, and dedicated esophageal Doppler probe devices have been developed, such as the HemoSonic 100 (Arrow International, Reading, PA [now a subsidiary of Teleflex Medical]) and the CardioQ (Deltex Medical, Chichester, UK). Deltex Medical also produced a pediatric version, the CardioQP.30,31 Similar to TEE, they measure blood flow in the descending aorta, and assumptions about how this relates to total CO are made, which can lead to imprecision. Also the cross-sectional area of the descending aorta varies in diameter during systole causing further imprecision. The HemoSonic probe has an imaging function to measure the cross-sectional area and angle of beam to the aortic flow. The CardioQ uses an algorithm to determine these calibration constants, and this may lead to further imprecision. Validation studies against thermodilution show these devices to be inaccurate, particularly when used in children. However, if the probe is well positioned in the esophagus, these devices can be used as trend monitors and rapidly detect changes in CO, making them useful for monitoring therapeutic interventions such as fluid administration32 – 34 in anesthetized or critically ill patients.
CO measurements can be derived from the arterial pulse wave. The area under the pulse wave is related to stroke volume and thus CO. Conversion of the pressure wave to a flow wave is required for reliable CO monitoring. The classic transformation involves using a Windkessel model of the circulation.35 Wesseling et al.35 developed a method called model flow to determine CO. Today, there are 3 well-known commercial devices on the market, the FloTrac-Vigileo (Edwards Lifesciences), the PiCCO (Pulsion Medical Systems), and the LiDCO (LiDCO Ltd., London, UK). The most investigated of these systems is the FloTrac-Vigileo with >20 validation studies in the last few years. Pulse contour systems require calibration, usually with an indicator dilution technique, but recently self-calibrating software has been developed for the FloTrac. However, in a recent study and literature review by Chatti et al.,36 only 3 of 15 published studies validating the FloTrac had limits of agreement of <30%. Similarly, Biancofiore et al.37 found only 2 of 14 FloTrac studies that satisfied the criteria. These later authors also showed the lack of reliability of the FloTrac algorithm after changes in peripheral resistance; their cohort was cirrhotic patients undergoing liver transplantation.37 Patients with cirrhosis have high CO and low peripheral resistance that fluctuates during transplant surgery. Other authors have also shown the device's inability to correctly adjust for peripheral circulatory changes.38 Recently, de Wilde et al.39 compared the trending abilities of 3 devices: the FloTrac, the HemoScope (esophageal Doppler), and a model flow device (BMEYE, Amsterdam, The Netherlands [patient monitor that includes finger cuff technology]) against thermodilution CO in intensive care patients. Three maneuvers that altered CO were used: (1) increased intrathoracic pressure, (2) leg raising, and (3) head-up tilt. Of the 3 devices, only the FloTrac failed to detect CO changes,39 which was surprising because the finger cuff model flow method was able to cope with circulatory changes. Edwards Lifesciences has recently modified the FloTrac CO algorithm, and validation data collected by Mayer et al.40 showed improved agreement with thermodilution when using the most recent software upgrade. There have also been recent calls for studies that specifically observe the validity of changes in pulse contour CO.6 At present, there are only a few studies or data analyses that support the trending ability of any of these 3 devices. Compared with their main minimally invasive competitor Doppler CO, pulse contour methods are less reliable as trend monitors because they currently fail to compensate for circulatory changes, such as peripheral resistance, a factor that does not seem to affect Doppler readings.41
PERFORMING TREND ANALYSIS
Results of Literature Search
This review of the CO monitoring literature published between 1997 and 2009 showed that the majority of published studies only evaluated the measurement of the actual value of CO and that less than one-fifth addressed the issue of trending (Table 1). Two hundred two articles were identified, but only 41 of these addressed trending. Three additional articles published before 1997 that contained key statistical methods were also included.23,42,43 The reference methods most often used were a surgically placed flowprobe on the aorta in 3 trend analysis studies (animal studies) and thermodilution in 34 studies (animal and human) (the single bolus pulmonary artery catheter method was used most often). These studies compared serial CO measurements from a reference and 1 or more (up to 5) new devices used simultaneously in the same subject. In 18 of these studies, absolute change in CO was used, in 9 studies, the percentage change in CO was used, and in 14, the direction of change in CO (i.e., ΔCO increases or decreases) was used as the principal method to assess trending (Table 2).
We were able to identify several common statistical themes (Tables 2 and 3). Trend data could be analyzed:
- By using a table or histogram format and applying serial statistical (Bland and Altman) comparisons,50,55
- Graphically as a time plot, which was most useful in animal studies,32,51
- By plotting data on a scatter plot and using regression analysis and/or the Bland and Altman method, or
- By using the direction of change as a statistic (mainly clinical studies).
When using direction of change, some authors (1) calculated trend scores based on agreement of the direction of change of serial CO readings (mainly animal studies), whereas others (2) drew a 4-quadrant plot to assess the degree of agreement of ΔCO readings from groups of subjects (mainly clinical studies).
Some authors further refined the 4-quadrant plot by applying exclusion zones for small changes in CO (Table 3). Receiver operating characteristic (ROC) curve analysis was used to determine an optimal exclusion zone on the 4-quadrant plot.
In the 23 studies in which a more in-depth trend analysis was performed, drawing a 4-quadrant plot and analyzing the concordance were the most frequently used methods of data analysis (Tables 2 and 3). All except 2 of these were human studies.3,56 Trend analysis was performed most frequently in studies that evaluated pulse contour methods (Table 1).
Discussion of Animal Studies
Laboratory animal studies allowed the trending ability of a CO monitor to be vigorously tested over a range of circulatory conditions, to an extent that was not possible in human studies. Furthermore, an accurate and reliable reference method, such as a flowprobe placed surgically around the ascending aorta, could be used to determine the CO with a high degree of certainty. The flowprobe is a true “gold standard” reference method with a precision of ±1% to 2%.59,60
Regression analysis seems to be appropriate for these types of data, particularly if a gold standard reference method, such as an aortic flowprobe, is used. Regression shows the relationship between repeated measures of CO (Fig. 1). Four laboratory studies were identified that demonstrated the use of regression to show trending.48,56,58,61
A number of authors used a modification of regression analysis62 – 65 known as Lin's concordance,66 or the interclass correlation. Unlike Pearson's correlation coefficient (r), which is based on the line of best fit (y = mx + c), Lin's method uses the line of identity (y = x) (Fig. 1). Thus, Lin's method assures that the calibrations of the 2 methods being compared are of equivalent scale.
Some authors conducting laboratory studies showed trending ability using time plots.32,51 When a gold standard reference method accurate to ±1% to 2% was used, these authors were able to show visually whether the test device accurately tracked changes in CO. This approach was further refined by some authors by calculating a trend score based on the direction of change. Bajorat et al.32 used this method in animals to compare 5 different test methods against a flowprobe reference. Bein et al.51 compared pulse contour to the less-reliable thermodilution method using an animal model of uncontrolled hemorrhage from the incised liver. Although thermodilution is less precise, these authors were able to average data from 13 animal experiments and show changes in CO at 8 interventional steps (Fig. 2). From their CO against time plot, they had sufficient evidence to conclude that pulse contour did not track CO during extreme hemorrhage because the 2 sets of CO measurements were shown to diverge. Several other authors have since used hemorrhage followed by resuscitation animal models to show trending.56,58 Although very simple in design, and often lacking any statistical significance testing, time plots clearly have a role in showing trending ability when experimental animals are used.
Discussion of Clinical Studies
In the clinical arena, the number and range of CO readings that can be collected from each subject are reduced compared with animal studies, and the reference methods available are less precise. Fewer readings from a larger cohort of subjects is the usual practice, and this prevents the effective use of time plots or regression analysis to demonstrate reliable trending. Animal studies consisted of 10 (6–13) animals (median [quartiles]), whereas clinical studies enrolled 29 (20–42) subjects (data from review, 1997–2009). Therefore, alternative analytical approaches are needed. The review showed that analytical methods based on the difference between consecutive CO readings, or ΔCO, were used mainly when single bolus thermodilution was the reference method. Adaptations of the Bland and Altman method and regression analysis were used, with the notable development of direction of change or concordance analysis (Table 2).
The majority of clinical studies in our review in which trending was assessed used the following: (1) a setting with potentially wide fluctuations in CO values, such as cardiac, or more recently, liver transplant surgery and its aftercare; (2) a set number of data collection points at well-defined stages throughout the study period, usually 8 to 1037,50,51,55,67 – 69; and (3) the recruitment of patient numbers of at least 20 to 25.6,46,47,49,52,53
It was noticeable that the more recently published studies tended to have more structured design protocols, with multiple well-defined times for data collection.
Use of the Bland and Altman Method
In 2002, Linton and Linton70 recommended the use of the Bland and Altman method in preference to regression for analysis of ΔCO data. However, it is not particularly clear from the article by Linton and Linton or from other subsequent articles how the limits of agreement from the Bland and Altman plot of ΔCO should be interpreted and which acceptance criteria should be used. We found the Bland and Altman method useful only when comparisons between more than 2 devices were made, and the reference method, usually thermodilution, acted as a common reference point. For example, de Wilde et al.39 (2009 article) used Bland and Altman comparisons at 3 intervention steps to compare 3 different minimally invasive devices, thermodilution providing this common reference point.
When CO measurements are compared, classic Bland and Altman analysis assumes that data points are unrelated and from separate subjects and experiments.4 However, in studies that address trending, repeated measurements from the same subject or clinical case must be used. This coupling of data results in smaller standard deviations (SDs) and produces limits of agreement that underestimate the true variability of the readings. Both Bland and Altman71 and Myles and Cui72 have published articles that provide guidance on how to correct the analysis and limits of agreement in the repeated-measures model.
However, this modification only addresses the precision of each reading, not trending. Furthermore, when Bland and Altman analysis is applied to trend data, 4 rather than 2 CO readings are used to generate each data point (ΔCO = COa − COb). Statistically speaking, the df for the analysis are increased from 2 to 4 and this increases the size of the SD and thus widens the resulting limits of agreement. If the SD of ΔCO is derived by the adding of variances method (SD = √[SDa2 + SDb2]), referred to in the article by Critchley and Critchley,7 one will appreciate that the limits of agreement are widened by a factor of 1.4 (or √2). Paradoxically, the SD used to derive these limits of agreement is also decreased because the measurement error of CO has 2 main components, random and systematic (calibration). Whereas the random effect is increased because of the increased number of df, the systematic (calibration) effect is eliminated because it is a constant due to the serial readings or coupling effect (ΔCO = COa − COb). Because the relative contributions from these different components are difficult to measure and proportion (appropriate) values to, one is unable to develop reliable criteria to test the limits of agreements from Bland and Altman plots in this setting. Therefore, we fail to see how Bland and Altman analysis can be used to confirm trending ability when analyzing ΔCO data for a simple comparison of 2 devices.
The Four-Quadrant Plot
In 1994, Perrino et al.43,44 first described an analytical method based on regression analysis and concordance. They plotted the test ΔCO against the reference ΔCO on a 4-quadrant scatter plot (Fig. 3). Inspection of the plot showed whether the data were randomly distributed or fell along the line of identity x = y, and thus indicated whether there was trending ability of the test device. The novel aspects of their methodology were the use of direction of change statistics, the measurement of concordance, and the refinement of their concordance analysis by using an exclusion zone, which they optimized using an ROC curve analysis. Ten clinical studies in our review used this type of analysis (Table 3).
At the center of the plot, data tend to be randomly distributed among the 4 quadrants, whereas more peripherally the data tend to fall into 1 of the 2 quadrants of agreement (upper right and lower left), depending on the degree of agreement between the reference and test methods. The concordance rate is simply a measure of the number of data points that fall into 1 of the 2 quadrants of agreement. The concordance is usually expressed as a percentage of the total number of data points used in the plot and is a direction of change statistic.
Data points at the center of the plot correspond to small changes in CO and do not reflect trending ability. The directions of change of these central data points are random and thus unpredictable when trending is assessed. They reflect random noise in the measurement system. It is only as the data points spread away from the center of the plot, and the change in CO becomes larger, that the change in CO becomes the dominant statistical effect and thus trending ability can be reliably assessed using direction of change as a statistical measure. If trending exists, the direction of change of these noncentral data points will usually agree; however, if trending does not exist, there will be a high degree of disagreement, and the concordance rate will be low. Thus, exclusion zones have been developed to eliminate the less-predictive data points that lie near the center of the plot (Fig. 3). However, guidance on suitable exclusion zones and what are acceptable concordance rates are currently lacking in the literature.
ROC Curve Analysis
Several different exclusion zone criteria have been described in the literature. In 1998, Perrino et al.44 excluded values when ΔCO was <1 L/min,44 whereas other authors46,52,53 have used criteria of <0.5 L/min. More recently, (2008–2009), exclusion criteria based on percentage change, such as <10% or 15% have been used.3,37,39 – 41,57
ROC curves have become popular for statistical analysis in medical research.73,74 Four studies were identified in this review in which ROC analysis was used. In 3 studies, ROC analysis was used to make judgments about the discriminative power of different ΔCO values.3,43,57 For a test method (usually pulse contour) versus thermodilution design, an optimal ΔCO exclusion value of 10% to 15% was found. Normalizing data and expressing results as percentages overcome the scaling problem that different study populations have different ranges of baseline CO. To perform an ROC analysis, study data are used to calculate concordance rates when applying different exclusion zones (0%–30%). The sensitivity and specificity for each exclusion zone are plotted to generate the ROC curve, and an optimal exclusion zone is determined from the curve. Perrino et al.43,44 were first to apply this method to CO validation studies. Boyle et al.41 have also used ROC curves to assess the agreement between the USCOM and thermodilution. Data from low, average, and high CO values were plotted. However, as was the case with many studies in the review, the purpose of the analysis was not particularly clear. Another interesting observation was that when the test method was an aortic flowprobe, rather than thermodilution, which lacks precision, the exclusion zone could be reduced to 5% and 10%.56
Acceptable Concordance Rates
Ten studies were identified in the literature in which concordance rates were quoted. In studies in which agreement was poor according to the >30% criteria,7 the concordance rate ranged from 67% to 88% when exclusion of central data was applied (Table 4).37,41,52 Zones of 0.5 to 1.0 L/min or 15% were used. In studies in which agreement was good, and not all of these provided limits of agreement, the concordance rates were 92% to 100% when exclusion of central data was applied.3,43,44,46,53,56 When exclusion zones were not applied to the data, the concordance rates decreased to <80%, even when there was trending ability because of the central zone effect (Fig. 3). Based on these data, we conclude that exclusion zones of 0.5 to 1.0 L/min or 15% are optimal, when thermodilution is the reference method, and a concordance rate of >90% to 95% indicates reliable trending ability.
Limitations of Concordance Analysis
Despite the apparently successful use of concordance analysis in several recent studies, the method has its weaknesses. Perrino et al.43,44 should receive credit for identifying the need for exclusion zones to reduce the noise from small changes in CO when using the 4-quadrant plot. However, just as small changes in ΔCO add little to the discriminating power of the analysis, so also do large changes in ΔCO, because they will nearly always be in agreement. There is an overall trend in the data as the value of ΔCO increases from 50% disagreement to total agreement. A critical band of ΔCO values can be defined somewhere between 0.5 and 1 L/min, or 10% and 20% change, where the ability to reliably detect changes in CO is maximal. Data that lie outside of this band should ideally be excluded for the analysis because they do not contribute to the assessment of trending ability. However, the position of this band on the ΔCO scale will also depend on the range of CO readings being studied. Thus, percentage changes in CO may be more appropriate. ROC curve analysis goes some way to defining this critical band by determining its lower limits.
Furthermore, the distribution or spread of ΔCO values will also affect the concordance rate. If the majority of ΔCO values tend to be small or large, then they will create a skewed distribution of data points, which will under- or overestimate the concordance rate, respectively. By restricting ΔCO data to a predetermined band of interest, this sampling bias can be reduced.
However, limiting data analysis to a narrow sampling band will result in a significant proportion of the data not being used and may cause problems because the sample size for the analysis may be insufficient.
DEVELOPING A NEW APPROACH
Use of Polar Coordinates
Direction of changes is a very simple but crude measure of how well 2 measurements trend. Important aspects of the measurement, such as (1) the magnitude of the underlying CO change, and (2) the degree of agreement, are totally ignored.
The 4-quadrant plot presents the ΔCO data as a cartesian (x, y) vector that has both direction and magnitude (Fig. 3). These attributes should be retained. Therefore, we suggest converting the x-y values to polar coordinates, where agreement is shown by the angle the vector makes with the line of identity (y = x) and magnitude of change by the length of the vector (Fig. 4). Thus, statistical measures that fully represent the magnitude of ΔCO and its degree of agreement are retained. From these data, a new polar plot that shows agreement as the angle θ (angle made by ΔCO vector with the line of identity [y = x]) against the change in CO as the radian (distance of data point from center of polar plot) can be drawn. In Figure 4, one can see 2 sequential sets of CO readings: (2, 2.5) and (6, 4). These 2 data points produce a vector that represents ΔCO. The origin of this vector (2, 2.5) has been superimposed onto a polar plot to show how the angle to line of identity (perfect agreement) is derived. Note that in the polar plot, the line of identity is rotated through 45 degrees to lie on the horizontal, zero rotation, polar axis. In the main polar plot (Fig. 5), data that agree will have an angle close to the horizontal axis (0–180 degrees), whereas data that show little agreement will have an angle close to the vertical axis (90–270 degrees). When the change in CO is a decrease (negative change), it is represented in the 2 left quadrants of the polar plot.
In Figure 5, 4 polar plots have been created using (1) simulated data generated randomly by an Excel spreadsheet (Microsoft Office Excel 2007; Microsoft Corp., Redmond, WA), and (2) data taken from 1 of our previous articles.37 In these 4 plots, we have used the average ΔCO value ([ΔCO(reference) + ΔCO(test)]/2) rather than the magnitude of x-y vector (i.e., hypotenuse of triangle: z = √[x2 + y2]) for the radius because mean ΔCO better represents the true change in CO. Details of how to create such polar data from cartesian (x, y) data are provided in Appendix 1.
In many aspects, the polar plot is similar to a Bland and Altman plot,4 and thus limit lines (horizontal dotted lines) have been added to the plots at 0.5 L/min ΔCO to facilitate assessment of the degree of agreement and hence trending ability (Fig. 5). In the good and acceptable trending plots (upper 2 plots), it can be seen that most of the data points lie within the 0.5 L/min boundaries, indicating that a ΔCO of >0.5 L/min, or 10% (mean CO for simulation was 5 L/min), would have a high chance of predicting a true change in CO (80%–90% with low chance of type II error). The simulation settings for the good and acceptable data plots were within those needed to fulfill the <30% criteria of Critchley and Critchley.7
In the lower 2 plots, data that do not fulfill the <30% criteria of Critchley and Critchley7 and do not show good trending are used (Fig. 5). The lower left plot uses simulated data where the precision of the test data was very poor (±60%), and the lower right plot uses data from liver transplant patients where limits of agreement and concordance analysis were poor.37 In these plots, a larger proportion of the data fell outside the 0.5 and 1.0 L/min limits. Thus, one cannot say with any certainty that even with a ΔCO of >1 L/min, or >20%, that a true change in CO has occurred and thus the chance of a type II error is high.
Although there have been >200 CO validation studies published in the last 12 years, only a minority of them addressed CO trending. Published studies on CO trending can be divided into those that involve laboratory animals and those that involve hospital patients. Trending should first be demonstrated in the animal laboratory against a true gold standard method, such as an aortic flowprobe, before human testing is performed. The statistical approaches to analyzing animal data are well described, and both time plots and regression analysis can be used. In contrast, there seems to be no satisfactory statistical method of showing trending ability in the clinical setting. The most popular method in use today is the 4-quadrant plot and concordance analysis, but these methods have limitations.
One possible solution, presented in this review under the section Developing a New Approach, is the use of the angle and length of the ΔCO vector (polar coordinates) to show the predictability between different values of ΔCO. The polar coordinates approach preserves and uses important information describing the data that are lost when using concordance analysis. Polar plots can also be used in a similar manner to Bland and Altman plots to determine the limits of predictability of ΔCO.
Finally, few studies in our review addressed the issue of the clinical utility of CO monitoring devices, because mainly comparative CO studies were reviewed. Randomized controlled trails are also needed to show whether there is any clinical benefit. One example was the BIG/ESCAPE trial that evaluated the BioZ.75 Therefore, to fully evaluate a new CO monitor, one needs to perform animal (phase 1), human/clinical (phase 2), and clinical utility/outcome (phase 3) studies.
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APPENDIX 1: CONVERSION OF CARTESIAN DATA TO POLAR COORDINATES
Conversion of change in cardiac output (ΔCO) in an (x, y) format can be conveniently performed using an Excel spreadsheet (Microsoft Office Excel 2007; Microsoft Corp.). The data should be arranged in 2 columns, X (reference ΔCO) and Y (test ΔCO). Each row represents a separate pair of ΔCO measurements. The first row should contain column headings. Serial CO measurements can be converted to ΔCO data by simple subtraction of CO data from successive rows (i.e., Xa − Xb, Ya − Yb). Both positive and negative directions of change should be used.
Four new columns need to be created. First, let column A contain ΔCO (X), or reference data and column B contain ΔCO (Y), or test data. The new columns are as follows:
- MEAN ΔCO (column C): Insert the function = ABS(A2 + B2)/2. This function generates the mean ΔCO value for the reference and test values in the first row of data (row 2). Row 1 contains column headings. ABS converts to the absolute or positive value of ΔCO.
- QUADRANT (column D): Insert function = IF(B2 > 0, 0, 1). This is a logic function that generates a 0 if the reference (X) value is positive and a 1 if the reference is negative. This variable is used to overcome the problem of generating the correct value in radians from the tangent equation when data come from different quadrants of the plot. Its purpose is made clearer in the next paragraph.
- RADIANS (column E): Insert the function = ATAN(B2/A2) + ([D2 − 0.25] * 3.142). This function generates the angle θ that the ΔCO vector makes with line of identity (y = x) in the cartesian plot. The units are radians and can be negative in value as well as positive. This angle will be used to generate, together with mean ΔCO (or radius), data points on the polar plot. By dividing the test ΔCO (Y-value[B2]) by the reference ΔCO (X-value[A2]), one is able to calculate the tangent of the angle that the XY vector makes with the X-axis in the cartesian plot. This tangent is converted to radians by the Excel function ATAN. However, to construct the polar plot, one needs the angle of the vector with line of identity, not the X-axis, which is offset 45 degrees. Also, the ATAN(B2/A2) function does not provide the correct number of radians for angles outside the first quadrant. Therefore, a second function ([D2 − 0.25] * 3.142) is added. Briefly, in this function, the D2 adjusts for the quadrant together with ATAN, which can return negative as well as positive values; the 0.25 introduces a 45-degree rotation, and the 3.142 is the value of π, which converts the value of D2 − 0.25 to radians. There are π radians in 180 degrees.
- ANGLE (column F): Insert the function = E2 * 180/3.142. This function simply converts the angle in radians to degrees, which are more comprehensible.
- Now use the FILL DOWN function in Excel to create columns of serial data from your serial ΔCO data.
The final step is to generate the polar plot. We used the software graph drawing program SigmaPlot 2001 for Windows version 7.1 (Systat Software, Inc., San Jose, CA). Data from column C, mean ΔCO, and column F, angle, were exported and used by the polar plot graph drawing function.© 2010 International Anesthesia Research Society