Print this Article 
Send to a Friend1 -- Introduction
You know of my close association for more than a quarter century with one institution as a full-time professional physician-investigator, and of my recent move to the Cleveland Clinic. However, despite many papers, scientific presentations, and the book Cardiac Surgery, it must be difficult for you to comprehend the mindset developed in Birmingham and which, to an extent, though with different emphases, we hope to transplant to Cleveland. Because it is an early morning hour when you are doing your prime thinking, I will describe some elements of that mindset that has informed much of what we do, from evaluating manuscripts, to collecting and analyzing data, to applying what we have learned to the clinical setting.
Like it or not, many elements of our mindset fall into the discipline of philosophy.
2 -- SLIDE: Philosophy definitions (1)
The dictionary defines philosophy in several ways. On the one hand, it tells us that philosophy is the investigation of causes and laws underlying reality; an inquiry into the nature of things; the critique and analysis of fundamental beliefs as they come to be conceptualized and formulated; the synthesis of learning; and a system of motivating concepts and principles.
3 -- SLIDE: Philosophy definitions (2)
On the other hand, it tells us that it embraces all learning EXCEPT technical precepts and practical arts, and all disciplines of learning and scholarly pursuit EXCEPT theology, law, and medicine! This latter qualification perhaps reveals why at times we seem to be marching to the beat of a different drummer, for we believe that philosophy cannot be escaped in clinical investigation, where, we are told, it has no place! By definition!
Now, before you conclude that I will draw up the philosopher’s rocking chair and muse for awhile, this talk, stripped of its philosophical aspects, may stimulate your thinking about the management of patients with ischemic heart disease and of babies born with pulmonary atresia with intact ventricular septum. So don’t despair too soon.
4 -- SLIDE: Patient 1 description
She was competitively athletic, but troubled occasionally over the last 5 years by mild chest pain following strenuous tennis matches. Her persistent concern resulted in coronary angiography that revealed the mild coronary artery disease you see here.
What treatment strategy should be pursued at this time? Medical management? PTCA? Coronary surgery?
Therapeutic recommendations can be made, often wisely, by intuition and good clinical judgment. However, supplementing judgement with comparative data about appropriateness of therapy is what we advocate. For this lady, it requires information about the results of continued medical management, PTCA, and surgery for her!
5 -- SLIDE: KUL life table
The surgical experience we will use is based on about 10,000 patients undergoing coronary artery bypass grafting in Leuven, Belgium. The construction of the data set represented more than a decade of painstaking work by one surgeon, Dr. Paul Sergeant, and is interesting to us for it contains 20-year follow-up information on use of arterial grafts. Along the horizontal axis is the interval after the intervention in years. Along the vertical axis is percent survival. The symbols every 2 years are skeletonized Kaplan-Meier life table estimates. Superimposed on these is an equation-based survival curve, shown by the solid line, enclosed in confidence limits equivalent to one standard error. The blue line is an age-sex-race matched population life table. The numbers in parentheses are the number of patients followed beyond various points in time.
6 -- SLIDE: KULeuven hazard function
The graph shows the overall instantaneous death rate across time after surgery, called the hazard function. The risk of death is highest immediately after surgery, falls to its lowest level by about 1 year, then steadily rises. The blue line is the hazard function for the matched general population.
Now, some of you anticipated that it wouldn’t be long before I tried to stuff hazard functions down your throats! So, let’s take a small historical digression to the origin of the concept.
7 -- SLIDE: John Graunt and Black Death
In 1603, during one of its worst plague epidemics, the City of London began collecting weekly records of christenings and burials. Each week’s figures were examined, but those "who constantly took in the weekly bills of mortality made little use of them, than to look at the foot, how the burials increased or decreased; and among the casualties, what has happened rare, and extraordinary, in the week current," complained John Graunt.
Unlike those that stopped at counting and relating anecdotal information, Graunt believed the data could be analyzed in such a way as to yield useful inferences about the nature, and possible control, of the plague, and to test differing medical hypotheses about the etiology, mode of transmission, and spread of the horrible disease.
That he succeeded when other contemporary astute minds failed might be attributed to his being an investigator at the interface of disciplines. By profession, he was not a doctor, but a storekeeper.
8 -- SLIDE: Progress at interfaces
We have learned that some of the most exciting developments take place at the interface of disciplines. In my case, this has ranged from collaboration with investigators in mathematics, computer sciences, statistics, engineering, acoustics and digital signal processing, as well as biologic disciplines such as biochemistry, cellular and molecular biology, immunology, and physiology. Effective collaboration has required overcoming several barriers, but has been facilitated by key individuals who have such secure grasp of their own discipline that they can impart an overview that is at once understandable and excites a curiosity to discover interesting common ground.
9 -- SLIDE: Graunt (continued)
It is not surprising that storekeeper John Graunt translated human population dynamics into terms of the marketplace. He described them in terms of the rate of incoming wholesale goods (the birth rate) and the rate of retail sales (the death rate); he could then calculate the inventory remaining on the shelf (those presently alive). In medicine, this thinking is analogous to biochemical reaction rates involving substrates and products.
He made another leap, this time a philosophical one. You see, to a storekeeper, one box of Wheaties is interchangeable with any other box. By assuming for a moment that one person was interchangeable with another, he could achieve an understanding of the general nature of the birth-life-death process, in the absence of dealing with specific, named individuals. He attempted to discover, as it were, the nature of the forest at the expense of the individual trees, that are at a lower level of hierarchy. He embraced continuity in nature on the macro level at the expense of the individuals at a micro level.
10 -- SLIDE: Continuity and discontinuity in Nature
Continuity in Nature is a key concept in the history of ideas. Historically, it has emerged in the fields of mathematics, science, philosophy, history, and theology. Over the course of the 200 years following Graunt, and leading up to major thought in early 20th century physics, the sciences of chemistry, thermodynamics, and mechanics recognized physical matter consisted of discrete particles. Yet, in some senses, "field theory" prevails for understanding Nature on the macro-hierarchical plane, over "particle theory" on the micro-hierarchical plane.
Continuity in Nature is a key philosophical concept in clinical investigation. It provides a framework for drawing inferences about groups of patients, as well as for inferring the probability of events for individual patients, and predicting the probable outcome for a new patient. However, in embracing the concept, we give up the ability to predict exactly WHO will experience the event or exactly WHEN an event will occur to a specific, named individual. The analogy is the Heisenberg Uncertainty Principle--the quantum mechanics of clinical research.
Now, back to John Graunt at the store thinking about merchandise management and its possible relevance to the birth-life-death process.
11 -- SLIDE: Birth and death process
This is a compartmental representation of that small portion of Graunt’s thinking that is important for our immediate discussion. Here we emphasize the kinetic rate at which people are being removed from the category labeled SURVIVORS (the inventory on the shelves) into the category DEATHS (the retail sales). The name of this rate was coined by Graunt as the HAZARD FUNCTION. He selected the name from a term used at that time in dice games, and which had crept into common language in reference to calamities.
With that background we are ready for a closer look at the hazard function for death after coronary bypass surgery.
12 -- SLIDE: KULeuven hazard decomposed
In developing a biomathematical approach to the analysis of the distribution of times until death and other events after initiation of therapy, we devised a method, a number of years ago, that begins by the decomposition of hazard functions, such as this, into a small number of simple, additive components.
The dashed line is the hazard function you saw previously. The colored solid lines are three hazard components that, when added together, sum to the overall hazard. This hazard function is seen to be composed of an early, rapidly declining component, a constant hazard component, and a rising component. The number of components, or phases, the form of the mathematical equation for them, and the values of the parameters in those equations are estimated from the data themselves, not arbitrarily.
From your knowledge of biochemistry, and from John Graunt’s knowledge of shopkeeping, it comes as no surprise that we must now think about factors that might modulate the hazard function. Indeed, in this instance we will separately modulate each of the three components. We seek simultaneously risk factors that increase the area beneath the early hazard component, that raise the level of constant hazard, and that pivot upward the line for late hazard.
13 -- SLIDE: John Graunt and hazard variability
John Graunt speculated that he could obtain clues about the cause and prevention of the plague by identifying factors influencing the death rate; that is, the magnitude of the hazard function. He identified a rise in hazard during weeks in which ships docked from foreign ports, increased hazard paralleling population density, and a higher hazard in households harboring domestic animals.
From these observations, he discarded definitively those theories about the cause of the plague that were incompatible with the data, though the direct cause was not known for another 200 years. His clinical inferences and recommendations seem crude to us today, but they were effective in neutralizing the plague in the interim until its cause and means of eradication became known.
14 -- SLIDE: Framingham investigators
In the mid 20th century, some 300 years after Graunt, the formal concept of risk factors was introduced by the Framingham Heart Disease Epidemiology Study investigators. They did not think foolishly they could discover the cause and cure for heart disease solely by epidemiology. Rather, they set about discovering factors associated modestly with increased incidence (or hazard) of cardiovascular disease, quantifying the importance of each factor jointly with other factors, and using that information to propose a plan to reduce the disease by modification of nonimmutable factors.
As the mounds of data piled up, the investigators became dissatisfied with the "standard" statistical treatment of their data and searched for more helpful methods. Specifically, they were frustrated by pile upon pile of univariable, stratified tables and cross-tabulations. They needed a methodology that looked simultaneously at multiple variables. Second, they were frustrated by the information-losing strategy of chopping up continuous variables into a few arbitrary categories. Third, they sought a method that would allow them, in the end, to compute absolute risk for a given set of risk factors, first for permitting group comparisons against data from other trial centers, and then for predicting individual patient risk.
They sought help!
Tavia Gordon writes that they approached Jerry Cornfield for help. From it emerged an interesting methodology, called logistic regression, that is a good prototype for examining how risk factors work together in most models of events, be they time-related or not.
15 -- SLIDE: Logistic equation
On this slide is the S-shaped logistic curve. Along the horizontal axis is a scale of risk. Along the vertical axis is the corresponding probability of experiencing the event. In a logistic analysis, magnitude of risk, or the risk factor coefficient, is measured in logit units, the horizontal axis. A particular risk factor may have a coefficient of 1.0. This corresponds to a 2.7-fold increase in risk. Notice, however, that a one unit increase in risk along the horizontal axis produces a trivial increase in the probability of experiencing an event if all other things position a patient far to the left on the curve. 2.7 times nearly nothing is still nearly nothing. But notice that as other factors move the patient closer to the center of the slide, a 1-unit increase in risk makes a huge difference. This is consistent with our medical perception of patients. Some are robust; they sit far to the left on the logit curve. Others are fragile; we rightly believe that one more straw could break the camel’s back!
It is this type of sensible medical relation that makes us want to deal ultimately with absolute risk rather than risk ratios.
16 -- SLIDE: Multivariable analysis
On this table, I indicate only in broad categories the risk factors that we found for death after coronary surgery and the hazard phase, or phases, in which groups of variables tended to congregate. For example, non-cardiac comorbidity risk factors influenced late risk more than early risk, while the patient’s clinical status at the time of operation influenced only early outcome.
Some individual risk factors affect all phases; others only one. This demonstrates that risk factors do not often operate uniformly across time. Some influence early events and others later events such as the use of arterial grafts.
17 -- SLIDE: Parsimony
Even though there were many hundreds of deaths across time, the risk factor model is comparatively sparse. This happens for at least two reasons. First, although this data set is rich in medically relevant variables, medical data are highly redundant. Thus the "effective number of variables" is not all that large. This becomes clear as variables are entered into the model and correlated variables cease to be important contributors. This gives rise to certain problems of communication. For example, we might say that renal failure is not a risk factor. However, the level of creatinine may be quite an important risk factor, so indeed people with renal failure are at higher risk. It is also the reason that two investigators may come up with different risk factors. The models, however, are likely to be similar if you dig beneath their surface to find surrogates. This is where the collaboration between analyzer and medical expertise is important, for it is essential, in our minds, to understand the analysis as fully as we can.
The second reason for there being relatively few variables in the model is because we actively seek as simple a model as gives justice to the information. This is not based on science, but on aspects of beauty and philosophy that are part of the foundation of science.
18 -- SLIDE: KULeuven nomogram: IMA
To help us understand the nature of the disease and its treatment as revealed by a multivariable analysis, we construct nomograms by solving the risk factor equation for survival given specific values for the variables that are retained in the analysis. For example, to see the isolated benefit of using an internal mammary graft, we set values for other risk factors to a common value, here for a median-risk patient, and then vary just that one factor. This is illustrated graphically for two such patients with otherwise identical characteristics, one (in green) receiving an IMA graft and one (in yellow) receiving only vein grafts. Keep the magnitude of this modest separation of curves in mind as we go to the next slide.
19 -- SLIDE: IMA stratified
These are risk-unadjusted data stratified simply according to the use or not of arterial grafts. Notice that the curves are more widely separated than my nomogram. This results from differences in prevalence of risk factors in the two strata. The nomogram puts the comparison on defined, risk-adjusted common ground.20 -- SLIDE: MHI PTCA survival
The second of the comparisons we want to make for our athletic lady is with angioplasy. We have analyzed 6200 patients from the Mid-America Heart Institute in Kansas City. They underwent aggressive, first-time intervention using PTCA, and have been followed for about 10 years. Their survival across time is shown along with that of a matched population life table in blue.
21 -- SLIDE: MHI PTCA hazard function
This is the corresponding hazard function. It consists of a small, rapidly falling early phase of hazard following the procedure, a constant hazard phase, and a rising late hazard phase. The blue dash-dot-dash line represents the matched general population. A multivariable analysis has been performed simultaneously for these three hazard phases, and the resulting categories of variables are similar to those identified for coronary surgery.
22 -- SLIDE: CASS natural history survival
The third option for our lady is medical management. To obtain an equation for natural history, we analyzed the group of about 24,000 patients from the historic CASS registry for the event "death before intervention." 18-year follow-up is shown.
23 -- SLIDE: CASS natural history hazard
The hazard function for death before intervention is shown here. There is an early hazard phase that gives way to a more-or-less constant level. This shape contrasts particularly with hazard after surgery, which fell to a lower level before rising in parallel with the curve for the general population shown in blue. A multivariable analysis has been accomplished for the two phases of hazard resolved among these patients.
24 -- SLIDE: Patient-specific comparisons: Method
With equations for surgery, PTCA, and natural history now in hand, we are prepared to make quantitative predictions from each equation for this specific lady and make comparisons among them as to the most appropriate initial therapy to prolong life. We justify these predictions by again invoking the philosophy of Continuity in Nature.
From the patient’s medical information we extract values for the variables in the multivariable equations. We then solve each equation across time. This generates curves that are adjusted for prognostic factors for survival by each management strategy. We then formally compare the curves to select the treatment strategy that is the most appropriate at this time.
25 -- SLIDE: Patient 1: survival
On this slide, 3 survival curves and their confidence limits are depicted for the athletic lady I introduced at the beginning of the talk. The uppermost curve, giving the best survival, is for medical management. The yellow middle curve is predicted survival were she to have PTCA at this time. The lowest green curve is predicted survival were she to undergo surgery. No matter what is decided, survival is excellent. Even the small risk of intervention, however, seems unnecessary and inappropriate if extending her life is the objective of treatment.
In fact, she underwent PTCA, followed in 3 months by repeat angioplasty. Eventually she had a stent placed, and we became aware of her when she sought an opinion about surgery for her now compromised LAD.
26 -- SLIDE: Patient 2: description
Let’s think about advising another patient. This patient is a man with moderate chronic stable angina. Comorbidity includes vascular disease. He has important proximal LAD disease, mild circumflex lesions, moderate right coronary disease, and mildly depressed ventricular function.
Should intervention be recommended? If so, should it be PTCA or surgery? This seems less clear-cut than our athletic lady.
27 -- SLIDE: Patient 2: survival curves
His predicted survival curves for each initial management strategy are shown here. His chances of surviving for the next 10 years are reasonable with any strategy. However, medical management, shown in white, is predicted to be less good than with intervention, and the intervention predicted to give him the best survival is PTCA, shown in yellow.
28 -- SLIDE: Patient 2: survival difference
One way to appreciate better the wisdom of recommending intervention for this man, is to look at the benefit of PTCA over medical management. On the vertical axis is the difference across time in absolute percent survival for the two strategies. The center horizontal line represents zero difference. Values above this line represent a PTCA benefit; values below it, a medical treatment benefit. Over the course of several years, it becomes increasingly apparent that multivessel PTCA at this time is an appropriate recommendation.
29 -- SLIDE: Patient 2: lifetime difference
We can examine the difference between management strategies in another way. On the vertical axis is plotted the area between the survival curves for PTCA and medical treatment. It represents the lifetime added by the intervention. PTCA is predicted to add 1.7 months to lifetime by 5 years, and a modest 7.7 months by 10 years.
30 -- SLIDE: Patient 3: description
I cannot resist illustrating one more patient with ischemic heart disease. He is an unfortunate, cachectic, insulin-dependent diabetic coal miner who presents with unstable angina. He has extensive three-system disease, importantly depressed ventricular function, and ischemic mitral incompetence.
31 -- SLIDE: Patient 3: survival
On this slide are his predicted survival curves. His long-term outlook with medical management (shown in white) is poor. If his coronary disease is managed by intervention, his outlook is predicted to be substantially improved. In his case, surgery (shown in green) is predicted to improve survival more than PTCA (shown in yellow).
32 -- SLIDE: Comparison of alternative therapies: General
To summarize the material presented so far; first, long-term follow-up is needed to assess appropriateness of alternative therapies. Intervention invariably has a short-term disadvantage, that may or may not later be outweighed. However, second, long-term data reflects older therapy. Those discounting older data assume current therapy is superior in the long-term. They may or may not be correct. Recall we are talking about palliative management of a chronic disease.
Third, not all alternatives may be feasible for a patient.
Fourth, decision-making for individual patients is not a one-time process. As conditions and therapies change, decisions can be reconsidered, new curves drawn, and appropriateness reassessed.
33 -- SLIDE: Comparison of alternative therapies: Requirements
Fifth, high-quality medical data across the spectrum of ischemic heart disease is required to develop the kind of equations we have demonstrated. This argues cogently for the computerized patient record that captures values for medical variables in a structured format.
Sixth, good data deserves good analyses. Expecting this to happen by a biostatistician, or anyone, working in isolation of expert clinical input is a serious error. It requires intense medical and statistical collaboration. The analytical methodology needs be tailored to the medical needs, which include the need for absolute risk and for predictive equations.
Finally, the type of comparison format I have shown you this morning is needed to facilitate examining all the alternatives to assist in making information-based recommendations for treatment. It should also be helpful to the patient and his or her family in making the decision concerning that recommendation and in giving truly informed consent to it.
Let me now answer what should be your first question of me. Is there evidence that predicative equations are any good when used prospectively?
34 -- SLIDE: Predicted and actual survival after CABG (KULeuven)
We have used two methods to assess predictive equations. First, from mid-1987 to 1992, 3,720 patient-specific survival curves were computed prospectively for a consecutive group of patients undergoing coronary artery bypass grafting in Leuven, Belgium, using the prediction equation published in the American Heart Association/American College of Cardiology Guidelines for Coronary Artery Bypass Surgery.
We summed the 3,720 curves across time, divided by n, and displayed them as a risk-adjusted group survival curve, shown by the white lines. After these patients were followed, their actual survival, shown by the white circles, was compared with predicted. We predicted slightly better survival than actual.
The second method requires knowledge of the length of follow-up of each patient. Using the theorem of conservation of events, we calculated the predicted number of deaths and compared them to the actual number. We predicted 5.7% mortality, but it was actually 6.5%.
35 -- SLIDE: Table of residual risk factors
A subsequent analysis of time-related unaccounted risk identified 5 risk factors. These reveal the limitations of the predictive method. The first two variables constituted such small subsets in the original analysis that I had been unable to obtain computationally stable estimates. The two preoperative rhythm disturbance variables were not available for developing the original equation. The final variable represents a subgroup of patients not appearing in the original data set.
36 -- SLIDE: Predicted and actual survival stratified by rare risk factors
In toto, patients in these rare subgroups constituted 8% of the prospective data set. On this slide the 3,720 cases are stratified according to the presence or absence of the 5 rare risk factors. The blue squares represent actual survival in this group of cases. The corresponding blue solid line is the terribly inaccurate prediction.
In contrast, among the remaining 92% of patients, shown in white, survival was well predicted. This result is important, for there was considerable alteration in the case mix in this recent group of cases compared with the original cases from 1971 to 1987 which formed the basis of the prediction equation.
There are three inferences from this analysis. First, when patients have important rare conditions that have not been accounted for in the analysis for any of several reasons, prediction may fail and clinical judgment must prevail. Second, when large, complete data sets are the basis for prediction equations, predictions should be suspect in only a small proportion of patients with unaccounted-for conditions. Third the multivariable equations appear capable of adjusting well for different case mixes.
37 -- SLIDE: Description and Prediction
The discussion so far has emphasized prediction, and testing those predictions. This reveals another philosophical bias: we are more interested in analyzing data to be helpful for the next patient than we are simply describing the data from the past. Even when we study the nature of observed phenomena, we have always in mind the drawing of inferences that are helpful in understanding the next patient.
The fact that we have developed specific statistical methods for analysis of time-related events reveals that we were dissatisfied with what was available to us for this task. We needed methods that permitted graphical displays useful for understanding the nature of what we were studying, that accounted for known medical phenomena (such as non-proportional hazards), and that could be used in making patient-specific predictions to assist in making clinical recommendations and to allow patients to give truly informed consent.
38 -- SLIDE: Use of Information, Data, and Analyses
This brings us to a short philosophical discussion about the appropriate use of clinical information, data, and analyses. Some of you understand what I mean when I say that one motivation for assembling clinical information is to sell shoes. I will be the first to admit that innovation stems more from aesthetically motivated curiosity, frustration with the status quo, sheer genius, fortuitous timing, favorable circumstances, and remarkable intuition than from purposefulness. The evidence for this is strong enough that I would argue that the analytical quantitative approach so respected in science is insufficient to generate needed medical innovation. With innovation, however, comes the need to promote and indoctrinate. But, promotional records of achievement should not be confused with determining clinical efficacy, effectiveness, and long-range appropriateness or formulating clinical inferences from new knowledge.
Of growing importance is the use of clinical information to censor or punish. At least, I think many surgeons perceive clinical report cards as a means for punishment or regulation, though I suppose that those institutions that rank well don’t suppress the opportunity to use the report card for institutional promotion! What troubles me, is that the notion is based on an outmoded manufacturing model of Quality Control by outlier identification. Since doctors are people, not machines, this approach brings at least two undesirable side effects: defensiveness and hiding the truth.
Yet another reason for interest in clinical information seems to be the planned use of it someday, somehow, for some ill-defined institutional or commercial purposes that does not include, generally, the generation of new knowledge.
In some settings, clinical research has the dreary aura of resident chart reviews. But what I am showing you today are seriously pursued clinical studies that have as their goal the generation of reliable new knowledge relating to heart disease and its treatment.
39 -- SLIDE: Title: Pulmonary atresia with intact ventricular septum
Let’s take another step, the last step for this morning.
The young couple was caught unprepared. In an instant, anticipation of joyous birth was transformed into a nightmare of new terms, new doctors, new surroundings, new uncertainties. The pediatric cardiologist tried to explain, in words and diagrams that could never be simple enough, that their baby had a rare heart condition. The artery from the heart to the lungs was completely blocked, and the right half of the heart had not developed. It didn’t help that the couple became the subject of a local evening news team that was determined to follow the progress, in detail, of this baby about to be born with "half a heart," as they sensationally headlined it.
They learned there were a number of alternative initial treatment strategies, that not one, but a series of operations would be needed, and that there was uncertainty as to which strategies might allow their child eventually to have two functioning ventricles.
After listening patiently to the surgical teams’ discussion of the risk of the first preparatory operation, they asked an interesting question. "In the end, after however many operations, how many babies like ours will end up with a one chambered heart, how many with a two-chamber heart, and how many might not even make it that far?"
This takes us into new territory. The information the parents were requesting relates to the prevalence of multiple possible end states for their baby, not simply the probability of one or another of them.
40 -- SLIDE: Bernoulli and Smallpox
This was not the first time such a complex question had been posed. For while the plague had been held in check, smallpox became the ravishing epidemic disease in England. In the early eighteenth century some progress was made in the area of inoculating people with tiny doses of small pox in the hope of establishing immunity to the full-blown disease. The technique had a 10% fatality rate. Nevertheless, there was considerable hope that smallpox could be definitively conquered. Since governments at that time were supported in part by annuities, it became of considerable economic importance to know what consequences the eradication of smallpox might bring upon the government’s purse.
Daniel Bernoulli tackled this problem by exploring the notion of classifying deaths according to cause. People did not just die, they died of something. He made the assumption that all causes of death were independent of one another. He then suggested that one could compute the rate of migration from the state of being alive to any one of several categories of being dead. It was like hanging a bucket of water with multiple different sizes of holes in the bottom. The size of each hole corresponded to one migration or hazard rate. If a separate container were placed beneath each hole, and if there were no interactions between the holes, he could compute from the various rates how full each container would be at any moment in time. Specifically, he could calculate how stopping up one large hole (smallpox) would influence both the number of people still alive and the redistribution of deaths into the other categories.
From this information he could then compute, on the basis of the maturation of the annuities, whether or not the government was about to face catastrophe on the heals of a medical triumph. That triumph came just 36 years later!
41 -- SLIDE: Purpose
Let’s use his strategy to answer the question of our bewildered, soon to be, young parents. We will estimate, based on the characteristics of this baby, the prevalence of various end states.
We will use data gathered in 346 neonates with this rare condition managed since birth in 32 centers between January 1, 1987 and October 1, 1993.
42 -- SLIDE: Status
As of follow-up at the beginning of 1995, none were alive without intervention, 137 had undergone a definitive repair, 77 were alive in an intermediate status without yet a definitive repair, and 132 had died before definitive repair.
43 -- SLIDE: Status: definitive repair
This is the same table with more detail about the mutually exclusive end states. Of the 137 that had undergone definitive repair, 67 had a 2-ventricle repair, 54 a 1-ventricle Fontan repair, and 12 a 2-ventricle repair plus a bi-directional Glenn (some would call this a 1-1/2 ventricle repair). Four had undergone heart transplantation.
44 -- SLIDE: Assumptions
We now make some key assumptions. We assume that a patient can migrate at some point in time from the category "alive without definitive repair" into one, and only one, of the several mutually exclusive end states, which are death and one of the definitive repair categories. Once a patient migrates to an end state, he or she is no longer at risk of migrating to any other end state. Technically speaking, patients are censored from being at risk of any other end state once they enter one of them. And we assume that the distribution of times of migration to any one state are uncorrelated with those into any other state.
45 -- SLIDE: Death before definitive repair
We can separately look, then, at each of the end states, censoring for all others, in an effort to determine, as it were, the size of hole this implies in the bottom of our proverbial bucket. This slide shows percent survival before definitive repair, with time along the horizontal axis, and both nonparametric Kaplan-Meier as well as parametric estimates along the vertical axis.
46 -- SLIDE: Hazard function for death before definitive repair
This is the hazard function for death before definitive repair. It decomposes into a rapidly falling early phase of hazard giving way to a constant hazard phase about 1 year after entry.
47 -- SLIDE: Multivariable analysis of death before definitive repair
There are a number of risk factors for death before definitive repair, including the size of the baby at birth, the diameter of the tricuspid valve as a reflection of right ventricular size, the degree of tricuspid valve incompetence, various details of associated cardiac morphology, level of right ventricular pressure, and some institutional factors.
48 -- SLIDE: 2-ventricle repair hazard function
Very briefly, this is the migration rate, or hazard function, into 2-ventricle repair. Predisposing factors for it include larger tricuspid valve dimension, absence of right ventricle to coronary artery fistulae, and several institutions.
49 -- SLIDE: 1-ventricle repair hazard function
This is the migration rate, or hazard function, into 1-ventricle repair, the Fontan operation. Predisposing factors were smaller tricuspid valve size, lesser tricuspid valve incompetence, and several institutions.
50 -- SLIDE: All hazards
This terribly busy slide depicts all the migration rates that are acting simultaneously to effect migration to one or the other of the several end states. They are all the holes of various size in our bucket, to continue the figure of speech. You recognize death before definitive repair, 2-ventricle repair, Fontan repair, and two other rates that I did not show you separately.
At this point, we invoke the kinetic mathematics developed by Bernoulli over 200 years ago, and which is identical to unidirectional substrate-multiple product kinetics in biochemistry, where these migration rates are analogs of individual reaction rates. Starting with only newborns alive and without definitive repair, we can watch the kinetics operate over time and ask at each moment in time how many of the original patients are left in that state, and how many are now in each of the end states. At any moment, all patients will be accounted for, since there must be conservation of people in exactly the same manner as there must be conservation of mass in reaction kinetics.
51 -- SLIDE: Competing risks, risk unadjusted
This is the risk unadjusted result of the kinetics of migration from alive without definitive repair to the various end states. Time is along the horizontal axis. The percent of patients in each labeled category is along the vertical axis. Naturally, the category "alive without definitive repair" is emptying over time, while the others are filling up at variable rates depending on the combined influences of the migration rates. Notice that death before definitive repair has the highest prevalence. By the end of the 8 years, about equal numbers are in 1 and 2-ventricle repair categories.
Now, the prevalence of patients in each category is risk-unadjusted.
52 -- SLIDE: TV size = -4, hazard function
Let me explore with you in the next slides something of the influence of just one risk factor: the right ventricular size as reflected in the dimension of the tricuspid valve. We have expressed the valve size in terms of the number of standard deviations it departs from mean normal size. Here we have depicted a dimension 4 standard deviations below normal. The slide shows that the migration rates have been modulated importantly by this value of tricuspid valve size, with, particularly, the migration rate for Fontan operations becoming prominent.
53 -- SLIDE: TV size -4, competing risks
This slide shows the consequences of the change in migration rates. It again is the prevalence across time in each category. Notice that death before definitive repair is still prominent. However, Fontan repair prevalence is considerably higher than 2-ventricle repair.
54 -- SLIDE: TV size 0, competing risks
In contrast, this depiction is for a normal sized valve. Notice that death before definitive repair is less prominent. 2-ventricle repair now has the highest prevalence.
Clearly, the size of the tricuspid valve is a strong predisposing factor for all these states. To explore the shape of that relation, let us take a slice in time at 5 years, and compute the prevalence in each category at that time interval for various tricuspid valve sizes.
55 -- SLIDE: Institution X
On this busy slide, the tricuspid valve diameter is shown along the horizontal axis in terms of the z-score for the typical institution. Recall that a value of 0 on the right end of the horizontal axis corresponds to mean normal size for that baby’s body surface area, while -2 is 2 standard deviations below normal. The four end states I want you to focus upon are death before definitive repair, that rises at smaller valve sizes, Fontan repairs that also rise at smaller valve sizes, 2-ventricle repair that rises at larger valve sizes, and alive without definitive repair in intermediate valve sizes. These are the babies that by 5 years are still in a palliative state of indecision.
56 -- SLIDE: Institution Y
This is a similar slide, but depicting an institution that is predisposed to attempt 2-ventricle repair as often as it can. Notice that 2-ventricle repair is prominent for both large and intermediate valve sizes. Notice also that the risk of death is about the same, so there appears to be no mortality penalty for this policy.
57 -- SLIDE: Institution Z
Finally, this slide depicts an institution that is a predisposing factor for the Fontan operation. Now, you can see that both Fontan operations and 2-ventricle repairs are prominent at the extremes of valve size, with patients thrown one way or the other in the middle. There are few patients waiting in indecision. Again, this policy does not have a penalty of increased mortality.
58 -- SLIDE: Inferences (1)
You might be interested in some of the inferences from this study. Overall, in a non-risk-adjusted sense, the prevalence of completed repairs in these 32 centers was low. However, the prevalence is influenced markedly by patient characteristics observed at birth. I have not shown you the fact that most of the mortality was associated with the initial palliative operations; we must focus attention on ways to lessen this.
59 -- SLIDE: Inferences (2)
As it stands today, death before definitive repair is prominent in babies born with a small tricuspid valve. The prevalence of 2-ventricle repair is highest in those institutions that aggressively pursue this policy, while the Fontan operation is in highest prevalence in institutions that pursue that policy. Neither policy appears to affect the prevalence of death.
60 -- SLIDE: New Knowledge
In closing, let me emphasize once again that in our heads is a clear philosophy about the use of clinical information, data, and analyses. Some have remarked that many of our analyses are tough to understand. For that I apologize and accept at least partial responsibility. It means we have not communicated well the essence of the work. Sometimes complex analyses are needed for the practical end of improving results. In the example of Pulmonary Atresia with Intact Ventricular Septum, you will notice that I said nothing about all those intermediate states. There are nearly two dozen of them. We think that by serious study of them, it may be possible to optimize treatment so that simultaneously there are as few as possible intermediate operations, as few as possible deaths, and as many as possible desirable 2-ventricle repairs.
61 -- SLIDE: Serious Clinical Investigation
We have described some aspects, then, of what we call serious clinical investigation in the area of the results of therapy. It is an exciting endeavor. It starts with a relevant question and doesn’t end until inferences are made that affect clinical practice. It requires the support and participation of senior clinician-investigators in the process. This generates tension between letting junior people initiate the work and see it through to publication, versus rather intensive guidance.
The process is not easy nor does it happen over night, often requiring considerable reflection, reanalyses, reassessment, and rewriting. The only part of it that I can imagine being considerably accelerated is the data gathering phase that might occur with the advent of computerized patient records of the variety that stores values for variables. Analytic time will likely stay the same, for as computer speeds have leapt by orders of magnitude, so have our demands on them for analyses that are more appropriate to the data and give answers more relevant to the questions being posed.