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The learning curve and the cost of heart transplantation.

The effect of learning on hospital outcomes such as mortality or adverse events (the so-called "practice makes perfect" hypothesis) has been studied by nemerous ivetigators. The effect of learning on hospital cost, however, has received much less attention. This article reports the results of a multiple regression model demonstrating a nonlinear, decreasing trend in operative and postoperative hospital costs over time in a consective series of 71 heart transplant patients, all treated in the same institution. The cost trend is shown to persist even after controlling for various preoperative demographic and clinical risk factors and the specific experience of individual surgeons. Using a reference case, the model predicts a cost of $81,297 for the first heart transplant procedure performed at the hospital. If this same patient had been the tenth case rather than the first, with the hospital having benefited from the experience gained in nine previous cases, the model predicts the cost would now be only $48,431, or approximately 60 percent of the cost of the first case. Had this patient been the twenty-fifth case, the predicted cost would be $35,352 (43 percent of the original cost), and had this been the fiftieth case, the cost would be $25,458 (31 percent of the original cost.) The longitudinal study design used in this analysis reduces the likelihood that the observed cost reduction is due to economies of scale rather than learning. The results have implications for a policy of regionalization as a tactic for containing hospital cost. Whereas others have pointed to a volume-cost relationship as an argument for the regionalization of expensive and complex hospital procedures, the present data isolate a learning-cost relationship as a separate argument for regionalization.

Numerous studies have noted a positibe relationship between the number of patients seen in a health care facility and the quality of the patient's outcome (Farber, Kaiser, and Wenzel 1981; Flood, Scott, and Ewy 1984a, 1984b; Hannan, O'Donnell, Kilburn, et al. 1989; Luft, Hunt, and Maerki 1987; Luft, Bunker, and Enthoven 1979; Maerki, Luft, and Hunt 1986; Riley and Lubitz 1984; Shortell and LoGerfo 1981; Showstack, Rosenfeld, Garnick, et al. 1987; Luft et al. 1990). This volume-quality relationship has been explained by some investigators in terms of a learning or practice effect (Flood, Scott, and Ewy 1984a, 1984b). According to this view, hospital staff and physicians who see larger volumes of patients have more opportunities to practice their skills. This increased opportunity for practice leads, in turn, to better outcomes for the patient.

If quality improves with practice, one might also expect to see an improvement in operational efficiency, with a corresponding reduction of costs, as hospitals and physicians gain more experience in treating a particular type of patient. In other industries it is well known that the average cost per unit procedure tends to decrease with increased production volume (Lieberman 1984; Wright 1936); there is good evidence that this volume-cost relationship is due, in part, to a learning curve whereby efficiency of production increases with experience (Belkaoui 1986). Methods for estimating the effect of learning on production costs have been incorporated into standard textbooks on operations management (Green 1984).

In the health services field, however, little attention has been devoted to systematic studies of the impact of learning on health care costs. The studies that have been done to examine volume-cost relationships have been relied on cross-sectional comparisons of different size programs at the same point in time. With this type of study design, however, it is difficult to separate effects on cost due to economies of scale from the effects of learning (Smith and Kaluzny 1986). An altenative approach is to examine cost trends in a longitudinal study at a single institution where the volume of a particular type of patient remains relatively stable over time, while the experience in treating those patients accumulates. If costs are observed to decline with the passage of time in a longitudinal study, the trends is more likely attributable to a learning phenomenon than to the effects of economies of scale.

In a recent study of the costs of heart transplantation, we were able to show that the costs of hospitalization in a single institution had decline systematically over the four-year period from the time the first heart transplantation was performed (Saywell, Woods, Halbrook, et al. 1989). Similar trends have been reported independently at another institution (Smith and Larsson 1989). Neither of these studies, however, examined the possible influence that changing patient selection criteria, case-mix factors, or surgical mortality rates might have on costs.

Our present study examines the trend in hospital costs for heart transplantation over time, taking into account various clinical factors that might be expected to influence costs. It was hypothesized that if costs decline with increasing experience, this effect should emerge as a systematic learning curve when plotted ever time. The purpose of this study was to model statisfically the trend in hospital costs for heart transplantation over time, while simultaneously controlling other potential influence on costs.


Study Setting

This study was conducted at Methodist Hospital of Indiana, Inc. (MHI), a private, not-for-profit, metropolitan teaching hospital. MHI has 1,085 acute care beds and processes more than 41,000 patient admissions annually. The heart transplant program was initiated at MHI in Fall of 1978 and the human heart transplantation procedure was first performed at this institution in October of 1982. MHI is a Medicare-designated center for heart transplantation and is approved by the Food and Drug Administration (FDA) as test site for the total artificial heart bridge to transplant program.

Patient Sample

The study sample consisted of consecutive patients (N = 71) who underwent a heart transplantation procedure at MHI from October 1982 through February 1988. The sample included all patients in the heart transplantation program beginning with the first patient to undergo the procedure at MHI (two artificial heart bridge to transplant patient were excluded because of the atypical nature of their hospital costs).


For each patient, hospital costs were estimated from the day of transplant surgery to the day of hospital discharge. Preoperative costs were exluded from the estimated because of variability in patient status prior to surgery (some patients had their preoperative workup as outpatients or during a previous hospital stay and home prior to surgery); variability in preoperative cost-finding methodology (some patients received part of their preoperative care at other local hospital); and the mix of inpatient and outpatient services provided preoperatively, which would have necessitated an arbitrary definition concerning the actual onset of illness.

To estimate the average cost for each patient, we used the traditional accounting method of multiplying each patient's recorded charge by an adjusted ration of department cost to charge (Berman and Weeks 1982; Neumann, Suver, and Zellman 1984; Lingeman et al. 1986; Woods, Saywell, and Benson 1988). The costs of labor, supplies, and other direct expenses for the hospital as a whole, for each fiscal year, were divide among 29 major cost-center groupings. Some of these centers, such as the laboratory and operating rooms, provide direct patient care services that appear as identifiable line items on the patient's bill. Therefore, these centers are considered to be revenue producing. Other centers, such as housekeeping as general administration, do not bill patients directly but instead pass on their expenses in a step-down fashion to the revenue centers. These expenses, called allocated indirect costs, are ultimately added to the direct expenses to derive an estimate of the total cost for a given center. Within a given center, the total cost can be compared with the total charges (i.e., the total amount that patients are billed for services rendered). More importantly, these two figures - costs generated and charges billed - can be used to form a ratio of cost to charge (RCC) for each center.

Cost-to-charge ratios provide a basis for estimating the cost to the hospital for treating an individual patient. This is accomplished by multiplying the ratios for each center by the corresponding charges for that center, as recorded on the patient's hospital bill. For example, using the hospital's fiscal year 1985 (FY 1985) cost-to-charge ratio of 0.879483 for routine services, one would calculate that a patient with routine service charges of $1,000 would have generated routine service costs of (0.879483) x ($1,000), or $897.

Unlike methods that use charge information from the patient's bill as a proxy for cost, use of cost-to-charge ratios estimates costs to the hospital for services actually received by each patient. The cost-finding process also permits each patient to bear share of the institution's indirect cost apportioned in relation to the level of direct patient care services received.

The cost-to-charge ratios used in this study were derived separately for each of the hospital's structure that may have occurred over time. The calculations for each fiscal year were adjusted for inflation and are expressed in constant FY 1988 dollars. The inflation factor was calculted as the overall percentage increase in hospital expenses between each fiscal year, and is therefore a more specific estimate of inflation for these cost data than is the National Medical Care Price Index.


We hypothesized that hospital cost per patient would decrease as the experience of the transplant team increased and that the function describing this learning effect would be nonlinear. To model the effect of learning, we created a variable that defined, for each patient, the number of previous heart transplants that had been performed at the hospital prior to that patient's transplat. We used this variable to represent the accumulating effect of hospital experience (HOSPEXP) as a linear trend. The natural log of HOSPEXP was used to define a transformed variable, LOGHSEXP, which permitted us to model the effect of learning on costs as a descreasing nonlinear trend.

Because the volume of procedures performed by individual surgeons has been found by some investigators to be as important as hospital volume (Hannan, O'Donnell, Kilburn, et al. 1989); Kelly and Hellinger 1987), we defined surgeon experience separately from hospital experience by counting the number of cases that each patient's transplant surgeon had previously performed. This variable was used to define the accumulating effect of surgeon experience (SURGEXP) as a linear trend. The natural log of SURGEXP (LOGSGEXP) was used to model the learning effect as a nonlinear trend.



A host of factors other than learning might be expected to influence cost. It has been suggested, for example, that in the case of coronary artery bypass graft procedures, the effect of surgical volume can be explained, in part, by the fact that high-volume surgeons tend to operate on less severely ill patients than do low-volume surgeons (Hannan, O'Donnell, Kilburn, et al. 1989). With respect to the current study, any changes in case-mix selection occurring over time, including changes in patient demographics, baseline severity of illness, or incidence of postoperative mortality, could produce systematic effects on cost that might masquerade as a learning phenomenon if not properly controlled.

For purpose of this study, we considered each of the variables listed in Table 1 as factors whose impact on cost might need to be statistically controlled before valid claims could be made for a learning phenomenon. The preoperative clinical variables were suggested by the primary transplant surgeon (HGH) as factors that might influence surgical or postsurgical cost.


Invasive line days (ILDAYS), defined as the number of days a patient is on indwelling arterial and/or venous catheters prior to surgery, might be related to the risk of postoperative infection, which can prolong the patient's lenght of stay and increase the hospital cost. Preoperative prothrombin time (PTT), an indicator of the patient's clotting factors, can influence operating room time by increasing the risk of postoperative bleeding. Preoperative serum bilirubin concentration is an indicator of liver function, and serum creatinine concentration is an indicator of kidney function. Abnormally increased preoperative pulmonary vacular resistance (PVR) is a risk factor for right heart failure. Patients were classified as being underweight or overweight if their preoperative body weight was outside of a gender-and age-specific normal weight interval based on insurance company tables. Weight status (UNDERWT or OVERWT) is an indicator of nutritional status and general health. Additionally, surgery can be more difficult and prolonged in patients who are grossly overweight. Surgery is also more difficult in patients who have had previous cardiac or thoracic surgery (PCS), which is associated with an accumulation of scar tissue. Whether or not the patient required a mechanical cardiac assist device (ASSDEV), was taking inotropic drugs (IDRUGS) to increase the heart's efficiency, or was at home (ATHOME) in stable condition prior to transplantation are indicators of general preoperative health status.

Any of the above factors could produce effects on cost that might be mistaken for a learning phenomenon if they were to change systematically (i. e., become less severe) with successive patients over time. In addition, patients who died during surgery or shortly after surgery (OPDEATH) would be expected to have lower costs associated with a shorter postperative hospital stay.


A three-step process was used to model the effects of learning on cost: (1) preliminary model specification, (2) model testing and evaluation, and (3) final model specification.

Preliminary Model

An initial plot of each patient's surgical and postsurgical costs ordered chronologically by the respective date of surgery revealed a nonlinear decreasing trend. To fit this trend, we created an initial logarithmic reference model using the variable LOGHSEXP in a least-squares regression to predict cost. AGE and SEX were included in this intial model to control for the effects of these demographic variables. Using the reference model as a base, we then performed a series of regressions by adding to the reference model one or more clinical variables from Table 1. LOGHSEXP was forced into each of these regression models, as were AGE and SEX. All additional variable from Table 1 were included based on their statistical contribution to the total model [R.sup.2]. The SAS R-SQUARE procedure was used to estimate the parameters for each of these tentative regression equations (SAS Institute, Inc. 1985). From this process a single regression equation was selected for further consideration by identifying the model that produced the largest incremental improvement in [R.sup.2] with the fewest number of parameters.

Model Testing and Evaluation

The tentative model generated in Step 1 was further evaluated by examining the standardized residuals and leverage statistics associated with each patient in order to identify outliers and influential observations. Once identified, these observation were selectively deleted from the data set one at a time and the model parameters were reestimated. Parameters were deleted from the model if, after discarding an observation that had a large influence on the regression equation, the parameter became nonsignificant.

Final Model Specification

The final model was generated by reapplying the SAS R-SQUARE procedure using a reduced list potential predictor variable that excluded those variable found in Step 2 to be highly influenced by a single observation. The final regression model was thus assured of having a high level of explanatory power (i.e., high [R.sup.2]) without being unduly influenced by a small number of unique cases.


The average cost of heart transplantation is displayed by fiscal year in Figure 1. As a point of comparison, the average annual cost of coronary artery bypass graft (CABG) surgery during this same period of time is also shown in Figure 1. The cost of both procedures have been adjusted for inflation using the global percentage increase in local hospital expenses per annum as the inflation factor. Costs are expressed in constant FY 1988 dollars. As shown in the figure, the cost of heart transplantation demonstrated a systematic decrease over time, while for CABG surgery the cost trend is flat. This suggests that the decrease in heart transplantation cost was program specific and not due to a more general effect associated with the cardiovascular surgery program as a whole.

Summary statistics for each of the potential predictor variables and their relationship with hospital cost are displayed in Table 2 and Table 3. The average heart transplant patient in this data set was 44 years old, spent 21 days in the hospital during the transplant admission, and accrued $39,151 in surgical and postsurgical hospital costs. The majority of the patients (76 percent) were men. Prior to surgery, 20 percent of the patients were being supported by a mechanical cardiac assist device, 42 percent were being supported by inotropic drugs, and 36 percent were at home in stable condition. Five patients (7 percent) died within seven days postoperatively.

Hospital experience (HOSPEXP), defined for each patient as the number of procedures performed prior to the current procedure, exhibited a stronger zero-order correlation with cost than any other variable considered (Table 2). When defined as the number of previous cases performed in the hospital prior to each patient's transplant surgery, the linear effect of accumulating experience was inversely realted to cost (r = -.32, p < .005). When defined as a nonlinear effect in terms of the natural logarithm (LOGHSEXP), the inverse relationship with cost was even stronger (r = -.45, p < .0001). The only preoperative clinical variable that had a significant zero-order correlation with cost was BILIRUBIN (r = .27, p < .05). Neither patient AGE nor SEX was significantly correlated with hospital cost.

Operative death (OPDEATH) was also significantly related to cost. As one might expect, patients who died during or within seven days after surgery cost less ($25,584) than those who survived ($40,179)(p < .01).



Table 4 presents the results of the multiple regression analysis showing the effect of hospital experience (LOGHSEXP) on cost, controlling for clinical variable that were found to have a simultaneous influence on Table 4: Regression Results Showing the Effect of Hospital Experience on Average (Per Patient) Cost Controlling for Age, Sex, and Significant Clinical Variables


cost. Two obvious cost outliers were temporarily deleted for purposes of model development. The parameters for the final model were then estimated twice, with and without the outliers included. The two outliers had costs of $146,357 and $150,984, placing them at 3.9 and 5.7 standard errors from their respective predicted costs. The model parameters are relatively insensitive to these outliers, however, given that the parameters are statistically significant when the two outliers are deleted. With the outliers included, AGE and SEX become nonsignificant, as does PTT. The coefficients themselves, however, do not change appreciably when the equation is recalculated with the outliers included. The model explains 38 percent of the total variability in hospital cost with the two outliers included, and 50 percent of the variability with the outliers deleted.

With the outliers included, the model projects a decrease in cost of $16,542 for each successive log unit of experience gained. The nature of the learning curve can be more easily depicted by retransformation from log units back into number of cases. If the first patient to undergo heart transplantation at the hospital had been a 45-year-old male with a PTT equaling 15 and with all other variables controlled (i.e., all binary variables set to zero), the model predicts that this patient would accrue surgical and postsurgical costs of $81,297. If this same patient had been the tenth case, rather than the first, with the hospital having benefited from the experience gained in nine previous cases, the model predicts this patient would now cost only $48,431, or approximately 60 percent of the cost of the first case. Had this patient been the twenty-fifth case, the predicted cost would be $35,352 (43 percent of the original cost), and had he been the fiftieth case the cost would be $25,458 (31 percent of the original cost).

The specific experience of individual surgeons was not an additional contributing factor, either as a linear (SURGEXP) or logarithmic (LOGSGEXP) effect, once the learning factor for the institution as a whole (LOGHSEXP) was taken into account.

Four preoperative variables were found to have a significant influence on cost: (1) number of days preoperatively in which the patient was supported by invasive arterial or venous lines (ILDAYS), (2) whether or not the patient was supported by inotropic drugs preoperatively (IDRUGS), (3) the patient's preoperative prothrombin time (PTT), and (4) whether or not the patient was sufficiently stable to be living at home prior to undergoing the transplant surgery (ATHOME).

As shown in Table 4, ILDAYS has a direct linear relation to cost. The model predicts an average increase in operative and postoperative cost of $1,277 for each additional preoperative day that the patient is with indwelling arterial or venous catheters. Likewise, PTT shows a direct linear relation to cost. Each one-second increase in the patient's preoperative prothrombin time is associated with an increase of $1,040 in operative and postoperative cost. The two remaining preoperative variables are inversely related to cost. Patients who are on inotropic drugs (IDRUGS) preoperatively are $13,936 less expensive with respect to average operative and postoperative costs. Similarly, patients who are at home (ATHOME) in stable condition prior to surgery cost an average of $17,096 less than patients hospitalized before surgery.

Operative death (OPDEATH), defined here as any mortality occurring during the surgical procedure or at any time within seven days postsurgery, is also inversely related to cost. The model predicts that these patients will be associated with an average reduction in cost of $25,147.

Table 5 shows the predicted learning curve for male and female patients who are at different levels of risk for increased costs based on their preoperative condition. For purposes of illustration, patients in Table 5 are considered not at risk for increased cost if they are at home prior to surgery (ATHOME = 1), are without invasive lines (ILDAYS = 0), and have an average prothtombin time (PTT = 15). Patients are considered at risk of accruing increased costs if they require hospitalization prior to transplantation (ATHOME = 0), are with invasive lines for seven days (ILDAYS = 7), and have a prothrombin time approximately one standard deviation above the average (PTT = 20). Table 5: Change in Expected Cost as a Function of Hospital Experience (Case #) for a 45-Year-Old Patient with or without Preoperative Risk Factors


(*) Patient is at home in stable condition (ATHOME = 1), without invasive, arterial, or venous catheters (ILDAYS = 0), with an average PTT (PTT = 15). [dagger] Patient is in the hospital prior to transplant (ATHOME = 0), with indwelling invasive, arterial, or venous catheters for seven days prior to surgery (ILDAYS = 7), and with a PTT one standard deviation above the mean (PTT = 20).

By comparing entries across any given row of Table 5, one can gain an appreciation of the effect of the risk factors at a fixed point on the learning curve. For example, an inspection of the first row reveals that if the first case to undergo transplantation had been a male with no risk factors, the predicted operative and postoperative cost would be $81,297. Had this first case been a female, the predicted cost would be $93,214. If the male patient had had the risk factors described earlier, the predicted cost would be $103,897, while a female patient with these same risk factors would have a predicted cost of $115,813. By scanning down the columns of Table 5, one can see how the presence or absence of various combinations of risk factors serves to raise or lower the level of the learning curve.


The principal finding of this study is that the reduction in the cost of heart transplantation over time can be explained to a substantial degree by a learning effect. The effect of learning on clinical outcomes, such as adverse events and mortality, has been demonstrated in a number of previous studies (Farber, Kaiser, and Wenzel 1981; Flood, Scott, and Ewy 1984a, 1984b; Hannan, O'Donell, Kilburn, et al. 1989; Luft, Hunt, and Maerki 1987; Luft, Bunker, Enthoven 1979; Maerki, Luft, Hunt 1986; Riley and Lubitz 1984; Shortell and LoGerfo 1981; Showstack, Rosenfeld, Garnick, et al. 1987; Luft et al. 1990). Similar effects of learning on cost, however, have been demonstrated only occasionally and without controls for potential confounding factors that might mimic a learning curve (Saywell, Woods, Halbrook, et al. 1989; Smith and Larsson 1989). This study has identified a learning phenomenon within the context of a longitudinal study design, which greatly reduces the likelihood that the observed cost reductions are due to economies of scale rather than to learning. Moreover, the learning phenomenon has been shown to persist even after statistically controlling for the effects of preoperative clinical factors that also influence cost. The present finding is consistent with observations in manufacturing industries that production costs tend to decrease as experience with the production process accumulates (Lieberman 1984; Wright 1936; Belkaoui 1986).

One must be mindful of the complexities involved when estimating the cost of a health care service. Many published studies of health services have used charges as a proxy for cost. However, charges are not equal to, nor are they usually a good approximation of, what a hospital pays for the resources needed to provide a service (Finkler 1982). The ratio of cost to charge (RCC) methodology used in this study provides a rational method for estimating costs from billing data, and represents an improvement over the use of patient charges. However, this methodology is not without limitations. First, hospitals accumulate cost information by department, not by individual patient. Thus, some degree of accuracy is lost when average departmental costs are allocated to individual cases. Second, the overhead allocation rules used in a given hospital are often designed more to optimize reimbursement than to track resource consumption. The overhead allocation process used in this study, however, has been applied consistently from year to year with adjustments for local inflation, and the derived costs represent internally valid estimates of resource consumption within the institution. The estimates reported here, though, are accounting costs derived from the hospital's cost accounting system, not economic costs reflecting specific resources at the patient level.

It must be recognized that any change occurring over time, which is correlated with cost but not included in the statistical model, might produce effects that can be misinterpreted as learning. We have been careful to control for a variety of preoperative clinical factors as well as early postoperative death in our model. Others might point to factors that we have not considered. Clearly, the stability of the surgical team might produce effects similar to a learning phenomenon if less sophisticated personnel were systematically being replaced over time with personnel who were more skilled or more conscientious. In this case, cost might be affected not because of the accumulating experience of a stable team of individuals, but because of systematic changes in the mix of individuals involved. We have included in our modeling process variables defining the experience of individual surgeons. However, we were unable to factor in the multiple changes that may have occurred over time with respect to the entire network of consulting physicians and support staff. While we have included some patient characteristics that might be expected to influence cost, such as age, gender, and body weight, other factors such as smoking history and pulmonary function have not been included. None of these factors, however, could produce trends in cost similar to a learning phenomenon unless they were changing coincedentally over the the course of time in a way that would produce a favorable impact on cost. Factors no more likely to be present early in a program's history than late would not mimic a learning effect.

Although the learning phenomenon as defined here appears to be robust, the intercept of the learning curve is sensitive to various clinical factors. This is illustrated by the predicted costs for various clinical subpopulations (Table 5). Our model suggests that costs can best be controlled during the early part of the learning curve by paying close attention to patient selection factors and by operating on patients with few or no preoperative risk factors.

The clinical variables in our model were introduced primarily for the purpose of isolating and controlling their effects in order to develop an unbiased and more precise estimate of the effect of learning on cost. The factors themselves are of interest as well. At least two factors that attained statistical significance in our model, AGE and ATHOME, are related to a patient's general physical condition prior to surgery. Age is often viewed as a proxy of physiological reserve and is commonly used by surgeons as one criterion in selecting candidates for transplant surgery. Younger patients are presumably more resilient and have a greater capacity to tolerate surgery and to recuperate after surgery. In our model, age is also shown to be predictive of cost. A more direct indicator of a patient's physical condition is whether the patient is stable enough to remain at home while awaiting a donor heart. In our model, patients who were at home in stable condition prior to surgery were approximately $1,700 less costly in terms of operative and postoperative expenses, compared to patients who required hospitalization prior to surgery.

The use of inotropic drugs properatively was associated with an average $13,900 reduction in cost. Use of these drugs preoperatively in a patient who is in a severely weakened hemodynamic state may improve the patient's chances of experiencing an uneventful and therefore less costly postoperative course. The cost of inotropic drugs, which are used to support the patient's diseased heart prior to transplantation, was not included in the postoperative costs predicted by our model. Thus, some of the postoperative savings that the model attributes to these drugs would be offset by the operative expense of the drug therapy itself.

The number of days that a patient is with invasive lines prior to surgery (ILDAYS) increases cost by approximately $1,276 per day. In addition to indicating preoperative illness severity, indwelling arterial or venous lines expose the patient to an increased threat of infection, which can increase postoperative cost and length of stay.

Prothrombin time (PTT) also had a direct, positive influence on cost. PTT is a measure of blood-clotting time. The higher the PTT, the more likely it is that bleeding will become a problem during surgery, resulting in longer operating room times. Higher PTT values may also be associated with postoperative bleeding, which can result in the need for a repeat surgery to stop the bleeding. In either case, high PTT values would be expected to increase the consumption of hospital resources. In our model, cost is increased approximately $1,000 for each one-second increase in preoperative PTT.

Operative death (OPDEATH), defined here as any death occuring during surgery or within seven days following surgery, is associated with an average $25,000 reduction in cost. Since the average length of hospital stay for this patient sample was 21 days, any patient suffering an operative death would, by definition, have a shorter than average length of stay and, therefore, lower than average hospital costs.

The specific experience of individual transplant surgeons, when defined in our model as either a linear or a logarithmic variable, had no additional effect on cost separate from the experience of the institution as a whole (which included surgeon experience). Previous studies of volume-quality relationships have shown that whether total hospital volume or individual physician volume is a more important predictor of patient outcome depends on the particular medical or surgical procedure being considered (Hannan, O'Donnell, Kilburn, et al. 1989; Kelly and Hellinger 1987; Luft et al. 1990).

Our study, which examines cost data rather than outcomes, implies that the effect of learning on resource consumption in heart transplantation is a product of the collective experience of the organization as a whole, not merely the experience of individual surgeons. If increased operational efficiency is the source of cost reductions, then it is likely that these efficiencies are learned at a system level as the entire transplant team (including the surgeons) gains experience in the successful coordination of activities and resources.

The empirical relationship between volume and cost has led to a consideration of regionalization as a cost-containment policy. The concept of regionalization is based on the notion that savings will accrue if specialized procedures, such as heart surgery, are centralized at a small number of high-volume hospitals (Finkler 1979). The expected savings would result from economies of scale whereby unit costs would be decreased by distributing the fixed costs of a service over a larger volume of procedures and by negotiating volume discounts for supplies. The present study contributes an additional factor to the argument for regionalization - namely, the concept that cost savings can accrue as a result of learning or experience. It is unlikely that the decrease in cost for our longitudinal series is due to economies of scale, since the patient volume per year remained relatively stable across time. The decrease in cost is consistent, however, with a theory that invokes a learning-cost relationship. The policy implication is that a center that accumulates sufficient experience can expect to become more cost efficient independent of any additional effects on cost associated with volume.

Although our model describes a learning phenomenon, it does not postulate a formal mechanism to explain how learning occurs. One might assume that the experience gained from operating on more patients leads to more appropriate patient selection, better preoperative patient management, improved operating room skills, and fewer postoperative complications, all of which might reduce costs. An unanswered question, however, relates to the span of time during which learning matters.

One might generate competing predictions about the time course of learning relative to the rate of patient accrual.(1) Consider, for example, two hospitals, one that performs 100 procedures at a uniform rate over ten years, the other that performs them uniformly over two years. If learning is solely a function of the absolute number of procedures performed, then the cost curves for both hospitals (adjusting for inflation) will be the same. However, if the time span during which learning occurs is an important factor, then the curves for the two hospitals will be different.

We would expect that the form of the learning curve might depend on both of these variables interacting in some yet-to-be-determined manner. That is, each additional procedure would provide an additional opportunity for learning that should result in an incremental improvement in efficiency. However, the rate at which these cases accumulate would probably exert an influence as well, with some optimum rate of accrual resulting in an optimum rate of learning.

The effects of these two factors (i.e., absolute number of procedures performed and rate of accrual) cannot be isolated and examined separately in a case series, such as ours, drawn from a single institution. The ideal approach would be to examine ordered time series from multiple institutions where the accrual rate varies from one institution to another. Such an approach would provide a cross-sectional comparison among institutions (allowing for an examination of economies of scale, based on differences in volume at a given point in time), and a longitudinal comparison within institutions (allowing for an examination of learning based on differences in rates of accrual across time). Such an analysis would have an important bearing on public policies that seek to influence aggregate costs by concentrating expensive medical procedures in designated regional centers based on volume considerations alone. Future studies of national data files designed to permit both cross-sectional and time-series comparisons in the same analysis would have obvious relevance for such policies. Further research should also be conducted at a micro level in order to elucidate the mechanisms by which experience with surgical procedures is translated into cost savings.


(1.) We are indebted to an anonymous reviewer who suggested these two possibilities.


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Author:Woods, John R.; Saywell, Robert M., Jr.; Nyhuis, Allen W.; Jay, Stephen J.; Lohrman, Rosemary G.; Ha
Publication:Health Services Research
Date:Jun 1, 1992
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