Ann Thorac Surg 1995;60:1640-1651
© 1995 The Society of Thoracic Surgeons
Original Articles: Cardiovascular
Influence of Ejection Fraction on Hospital Mortality, Morbidity, and Costs for CABG Patients
Gregory L. Kay, MD,
Guo-Wen Sun, PhD,
Atsushi Aoki, MD,
Curtis A. Prejean, Jr, MD
The Heart Institute, Good Samaritan Hospital, Los Angeles, California
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Abstract
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Background. Preoperative ejection fraction (EF) has been shown to adversely affect postoperative hospital mortality and morbidity for patients undergoing isolated coronary artery bypass grafting.
Methods. To investigate influence of EF on isolated coronary artery bypass grafting outcomes (overall hospital mortality, hospital cardiac mortality, hospital morbidity, and hospital costs), data were reviewed from 1,354 consecutive patients who underwent isolated coronary artery bypass grafting between January 1, 1990, and April 30, 1992, at a single nonprofit hospital. Overall hospital mortality was 4.06% (cardiac, 2.36%). Hospital morbidity was 14.25% (including mortality). Hospital costs (not charges) averaged $16,673 per patient. To explore the impact of preoperative EF, EF was stratified into regular intervals. Each interval was then compared with regard to hospital mortality, morbidity, and average costs. A new statistical tool, discharge analysis, was developed to analyze the cost data. This was necessary because previous efforts at cost analysis have used tools inappropriate for real world cost data.
Results. The statistical analysis showed that patients with EF of 0.40 or greater had the best outcomes (lowest mortality, morbidity, and cost). Once the EF is 0.40 or greater the EF does not carry further predictive value. At EF less than 0.40, patients with EF less than 0.30 have a poorer outcome than patients with EF of 0.30 to 0.39.
Conclusions. (1) Ejection fraction is a valid predictor of mortality, morbidity and resource utilization based on statistical analysis. (2) Patients can be broadly grouped as having EF greater than 0.40, less than 0.30, or from 0.30 to 0.39 with regard to clinical and cost outcomes. (3) Postoperative length of stay is not predicted by risk-adjusted EF. (4) A new tool, discharge analysis, is presented to facilitate cost analysis.
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Introduction
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See also page 1651.
Poor preoperative ejection fraction (EF) has been shown to be significantly associated with higher mortality and morbidity for patients undergoing isolated coronary artery bypass graft (CABG) procedures. By extension, EF should also be highly correlated with hospital cost. Thus far, little is known about the influence of EF on hospital cost (not charges) [1–7]. To date there is no standard for judging ``good'' versus ``bad'' ventricular function [1–27]. We sought to develop a statistical basis for such a distinction. During the course of analysis our biostatistician (G.S.) discovered that standard approaches to cost analysis using techniques such as linear regression and Student's t test are inappropriate. This is because these techniques assume that cost data are normally distributed and not censored. Real world health care cost data are neither normally distributed (even after logarithmic transformation) nor uncensored. As a result a new tool for analysis of cost after cardiac operations was developed. This tool, discharge analysis, uses techniques of survival analysis. These techniques are specifically intended to deal with skewed and censored data.
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Material and Methods
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Patient Population and Data
A computerized database is maintained on all patients undergoing myocardial revascularization at a single nonprofit hospital. Between January 1, 1990, and April 30, 1992, 1,376 consecutive patients underwent isolated CABG. Patients requiring procedures involving heart valves, automatic implantable cardioverter defibrillator, left ventricular aneurysms, the carotid artery, peripheral vessels, or lungs alone or with CABG were not included in this study. Because there are 22 patients (1.6%) with missing preoperative EF, only 1,354 patients were included in the current study. The following information was available for analysis: patient demographics (age, sex, body surface area, ratio of actual weight to desirable weight, body mass index, patient preoperative risk factors (priority of operation, preoperative use of intraaortic balloon pump [IABP] support, history of previous CABG, history of diabetes, preoperative EF, preoperative myocardial infarction [MI] days), procedural factors (type of cardioplegia: warm or cold blood; type of graft: vein graft alone versus internal mammary artery [IMA] graft; total number of grafts), hospital death (for all causes), cardiac death (due to mechanical heart failure or arrhythmias), and postoperative complications (cardiac arrest, sternal infection, disseminated intravascular coagulation, respiratory failure, MI, reoperation for excessive bleeding, cerebrovascular accident, renal failure, and postbypass initiation of IABP support).
In this series, EF was measured or estimated by the cardiologist, surgeon, or cardiac radiologist in 95% of patients based on diagnostic ventriculogram. A single plane was used in 85% of studies. Ejection fraction was determined by planimetry 25% of the time. Only an EF by echocardiogram was available for the remaining 5% of patients.
Hospital total length of stay (LOS), hospital preoperative LOS, hospital postoperative LOS, total hospital costs (not charges), and patient discharge dispositions were obtained using the hospital's cost accounting system (Transition Systems, Inc, Boston, MA). A patient's total hospital cost was defined as the total adjusted direct cost of all intermediate products required by that patient during the hospitalization. These would be the costs for the operating room, intensive acute care, regular acute care, pharmacy, clinical laboratory, surgical supplies, therapy or rehabilitation, radiology, cardiac catheterization laboratory and supplies, pulmonary function, electrocardiology, electrophysiology, blood treatments, dialysis, and other hospital services. To reflect true resource consumption, only costs directly related to patient care (fixed direct) or costs that vary with patient volume (variable direct and variable indirect) were used in this study (independent of charges or bills and not derived using charge-to-cost ratios). Professional fees are not included in this analysis.
Preoperative cardiac catheterization or angioplasty was performed in 591 of the patients (43.6%) in this series during the same hospitalization. Cost analysis was completed with the cost for cardiac catheterization/angioplasty included and excluded.
We defined two groups of patients: the low-risk group was less than 70 years of age, had a body surface area greater than 1.6 m2, had no MI within 14 days, was not undergoing a reoperation or emergency procedure, and did not have an IABP preoperatively. The non-low-risk patients lacked one or more of the above characteristics. There were 485 low-risk patients and 869 non-low-risk patients. In the patients with EF greater than 0.40 (n = 1,034) the IMA was used in 62% of patients in the low-risk group and in 30% in the other group. For EF of 0.30 to 0.39 (n = 210) IMA was used in 43% of the low-risk patients and 18% of the other group. For EF less than 0.30 (n = 110) IMA was used in 12% of low-risk patients and 9% of the other group. Clearly other factors also influenced the use of the mammary artery. In general we reserve the IMA for left anterior descending coronary artery revascularization.
Statistical Methods
Ejection fraction was measured as a continuous variable. Whether data analysis should use the variable as a continuous variable or use a regrouped variable instead is a statistical question and should depend on the data. A continuous variable need not always be analyzed as a continuous function, and although it is true that a continuous variable may provide more information than a discrete variable, an appropriate grouping of a continuous variable may allow for more effective data analysis.
In this study, we first explore whether there is a cutoff point for preoperative EF such that the EF is not significantly associated with outcomes in isolated CABG (overall hospital mortality, hospital cardiac mortality, hospital morbidity, and hospital costs) for patients with EF at or above the cutoff point. We next investigate the influence of the EF on outcomes in isolated CABG and present hospital cost data.
For discrete variables comparisons were made using the 
2 test (or Fisher's exact test when appropriate). For continuous variables we used Student's unpaired t test (or the F test for more than two comparison groups). Stepwise logistic regression was used to evaluate the influence of the EF on clinical outcomes (hospital mortality, cardiac mortality, and morbidity). Linear regression was applied for analysis of hospital LOS and cost data after logarithmic transformation of LOS and costs was performed to achieve normal distribution.
Technically, there are two types of nonmissing cost data available based on discharge disposition. When a patient is discharged ``to home'' (ie, has reached a level of health where home care is appropriate), the observed total hospital cost for this patient is considered complete (noncensored). This means the patient has achieved an appropriate home discharge condition (AHDC) after consuming the given amount of hospital resources. Hospital cost data are considered incomplete (censored) when patients leave hospital before reaching AHDC. Cost data are censored when a patient is transferred to another health care facility for continued medical care or if the patient leaves against medical advice, or if the patient dies in the hospital. Under these circumstances, the real cost of the hospitalization required to reach AHDC remains unknown. It is only known that the cost will exceed the observed hospital cost. This concept is key.
Conventional methods used in cost analysis (t test or linear regression) require normally distributed and noncensored data. Censored data distort the analysis, and conclusions based on analysis of censored data may be erroneous. To avoid this pitfall, we analyzed hospital cost data using the technique of discharge analysis (a modification of survival analysis) [1]. This method allows us to compare the estimated discharge distributions for the different patient groups at every level of hospital cost. Patients discharged after the reaching AHDC are referred to as discharged ``to home.'' Patients who do not reach this AHDC are referred to as discharged ``not to home.''
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Results
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Distribution of Preoperative Ejection Fraction
The cumulative distribution of the preoperative EF from the 1,354 patients undergoing isolated CABG is shown in Figure 1
with an average of 0.53 and a standard deviation of 0.18. The minimum and maximum EFs are 0.10 and 0.85. There are 320 patients (23.6%) with EF less than 0.40, of whom 51 patients (15.94%) had censored hospital costs. There are 213 patients (15.7%) with EF less than 0.35 of whom 41 patients (19.25%) had censored hospital costs. The overall censoring in this series is 9.75% (132 of 1354).
Strategies for Stratifying Ejection Fraction
We first stratified EF into regular intervals: 0.10 to 0.19, 0.20 to 0.29, 0.30 to 0.39 ...0.80 to 0.89 (referred to strategy I). The observed distributions of outcomes for each EF interval are summarized in Table 1. There is a trend in outcome between intervals less than 0.40 and a clear difference between intervals of 0.30 to 0.39 and 0.40 to 0.49.
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Table 1. . Summary of Distributions of Isolated Coronary Artery Bypass Grafting Postoperative Outcomes by Preoperative Ejection Fraction Intervals (Strategy I)
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No apparent difference in outcomes exists for the intervals greater than 0.40. A critical cutoff point of 0.40 is suggested. Taking into account random fluctuation we suspect that EF is not a significant risk factor for patients with EF of 0.40 or greater, but EF is a significant risk factor for patients with EF less than 0.40. To test our hypothesis, techniques of logistic regression, linear regression, and discharge analysis were applied to two subsets of patients: patients with EF less than 0.40 and patients with EF of 0.40 or greater. The significance levels (ie, the p value) are shown in Table I. Consistently for every outcome, p values are less than 0.05 in the EF less than 0.40 group and are greater than 0.2 in the EF 0.40 or greater group.
To verify that 0.40 is the best uniform EF critical cutoff point for all isolated CABG outcomes, we tested another EF stratification strategy (strategy II): <0.14, 0.15 to 0.24, 0.25 to 0.34, 0.35 to 0.44 ...0.85 or greater. The results are presented in Table 2. Table 2 suggests that neither 0.45 nor 0.35 is a critical cutoff point.
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Table 2. . Summary of Distributions of Isolated Coronary Artery Bypass Grafting Postoperative Outcomes by Preoperative Ejection Fraction Intervals (Strategy II)
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Ejection fraction measurements of 0.36 to 0.39 and 0.41 to 0.44 are not commonly recorded due to a tendency to round off. Based on the data set, 0.40 appears to be the best cutoff measurement. This is consistent with other reports in the literature.
There is a trend in outcomes when comparing EF less than 0.20, EF of 0.20 to 0.29, EF of 0.30 to 0.39, and EF of 0.40 or greater. However, because the sample size for patients with EF less than 0.20 is relatively small (n = 13), for purposes of further analysis we stratified EF into three groups: EF less than 0.30 (n = 110), EF of 0.30 to 0.39 (n = 210), and EF of 0.40 or greater (n = 1,034).
Comparison of Patient Characteristics Between Ejection Fraction Groups
There is no significant difference in distributions of the patient age (p = 0.392), sex (p = 0.397), history of previous CABG (p = 0.407), type of cardioplegia used (p = 0.261), and preoperative catheterization or percutaneous transluminal coronary angioplasty during the same hospitalization (p = 0.743) (Table 3). Significant associations are found between poor EF and small body surface area (p < 0.01), small body mass index (p < 0.01), cachexia (p < 0.01), prior MI (p < 0.01), priority of operation (p < 0.01), history of diabetes (p < 0.01), use of preoperative IABP support (p < 0.01), and average number of grafts (p = 0.06).
Unadjusted Comparisons
Unadjusted comparisons are shown in Table 4.
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Table 4. . Unadjusted Comparisons of Isolated Coronary Artery Bypass Grafting Outcomes Among Ejection Fraction Groups
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HOSPITAL MORTALITY, AND MORBIDITY: UNADJUSTED.
Compared with patients with EF of 0.40 or greater, patients with EF less than 0.30 have almost five times greater hospital mortality (p < 0.01), more than 11 times greater cardiac mortality (p < 0.01), and about two and half times greater morbidity (p < 0.01).
HOSPITAL LENGTH OF STAY UNADJUSTED.
If we consider patients with EF of 0.40 or greater as the baseline group, on average, hospital costs were $6,031 per case higher for patients with EF less than 0.30 and $2,396 per case higher for patients with EF of 0.30 to 0.39 (p < 0.01). Poor EF is also found to be significantly associated with longer total hospital LOS (p < 0.01), preoperative hospital LOS (p = 0.02), and postoperative hospital LOS (p = 0.03).
Note, however, the cost analysis in Table 4
does not account for censored costs. Because poor EF is significantly associated with hospital mortality, the average costs per case were biased (down) due to patient death during hospitalization (AHDC was not achieved). The important requirement that data are noncensored severely limits any interpretation of the previous comparisons of cost and LOS [1]. Hospital cost data are incomplete or censored when a patient is discharged not to home. This occurred in almost 10% of the sample. Conventional techniques such as linear regression or t test cannot deal with censored data. To avoid these limitations and to reflect differences in patient discharge dispositions (to home versus not to home), techniques adapted from survival analysis (such as the Kaplan-Meier method) were applied to compare patient discharge distributions for various EF groups. We call this approach discharge analysis. These should give a more accurate indication of true costs. The Kaplan-Meier estimated median hospital costs are also reported in Table 4.
Figure 2 compares three discharge curves estimated using the Kaplan-Meier method. The upper curve (for EF 
0.40; n = 1,034; censoring = 7.8%) is always higher than the middle curve (EF = 0.30–0.39; n = 210; censoring = 14.3%) and bottom curve (EF < 0.30; n = 110; censoring = 19.1%). Thus, given the same level of hospital resource consumption, patients with EF of 0.40 or greater were more likely to have been successfully discharged to home than patients with EF less than 0.40 (p < 0.001). For example, by spending $15,000 the estimated discharge to home probabilities are 65%, 47%, and 42% for patients with EF 0.40 or greater, 0.30 to 0.39, and less than 0.30, respectively. Conversely, to achieve a discharge to home probability of 80% requires an estimated average cost of approximately $17,702 for patients with EF of 0.40 or greater, $20,780 for patients with EF of 0.30 to 0.39, and $28,398 for patients with EF less than 0.30 (p < 0.001).
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Fig 2. . Discharge distributions of patients with preoperative ejection fraction (EF) of 0.40 or greater (the top curve), 0.30 to 0.39 (the middle curve), and less than 0.30 (the bottom curve): the Kaplan-Meier estimates. The p value is derived by the Wilcoxon test of equality over strata.
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Adjusted Comparisons of Outcomes Among Ejection Fraction Groups
One of the limitations in interpreting results of the unadjusted comparisons is that estimates reported do not take into account the effects of other known risk factors. The differences shown between and among EF groups are also significantly affected by other risk factors such as patient age, emergency status, history of diabetes, and co-morbidities. In other words, the differences shown in Table 4 and Figure 2 are not only due to the status of EF but also to other factors that can confound the analysis. When estimates are not adjusted for possible confounders, results obtained could be distorted and lead to incorrect conclusions. To reduce such bias, we examined other risk factors associated with hospital costs or EF status.
HOSPITAL MORTALITY AND MORBIDITY: RISK ADJUSTED.
To adjust the influence of EF on hospital mortality and morbidity, stepwise logistic regression was used. Table 5 represents a summary of logistic regressions of postoperative outcomes on EF and all other factors included in Table 3. If we consider patients with EF of 0.40 or greater as a reference group, the estimated hospital mortality for all causes will be increased by 134% (p = 0.016) for patients with EF of 0.30 to 0.39 and by 171% (p = 0.014) for patients with EF less than 0.30. For cardiac mortality, the estimated corresponding increases are even higher (373% for EF of 0.30 to 0.39 versus EF 0.40 [p < 0.001] and 574% for EF < 0.30 versus EF 0.40 [p < 0.001]). The estimated probabilities of postoperative complications are 63% (p = 0.018) and 87% (p = 0.015) greater for patients with EF of 0.30 to 0.39 and EF less than 0.30, respectively, compared with patients with EF of 0.40 or greater after risk adjustment. Appendix A gives details with respect to other variables used to adjust hospital mortality, hospital cardiac mortality and hospital morbidity.
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Table 5. . Adjusted Comparisons of Isolated Coronary Artery Bypass Grafting Outcomes Among Ejection Fraction Groups
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HOSPITAL LOS AND COSTS RISK ADJUSTED.
Compared with patients with EF of 0.40 or greater, the total hospital LOS is generally longer by 5.1% (p = 0.15) for patients with EF of 0.30 to 0.39 and by 9.2% (p = 0.06) for patients with EF less than 0.30 (Table 6). Table 6 also suggests that patients with EF less than 0.30 generally are in the hospital longer before operation (p < 0.01), compared with patients with better EF status. Unlike the unadjusted analysis, however, EF status does not significantly influence postoperative hospital LOS after risk adjustments.
Due to the limitations of linear regression and the t test (specifically the requirements of normalized and noncensored data), hospital cost data were analyzed using discharge analysis [1]. The Cox proportional hazard model makes it possible to adjust discharge distributions for the effects of other risk factors and to study them graphically. Table 7 represents a summary of discharge ratios by EF groups. A discharge ratio greater than 1.0 indicates that patients will consume more hospital resources to reach AHDC than the reference group. The interpretation of the discharge ratio is equivalent to that for the risk ratio, which is commonly used in the analysis of clinical outcomes (refer to Appendix B for details).
A total of 591 patients (43.6%) underwent preoperative cardiac catheterization or percutaneous transluminal coronary angioplasty procedures during the same hospitalization. The costs in the catheterization laboratory averaged $1,423 per patient (standard deviation, $1,094; median, $1,024). To investigate how and to what extent the presence or absence of the cardiac catheterization or angioplasty procedures influence the estimates of parameters, discharge analysis was performed for hospital costs excluding those consumed in the cardiac catheterization laboratory and associated cardiac diagnostic supplies. Results are shown in Table 7. No significant difference was observed.
Another way to assess the association between EF status and hospital costs is to use graphic presentations. If we consider that a baseline is a population of patients who are 70 years old, male, with medium weight ratio, medium body surface area, and medium body mass index, requiring three grafts, then the three curves in Figure 3 from the top to the bottom are the Cox adjusted estimates of discharge to home distributions for the baseline patients with EF of 0.40 or greater, 0.30 to 0.39, and less than 0.30, respectively. We can read from the figure that at a level of $14,000 resource use, the estimated discharge to home probabilities are 75.6%, 67.1%, and 61.7% for patients with EF of 0.40 or greater, 0.30 to 0.39, and less than 0.30, respectively. In like fashion, to achieve a discharge ``to-home'' probability of 90% requires approximately $15,968 for patients with EF of 0.40 or greater, $17,303 for patients with EF of 0.30 to 0.39, and $18,220 for patients with EF less than 0.30. These differences are statistically significant (p < 0.01).
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Fig 3. . Discharge distributions of patients with preoperative ejection fraction (EF) of 0.40 or greater (the top curve), 0.30 to 0.39 (the middle curve), and less than 0.30 (the bottom curve): the Cox adjusted estimates. (Group 1 versus group 2 p = 0.004; group 1 versus group 3 p = 0.001).
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Case Mix: Risk Adjusted
Multivariate predictions of outcomes can be made for typical patients with various combinations of risk factors. To demonstrate the results more efficiently, we use graphic presentations. The baseline population is, for example, male patients with medium body surface area (1.6 to 1.99 m2), medium ratio of body weight to ideal weight (1.0 to 1.59), and medium body mass index (22 to 29.9 kg/m2), requiring three grafts, and experiencing none of other risk factors included in this study. We define six typical patient groups as follows: group 1 (baseline), group 2 (baseline, history of prior CABG and EF of 0.30 to 0.39), group 3 (baseline, preoperative IABP, EF < 0.30), group 4 (baseline, prior MI 1 to 2 days, EF < 0.30), group 5 (baseline, history of CABG, preoperative IABP, EF of 0.30 to 0.39), and group 6 (baseline, preoperative IABP, prior MI 1 to 2 days, EF < 0.30).
HOSPITAL MORTALITY AND MORBIDITY: RISK ADJUSTED.
To evaluate how postoperative outcomes can differ, we present Figures 4, 5, and 6. for comparisons of hospital mortality for all causes, hospital cardiac mortality, and overall hospital morbidity, respectively, using the six patient groups defined. These curves also show the impact of age on outcome.
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Fig 4. . Estimated hospital mortality by age for the 6 typical patients (refer to text for detailed definitions).
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Fig 5. . Estimated hospital cardiac mortality by age for the 6 typical patients (refer to text for detailed definitions).
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Fig 6. . Estimated hospital morbidity by age for the 6 typical patients (refer to text for detailed definitions).
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HOSPITAL COSTS: RISK ADJUSTED.
There are two practical questions to be asked for each of the six patient groups. First, what hospital cost is required to achieve a given level of probability of reaching AHDC? Second, given hospital expenditure, what is the probability that this patient is well enough to go home? In Figure 7, for example, by spending the last dollar of $20,000 the estimated probabilities of discharge to home are 98.2% for case 1, 84.5% for case 2, 71.5% for case 3, 75.1% for case 4, 57.5% for case 5, and 47.1% for case 6. The lower the curve in Figure 7, the higher the risk for hospital costs.
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Fig 7. . Estimated probability of discharge to home by total hospital costs for the 6 typical patients with age = 70 years old (refer to text for detailed definitions).
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Comment
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The relationship between preoperative EF and outcome after isolated CABG has been examined over the years [1, 2, 6, 7]. Although various clinical reports have focused on EFs between 0.30 and 0.40 as a ``critical number'' in determining outcomes, the importance of these numbers has not been supported by formal statistical analysis. Using a contemporaneous data set and clinical as well as cost outcomes as benchmarks, we have demonstrated using statistical techniques that 0.40 is one critical cutoff point for EF. Patients with EF less than 0.40 have demonstrably poorer clinical and cost outcomes than patients with EF of 0.40 or greater. However, at less than 0.40 we find that EF can be grouped as EF less than 0.30 and EF of 0.30 to 0.39, with the lower EF group having statistically poorer cost and clinical outcomes (p < 0.05). Although it is our impression that patients with EF less than 0.20 may actually be a separate group with the poorest clinical and cost outcomes, the numbers in this series were too small for proper analysis.
Table 5 and Table 6 show the adjusted comparisons, based on EF, for clinical outcomes and LOS. Patients in the highest risk group have 2.7 times greater hospital mortality, 1.9 times hospital morbidity, and 6.7 times cardiac mortality. The LOS is often used as an indirect indicator for hospital cost. Our results make us question this practice: preoperative risk-adjusted EF does not predict LOS after operation. We believe this is due to two factors. First, LOS does not necessarily reflect intensity of services. Second, early deaths will distort the analysis.
We therefore set out to confirm or reject the hypothesis that hospital cost, like any clinical outcome, is influenced by EF once adjusted for other risk factors. In analyzing the data, our biostatistician (G.S.) identified an underlying methodologic problem with ``standard'' analytic methods. When a patient is well enough to go home, the total hospital costs for that episode of care are known. These data are considered complete or uncensored. Unfortunately, not all patients achieve what we now refer to as AHDC. The cost of hospitalization for patients who have not achieved AHDC is considered incomplete or censored. This is because the recorded cost does not reflect the resources that would have been required to get the patient well enough to go home, it only reflects the resources needed to ``get the patient somewhere else.''
In our experience 9.8% of the patients did not achieve AHDC and so had censored cost data. Further compounding the problem is the nonnormal distribution of cost data, even after logarithmic transformation. Statistical tools such as linear regression and t test assume the data are not censored and are normally distributed. An analysis of data that are not normally distributed and have a high proportion of censored observations, using these tools, will necessarily be flawed.
It occurred to our biostatistician (G.S.) that the techniques of survival analysis (Kaplan-Meier curves and Cox regression analysis) do not require noncensored and normally distributed data, and so he developed the technique of discharge analysis by adapting for cost analysis standard techniques of survival analysis. Subsequent literature review uncovered support for this approach [1]. Discharge analysis allows accurate prediction of resource consumption to achieve a given probability of discharge to home as well as probability of discharge to home with a given resource allocation (see Figs 2, 3).
We put this technique forward as an improvement over the techniques of cost analysis used heretofore and believe that the technique of discharge analysis should become the standard. Previously used techniques produce conclusions that cannot be trusted because they are not intended for analysis of data that are nonnormally distributed or censored. Discharge analysis is designed for dealing with such real world cost data.
To evaluate whether the Cox proportional hazards model assumption was met in these data, the estimated log-log curves were graphically inspected. Under this assumption, the log-log curves should be parallel across strata, and in these data, they are approximately parallel.
It has been questioned whether the costs of patients who die in the hospital should be treated as censored observations in discharge analysis [1]. We believe it is necessary to distinguish cost data for patients who reach AHDC from those of patients who do not. There must be a ``standard'' (AHDC in this case) to compare costs for patient health care. Some investigators argue that hospital cost is the real outcome of resource use and death simply modifies the use of resources. However, the cost for an episode of care is an incomplete measurement of resource use unless the discharge disposition of the patient is taken into account. When $10,000 is spent on a patient who is discharged home and requires no further care, the health care system has achieved a certain outcome. Quite a different outcome has been achieved if $10,000 is spent on a different patient who is then transferred to another acute care facility. Similarly, $10,000 spent on a patient who dies in the hospital does not reflect the entire cost of hospitalization had the patient survived to receive the care needed to achieve AHDC. When a patient is not discharged to home, the hypothetical $10,000 cost is ``censored'' because it does not truly reflect the total resources required to treat the patient to the ``standard'' of care. We believe that the true costs of patient care should be defined as the resources for the patient to reach AHDC.
As data collection and patient tracking become more sophisticated analysis can be modified to include, for example, a 30-day postdischarge cost component as part of the true cost of an episode of care. That is not possible at this time.
If our goal is to identify ever better ways to care for patients, it will be necessary to compare the cost-effectiveness of hospitals, programs, treatment strategies, and individual doctors. Inherent in this concept is a standardized outcome as the basis for comparison. The effect of death or transfer to another facility on cost must be considered. It is always more expensive when a ``high-risk'' patient survives a difficult operation than when such a patient succumbs in the early postoperative period. Because our goal is both high quality and low cost, both cost and outcome must be examined. It would be wrong to reward physicians, therapies, or hospitals that produce lower costs but higher mortality. This could happen if AHDC is not adopted as the standard for cost comparisons.
Finally, it cannot be overlooked that certain doctors and hospitals treat a higher percentage of high-risk patients. The true cost of treating these patients is not reflected if the patient dies in the hospital. This may result in an underestimation of the importance of high-risk characteristics.
One limitation to the use of discharge analysis revolves around ``independent censoring.'' This statistical concept stresses the random occurrence of censoring costs. Cost censoring may not be truly random in some cases, and incomplete availability of hospital cost data is likely to be related to patient characteristics or risk factors. This drawback, however, is minor compared with the disadvantages of other forms of analysis and, in fact, discharge analysis can be performed with or without censoring.
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Appendix A. Other Significant Risk Factors Used to Adjust Hospital Mortality, Hospital Cardiac Mortality, Hospital Morbidity, and Hospital Costs
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Appendix B. Discharge Ratio
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Discharge ratio is a newly defined statistic measuring the association between a risk factor and hospital cost and can be interpreted as the ratio of likelihood of discharging patients to home with AHDC when a patient in the reference group is compared with a patient in the risk group. Mathematically, discharge ratio is the inverse of the conditional risk ratio estimated from the Cox proportional hazards model when cost data are used.
Briefly, in the Cox model settings, if the hazard is d0 when a specific risk factor is absent and d1 when the risk factor is present, then the discharge ratio is defined as the ratio of d0/d1. The hazard d(r) by hospital cost r is associated with the AHDC probability D(r) by D(r) = 1 - exp{-d*(r)}, where cumulative hazard d*(r) = integration of d(•) over (O, r). Thus, the AHDC probability D(r) is a strictly increasing function of d*(r). This relationship suggests that the larger the hazard of a patient, the larger the AHDC probability so that the less the resources will subsequently be required for that patient to reach an AHDC. In many ways, this concept of the discharge ratio is equivalent to the concept of ``risk ratio'' or ``odds ratio'' used in mortality analysis. Therefore, an estimated discharge ratio greater than 1 means that the factor increases risk of cost. In fact, a discharge ratio greater than 1 implies an AHDC probability ratio greater than 1.
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Acknowledgments
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We gratefully acknowledge the invaluable assistance of Ms Irma Larsen in preparation of the database used in this project. Support for this work has been provided by The Los Angeles Thoracic and Cardiovascular Foundation. Doctor Sun is partially supported by a research grant from the B.C. McCabe Foundation, Whittier, CA.
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Footnotes
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Presented at the Thirtieth Annual Meeting of The Society of Thoracic Surgeons, New Orleans, LA, Jan 31–Feb 2, 1994.
Address reprint requests to Dr Kay, Cardiothoracic and Vascular Surgery, The Heart Institute, Good Samaritan Hospital, 1225 Wilshire Blvd, Los Angeles, CA 90017-2395.
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References
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Abstract
Introduction
