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Ann Thorac Surg 1996;62:1351-1358
© 1996 The Society of Thoracic Surgeons
Department of Thoracic and Cardiovascular Surgery, Lahey Hitchcock Medical Center, Burlington, and Boston University Graduate School of Management, Boston, Massachusetts
Accepted for publication June 5, 1996.
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Abstract |
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 TopFootnotes Abstract IntroductionMaterial and MethodsResultsCommentAppendix 1. The Statistics...References |
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Methods. We employed statistical quality control charts (X - s, p, and u) to analyze perioperative morbidity and mortality and length of stay in 1,131 nonemergent, isolated, primary coronary bypass operations conducted within a 17-quarter time period.
Results. The incidence of the most common adverse outcomes, including death, myocardial infarction, stroke, and atrial fibrillation, appeared to follow the laws of statistical fluctuation and were in statistical control. Postoperative bleeding, leg-wound infection, and the summation of total and major complications were out of statistical control in the early quarters of the study period but showed progressive improvement, as did postoperative length of stay.
Conclusions. The incidence of morbidity and mortality after primary, isolated, nonemergent coronary bypass operations may be described by standard models of statistical fluctuation. Statistical quality control may be a valuable method to analyze the variability of these adverse postoperative events over time, with the ultimate goal of reducing that variability and producing better outcomes.
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Introduction |
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TopFootnotesAbstractIntroductionMaterial and MethodsResultsCommentAppendix 1. The Statistics...References |
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Just as the modern industrial age and factory production represented a paradigm shift in the late 19th century, the refinement of mass production techniques through the application of statistical quality control (SQC) represented a similar evolutionary change in the 20th century. Statistical quality-control concepts were first elucidated by Dr Walter Shewhart [1, 2] of the Western Electric Bell Laboratories more than 60 years ago and were popularized through his seminal works, Economic Control of Quality of Manufactured Product [1] and Statistical Method From the Viewpoint of Quality Control [2], published in the 1930s. These concepts were expanded on and incorporated into the concept of total quality management, first in Japan in the 1950s and subsequently in this country by such leaders as W. Edwards Demming, Joseph Juran, and Armand Feigenbaum. Today, these methods are an integral part of most large manufacturing or service industries throughout the world. The goal of these techniques is to improve process by achieving optimal output with a minimum of variability, nonconformities, and rejects.
This article explores the possibility of applying the techniques of SQC to a surgical procedure that, despite the greater inherent variability of its biological subject, still bears some similarity to the manufacturing process. Most coronary artery bypass graft (CABG) operations are performed frequently by a small group of individuals who constitute a team. They follow certain regular routines and protocols and have both a desired output and well-characterized and defined adverse outcomes (for example, death, myocardial infarction, or stroke).
In this study, we investigate whether the fluctuating incidence of certain surgical outcomes follows the laws of statistical probability, thus permitting them to be analyzed by standard SQC techniques. If so, then it may be possible to distinguish this random fluctuation from real changes (favorable or unfavorable) in surgical results.
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Material and Methods |
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TopFootnotesAbstractIntroductionMaterial and MethodsResultsCommentAppendix 1. The Statistics...References |
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Statistical Methods
Standard SQC methodology and formulas were employed [3–12] and are presented in the Comment section and Appendix 1. X - s Charts, based on the normal distribution, were used to analyze the variability of postoperative length of stay. Attribute (p) charts, based on the binomial distribution, were used to analyze the presence or absence of specific adverse postoperative outcomes, including death, myocardial infarction (a new Q-wave or a postoperative creatine kinase-MB level 
150 IU), stroke (a new, persistent neurologic deficit), reexploration for bleeding or tamponade, sternal infection or mediastinitis (infection of the sternal wound requiring reoperation), acute renal failure requiring dialysis, leg wound infection, and atrial fibrillation. Occurrence or nonconformity (u) charts were employed in the serial analysis of total complications per patient and total major (total minus atrial fibrillation) complications per patient. Only events that occurred in the hospital were recorded and analyzed, and we recognize that some important late complications may not be included.
In all cases, the common practice of employing ± 3 sigma (
= standard deviation) upper and lower control limits (UCLs and LCLs) was followed. For variable subgroup sizes, which were always the case in our study, separate control limits were calculated for each sample rather than employing averages.
Commonly accepted criteria for determining the presence of statistical control were employed [6, 7, 9–11]. These criteria are found in the Comment section and Appendix 1.
The control charts in this article were adapted from data generated by SPSS version 6.1 for Windows, Base System (SPSS, Inc, Chicago, IL) and were run on a 486DX33 personal computer.
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Results |
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TopFootnotesAbstractIntroductionMaterial and MethodsResultsCommentAppendix 1. The Statistics...References |
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charts in Figure 2, and the X - s chart in Figure 3. Table 1 summarizes the process mean values and the statistical control chart pattern for these charts. Review of the p, u, and X - s charts from our data from 17 consecutive quarters reveals that the major adverse outcomes, including death, myocardial infarction, and cerebrovascular accident, appear to be in stable statistical control and to follow the laws of statistical fluctuation. Interestingly, the charts of myocardial infarction and cerebrovascular accident rates appear to mirror each other despite obvious difference in the risk factors that might contribute to these two complications. Atrial fibrillation, the most common complication after heart operations, was also in statistical control. Postoperative bleeding was initially out of statistical control (seven consecutive points above the central line). This was subsequently corrected with minor changes in our postoperative management of the coagulation system. Leg wound complications showed an early lack of control (two of three consecutive points beyond 2 sigma). Subsequently, a more favorable out-of-control state was evidenced by six consecutive points below the central line. This improvement was attributed to minor changes in our techniques for harvesting vein and closing leg wounds. The incidences of acute tubular necrosis and sternal infection were so low as to preclude the use of control-chart methodology. Occurrence charts revealed that total complications per patient were out of statistical control in quarter 2 but were in control for the remainder of the study period, as were major complications. The X chart of postoperative length of stay revealed unfavorable lack of statistical control in the early part of the study period (one point beyond 3 sigma, seven consecutive points above central line), but this improved significantly over time. The s chart demonstrated multiple points beyond the control limits, then a favorable downward trend in quarters 13 through 17, which suggests a progressive reduction in variability and a more predictable and stable length of stay. We attribute this improvement to a number of factors, including refinement of practice patterns, an increase in case volume leading to greater efficiency and standardization, the introduction of critical pathways and case management, and the addition of new staff with experience in short-stay protocols after open heart operations.
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Comment |
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TopFootnotesAbstractIntroductionMaterial and MethodsResultsCommentAppendix 1. The Statistics...References |
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Any measurable output, such as size of a manufactured product, the number of defects in a bolt of cloth, or the fraction of defective units in a manufacturing run, has variability over time. Depending on the type of data being studied, SQC models this variability using a normal, binomial, or Poisson distribution. When the appropriate distribution and the corresponding control chart are determined, the data are analyzed graphically to determine whether they fall within appropriate UCLs and LCLs.
Traditionally, based on the empiric work of Shewhart [1, 2], UCLs and LCLs have been established at ± 3 sigma (standard deviations) on either side of the mean. For distributions that are normal or that can be approximated by the normal distribution, 99.7% of observations should lie within these limits. Because some data are clearly nonnormal and because the normal distribution is often not an accurate approximation to the Poisson or binomial distributions, exact probability limits are sometimes recommended [9]. However, it is the usual convention to ignore nonnormality and empirically use ± 3 sigma limits as a practical compromise [3].
Fluctuation within the UCL and LCL is known as common or inherent variation and is caused by many small, persistent sources of fluctuation in the input materials or the process itself [6, 9, 10]. In the instance of a surgical procedure, such normal perturbation might include fluctuations in severity of patient risk factors, operating team members, or equipment. A process whose output falls entirely within the ±3 sigma range of common cause variability is said to be "in statistical control." This term does not necessarily imply that the result is optimal but simply that further improvement will require changes in the process itself by reducing inherent variation.
Fluctuation outside the UCL and LCL is referred to as extrinsic or special variation and is the result of factors that are extraneous to the process. Control charts exhibiting such variation are said to be "out of statistical control." This term does not necessarily mean that the output is unacceptable but simply that the variation is statistically greater than that which could be accounted for by inherent fluctuation in the process. In the case of p or u charts or the s portion of an X - s chart, out-of-control points below the LCL may actually indicate an improvement in the process. By establishing the normal limits of variability for a process, control charts help prevent overadjustment ("false alarm") or type I errors, which are changes made to a process to correct for variation that is actually inherent, and underadjustment or type II errors, which represent failure to respond to extrinsic causes of variation because of the false belief that they represent inherent fluctuation [6, 9]. These errors are analogous to the type I and type II errors of traditional statistics.
In the health-care profession, surgeons have always been at the forefront of efforts to assess the end results of their interventions. These efforts include the prescient work of Dr E. A. Codman at the Massachusetts General Hospital in the early 20th century [13]. Traditionally, quality and end-result assessment by surgeons has consisted of morbidity and mortality conferences that focused on poor results and often resulted in placing physicians in a defensive posture. The other primary focus of such efforts has been for research and academic purposes, typically comparing the results of two treatment periods or methods, protocols, or groups. Statistical quality control differs in that it focuses on the overall process and its variability when followed over time. Furthermore, unlike traditional statistical methods of comparing surgical data, which often require assumptions regarding the underlying probability distributions, statistical process control sets up hypotheses regarding such distributions that are then tested graphically [10]. Statistical quality control also takes into account the order of the data over time.
Statistical quality control methodology cannot be applied to all surgical procedures. In general, the most appropriate operations for such analysis are those performed frequently and in a relatively standardized fashion by a small team. Examples of surgical procedures that might be appropriate for such analysis would include coronary artery bypass, total joint replacement, transurethral resection of the prostate, laparoscopic cholecystectomy, hernia repair, laminectomy, and cataract extraction with lens implantation. Procedures that would not be appropriate, at least in most institutions, would include the Whipple procedure, shunts for portal hypertension, and resection of cardiac tumors. The patients should also be separable into homogeneous subsets for purposes of analysis, the procedures should have a well-characterized range of favorable and unfavorable outcomes, and the statistical conditions must be met for the use of each specific type of control chart (see Appendix 1).
Several important caveats must be acknowledged with regard to the use of SQC in cardiac surgery. First, although SQC models the variability of events over consecutive time periods, it should not be confused with hazard function analysis. The latter is used to describe the time-dependent, instantaneous risk of an event after an operation, whereas SQC simply records the event as absent or present for each patient in a series of sample periods. Second, this is not a risk-prediction methodology for individual patients but rather a method of studying process variability over time. Third, except in the most general terms, it is difficult to compare this type of SQC analysis from one institution to another.
Finally, it may be argued that the CABG procedure has so much inherent variability (patient type and risk severity) compared with a manufacturing process that it is impossible to use SQC methodology. We have attempted to satisfy this objection by limiting the study to nonemergent, isolated, primary CABG procedures, thus eliminating some of the most significant factors that increase the odds ratios for morbidity and mortality. However, even within this grouping, appreciable inherent variability remains, particularly with respect to the impact of such variables as ejection fraction, age, and risk of stroke. One way to resolve this objection would be to stratify the study groups further (for example, patients between the ages of 40 and 60 years with no history of stroke and an ejection fraction greater than 0.40), which would result in a large number of even more homogeneous groups for analysis. However, only the busiest of surgery programs would have enough patients to ensure adequate size of each sample. We chose not to stratify patients further, based on the following assumptions: (1) some inherent, common-cause variability of input is present in all processes [6], including factory production; (2) most risk factors, such as age, ejection fraction, and recent myocardial infarction, are distributed evenly throughout the study groups; (3) for most patients within the study group we defined, the absolute value and dispersion of risk is relatively low; (4) modern surgical techniques have ameliorated the adverse impact of many important risk factors (for example, modern cardioplegic protection of the depressed or acutely ischemic myocardium); and (5) true "outliers" with disproportionately high risk occur randomly and infrequently within the study groups. Although patient-to-patient variability of risk is a theoretical disadvantage to the use of control charts for surgical data, our results did not demonstrate frequent "false alarms" exceeding the control limits, which would have occurred if the occasional very-high-risk patient distorted the data.
A quality-control approach to high-volume surgical procedures offers numerous potential advantages to the health-care system. These advantages include (1) graphic methodology; (2) the ability to distinguish inherent from extrinsic causes of variability, thus avoiding type I and type II errors; (3) fewer adverse events once the extrinsic sources of variability are determined and their causes are established and corrected; (4) for measurement data, such as postoperative length of stay or cost, SQC monitors the progressive shift of the process mean to optimal levels; (5) improved ability to assess the impact of changes in the process (for example, conversion from crystalloid to blood cardioplegia, or the addition of retroplegia); and (6) a more predictable outcome for patient, physician, and insurer. Finally, when the outcome of the process is more predictable, (7) the need for capital resources and personnel can be estimated better and is subject to less variability. Scheduling, stocking, and competitive pricing can be achieved more efficiently and cost-effectively.
Application of SQC does not require the collection of additional data beyond that which any cardiothoracic program should already have available. It simply represents a different way of analyzing this data. Computer programs are available that will expediently perform these analyses. The most difficult task is deciding which probability distribution, and thus which control chart, is most appropriate for the data, and then choosing homogenous and rational subgroups to analyze.
Control-Chart Basics
RATIONAL SUBGROUPING.
The process being studied must be homogenous, so that the differences between inherent and extrinsic variability can be determined. For example, it would be inappropriate to analyze patients undergoing isolated primary CABG with patients who had reoperation or concomitant replacement of the aortic valve. The latter, more complex procedures would represent separate processes.
ADEQUATE SUBGROUP SIZE.
In manufacturing processes, it is common to have a set number of output measurements in each subgroup. For the analysis of coronary bypass operations, it is much more convenient to analyze the patients on a time interval, typically by week, month, or quarter. This analysis will result in some variability in the size of the subgroup. If not more than 25% variation exists in the number of cases per subgroup, it is usually acceptable to use the mean subgroup size [6, 8] in deriving the control limits. Otherwise, especially because computer programs are readily available, the accepted practice is to calculate varying control limits for each subgroup. Subgroup size should be small enough so that conditions during the sampling period are uniform (minimal within-group variation) and so that the averaging of a large number of observations does not obscure real differences. Conversely, particularly for p or u charts, the size of the subgroup should be large enough to yield a few nonconforming units per subgroup [3, 6]. In the instance of cardiac surgical morbidity and mortality, which ranges from 2% to 5% for most adverse outcomes, a subgroup size of about 50 to 100 patients would be desirable. It is this goal that led us to choose quarterly recording of data, but other programs might accomplish this goal in a biweekly or monthly time frame.
ADEQUATE NUMBER OF SUBGROUPS.
Usually, 20 or more reporting periods are desirable, and no fewer than 10 periods are acceptable for statistical validity [10]. We analyzed 17 consecutive quarters for our pilot study. If major changes occur in the patient population, staff, procedures, or equipment, the relevant dates should be noted to aid in interpreting the control chart. Profound and permanent changes in these components of the process may necessitate the start of a new control chart.
INTERPRETATION OF CONTROL-CHART PATTERNS.
Control charts usually consist of a central line (the process mean), a UCL, and an LCL, which are typically set at ± 3 sigma in standard practice [6, 7, 9–11]. Most points should lie near the central line (two-thirds within ±1 standard deviation of the mean), few points should lie near the control limits, and no points should be outside the control limits. Other commonly accepted criteria for lack of statistical control (nonrandom variation) include (1) two of three consecutive points beyond 2 sigma on the same side of the central line, (2) four of five consecutive points beyond 1 sigma on the same side of the central line, (3) more than 7 or 8 consecutive points on the same side of the central line, and (4) more than 7 consecutive points increasing or decreasing.
In addition to these numeric criteria based on statistical probabilities, certain unnatural patterns also suggest lack of statistical control: (1) sudden shifts in level; (2) trends, up or down; (3) grouping or bunching; (4) freaks; (5) cyclic patterns; (6) interaction between variables; (7) unstable mixture or instability patterns indicating excessive variation between groups; and (8) stratification, or an unnaturally "quiet" pattern with many points near the central line, resulting from a composite of numerous distributions within the same sample.
PRACTICAL IMPLICATIONS OF SQC ANALYSIS.
When special or extrinsic sources of variability are determined, their causes should be identified. If they are eliminated and are thus no longer part of the process, then these data points can be deleted and the control limits recalculated. The long-term goals are elimination of extrinsic sources of variability, a shift toward the optimal value for measured data, and a decrease in the process mean if nonconforming items (p chart) or nonconformities (u chart) are being measured. When extrinsic sources of variability are eliminated, intrinsic sources of variability may be reduced by focusing on the many small aspects of the process itself that contribute to common-cause variation.
Summary
In summary, for certain high-frequency, standardized operative procedures such as coronary bypass, SQC offers another way to analyze data that are already being collected in most cardiac surgery programs. In relatively homogeneous patient subsets, the morbidity and mortality associated with CABG appear to vary over time according to the usual laws of statistical fluctuation, which apply to many other processes. If other factors are relatively constant, this methodology may help distinguish random fluctuations from real changes in surgical results. Statistical quality control offers the possibility of studying the most common complications and adverse outcomes sequentially over time with the ultimate goal of reducing the incidence of such outcomes and producing a more predictable result. It emphasizes the many components of the process rather than focusing on the practitioner whose patient experiences an isolated adverse outcome. Measurement data, such as length of stay or postoperative cardiac isoenzymes, may also be analyzed using SQC, with the goal of reducing variability and deviation from target values.
Statistical quality control is another mathematical tool, comparable to 
2 analysis or logistic regression, that can be used to analyze the complex process of providing surgical care. It is one more technique that may help us reach our common goal of providing the best possible care to our patients in an era of shrinking health-care resources.
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Appendix 1. The Statistics of Control Charts |
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TopFootnotesAbstractIntroductionMaterial and MethodsResultsCommentAppendix 1. The Statistics...References |
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Measurement charts are prepared in pairs. The X chart depicts the variation of the process mean between samples. It includes the mean value Xi for each subgroup, the central line (which is the process grand average (
i=1k Xi)/k, where k = number of samples), and UCL and LCL = ± 3
/(c4n), where n = subgroup size, s = average sample standard deviation (i=1ksi)/k, and c4 is a mathematical constant that relates s to the population standard deviation [7].
Process dispersion (within-sample variability over time) is analyzed using R (range) or s (standard deviation) charts, which are the most sensitive control charts. Range charts (X - R) are easier to calculate than standard deviation charts (X - s) and have been more commonly used in the past, particularly for small subgroup sizes. However, for subgroup sizes greater than 9, the X - s chart should be employed and is easily generated using modern computer programs. It is desirable to have the central line and control limits of the s chart as low as possible, indicating minimal variability. For subgroup size n and k subgroups, the central line of the s chart = s, and the control limits are:
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For variable subgroup size, as would usually be the case for surgical data, the mean subgroup size can be employed or the control limits can be calculated for each individual subgroup using subgroup size (ni) and weighted or unweighted averages of and s in the previous equations [3].
The use of ±3 sigma limits about the process grand average was originally adopted by Dr Shewhart [1, 2] and remains the standard. For a distribution that is normal or that can be approximated by a normal distribution, these limits should encompass 99.7% of all measurements. However, even if the distribution of individual measurements (X) is appreciably nonnormal, the distribution of sample means Xi approaches normality by the Central Limit Theorem [3, 6]. When even less is known about the underlying distribution, the use of three standard deviation limits is still statistically justified. The Camp Meidell inequality [6] states that for a unimodal distribution that meets certain other criteria, the probability of an observation being within j standard deviations of the mean is greater than or equal to 1 - (1/2.25j2), which equals 0.951 for ±3 standard deviations. For any finite distribution, regardless of shape, the Tchebycheff inequality [3] states that the probability of an observation lying within j standard deviations of the mean is greater than or equal to 1 - (1/j2), or 0.889 for ±3 standard deviations [6].
Attribute Charts (p or np)
Attribute charts are used for data that can be measured in the form of binary variables; for example, data that can be classified as conforming or nonconforming (unsatisfactory) with regard to a particular attribute. The fraction nonconforming is p, and the average for the population is p. Such charts are based on the binomial distribution. Requirements for the application of such charts are that only two possible states exist with regard to that attribute, that the probability of conformity or nonconformity for each trial is independent of the results of other trials, and that the probability of conformity or nonconformity remains roughly equal from one trial to the next [3].
For variable subgroup size, 
= 
number of nonconforming units (patients)/ number of units (patients), and the control limits for subgroup i of size ni are:
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In standard practice, 3 sigma limits are employed as they are with X - s charts. However, the probability limits of the normal distribution are only a good approximation to the exact binomial probability limits for values of np greater than or equal to 5. Because of the asymmetry of the binomial distribution for lower values of np, the use of 3 sigma limits may result in negative LCLs, which are plotted at 0, thus obscuring positive refinements in technique or results. At the other extreme, an excess of "false alarms" may occur [9]. Exact probability limits may sometimes be recommended.
In general, p charts are less sensitive than variable charts, and measurement of data in the form of continuous variables should be the next step in the control process. For example, p charts might be used initially to assess the incidence of perioperative myocardial infarction, but ultimately a measurement variable related to myocardial injury (such as creatine kinase-MB level) should be plotted as an X - s chart.
Area of Opportunity (c or u) Chart
Attribute charts describe events that are yes-no or present-absent with respect to a particular attribute and that are approximated by a binomial distribution. However, other events may occur multiple times within a given area of opportunity, or it may be convenient to chart the sum of various types of imperfections or nonconformities over time [9]. Despite multiple nonconformities, the finished product is not rendered completely unacceptable, but it is desirable to have as few nonconformities as possible. An example from the manufacturing industry would be the number of imperfections allowed within 100 feet of a textile product. In surgery, it might be the total number of all complications of various types that occurred per patient during a monthly or quarterly sampling.
The probability of such events, when they are measured over a constant area of opportunity, is best described by a Poisson distribution. This assumes that the events occur randomly, independently, and at a relatively constant and infrequent rate per unit of opportunity (for example, time). Even if these conditions are not strictly fulfilled, control charts based on the Poisson distribution may still be valid [3].
For variable subgroup sizes, an average value for n may be used if there is less than 25% variability, or a u chart (which does not have a Poisson distribution) may be constructed with actual subgroup size. The central line is:
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The control limits for subgroup i of size ni are:
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In our study, this type of chart was used to analyze the total of all complications and all major complications per patient.
As is the case with the p chart and its underlying binomial distribution, the normal distribution is often not an accurate approximation to the Poisson distribution. Actual probability limits may be calculated [6, 8], or 3 sigma limits may be employed empirically.
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