Background

Predicting outcome is a time-honored duty of physicians, dating back at least to the time of Hippocrates.¹ The need for a quantitative approach to outcome prediction, however, is more recent. Although the patient or family members will still want to know the prognosis, there is increasing pressure to measure and publicly report medical care outcomes. In today’s highly competitive healthcare environment, such information may be used to award contracts for care. Information of variable quality² is readily available on the Internet. The U.S. Department of Health and Human Services maintains a hospital comparison website,³ and comparative information is also available from sites such as www.healthcarechoices.org.⁴ Local and regional initiatives to assess quality of care are also common. Some “report cards” specifically address the performance of intensive care units (ICUs) by adjusting outcomes using risk stratification systems, so it is essential that the clinician understand the science behind these systems⁵ and how risk adjustment models may properly be applied. A focus on performance assessment, however, may detract from other potential uses for risk stratification, including more precise risk-benefit decisions, prognostication, resource allocation, efficient assessment of new therapy and technology, and modifications to individual patient management based on severity of illness.

Prognostication based on clinical observation is affected by memory of recent events, inaccurate estimation of the relative contribution of multiple factors, false beliefs, and human limitations such as fatigue.⁶ An outcome prediction model, on the other hand, will always produce the same estimate from a given dataset and will correctly value the importance of relevant data. In an environment in which clinical judgment may later be reviewed for financial or legal issues, an objective prediction of outcome becomes especially important. Yet, even the best risk stratification tools can generate misleading data when misapplied.⁷ Discussed in this chapter are the methods by which models are developed, the application of commonly used models in clinical practice, and common reasons why observed outcome may not match predicted outcome in the absence of differences in the quality of care.⁸

Well-established general methods for stratifying clinical outcomes by the presenting condition of the patient include the ASA Physical Status Classification⁹ and the Glasgow Coma Scale (GCS).¹⁰ ICU-specific systems typically adjust for patient physiology, age, and chronic health condition; and they may also assess admitting diagnosis, location before ICU admission or transfer status, cardiopulmonary resuscitation before admission, surgical status, and use of mechanical ventilation. An ideal approach to comparing outcomes would use variables that characterize a patient’s initial condition, can be statistically and medically related to outcome, are easy to collect, and are independent of treatment decisions.

Outcome of Interest

Mortality is a commonly chosen outcome because it is easily defined and readily available. Mortality is insufficient as the sole outcome measure, however, because it does not reflect important issues such as return to work, quality of life, or even costs, because early death results in a lower cost than prolonged hospitalization. There is poor correlation between hospital rankings based on death and those based on other complications.^7,11 ICU length of stay is difficult to use as a proxy for quality of care, because the frequency of distribution is usually skewed and mean length of stay is always higher than median owing to long-stay outliers.¹² Morbidities such as myocardial infarction, prolonged ventilation, stroke or other central nervous system complications, renal failure, and serious infection can be difficult to collect accurately, and administrative records may not reflect all relevant events.⁸ There is also little standardization on how morbidity should be defined.

Other potential outcomes include ICU or hospital length of stay, resource use, return to work, quality of life, and 1- or 5-year survival. Patient satisfaction is an outcome highly valued by purchasers of health care, but it is subjective¹³ and requires substantial effort to accomplish successfully.¹⁴ Evaluation of ICU performance may require a combination of indicators, including severity of illness and resource utilization.¹⁵

Databases and Definitions

The quality of a risk stratification system depends on the database on which it was developed. Outcome analysis can either be retrospective, relying on existing medical records or administrative databases, or developed prospectively from data collected concurrently with patient care. Retrospective studies using existing data are quicker and less expensive to conduct but may be compromised by missing data,⁸ imprecise definitions, interobserver variability,¹⁶ and changes in medical practice over time.¹⁷

Data derived from discharge summaries or insurance claims do not always capture the presence of comorbid disease¹⁸ and may be discordant with data that are clinically collected.¹⁹ Because some administrative discharge reports truncate the number of reportable events, diagnoses may be missed, and this coding bias is most apparent in severely ill patients.¹² Coding errors and use of computer programs to optimize diagnosis-related group reimbursement can also reduce the validity of claims-derived data. Augmentation of administrative data with laboratory values improves model performance.²⁰

A variety of methods can assess the quality of the database, such as reabstraction of a sample of charts by personnel blinded to the initial results and comparison to an independent database. Kappa analysis is a method for quantifying the rate of discrepancies between measurements (values) of the same variable in different databases (i.e., original and reabstracted). A kappa value of 0 represents no (or random) agreement, and 1.0 is perfect agreement, but this statistic must be interpreted in light of the prevalence of the factor being abstracted.²¹

Model Development

Once data integrity is ensured, there are a number of possible approaches to relating outcome to presenting condition. The empirical approach is to use a large database and subject the data to a series of statistical manipulations (Box 222-1). Typically, death, a specific morbidity, and resource consumption are chosen as outcomes (dependent variables). Factors (independent variables) thought to affect outcome are then evaluated against a specific outcome using univariate tests (chi-square, Fisher’s exact, or Student t-test) to establish the magnitude and significance of any relationship.

Independent variables should ideally reflect patient condition independent of therapeutic decisions. Measured variables such as “cardiac index” or “hematocrit” are preferred over “use of inotropes” or “transfusion given,” because the criteria for intervention may vary by provider or hospital. Widely used models rely on common measured physiologic variables (heart rate, blood pressure, and neurologic status) and laboratory values (serum creatinine level and white blood cell count). In addition, variables may consider age, physiologic reserve, and chronic health status. Items chosen for inclusion in a scoring system should be readily available and relevant to clinicians involved in the care of these patients, and variables that lack either clinical or statistical bearing on outcome should not be included. This requirement may necessitate specialized scoring systems for patient populations (pediatric, burn and trauma, and possibly acute myocardial infarction patients) exhibiting different characteristics than the general ICU population. For example, left ventricular ejection fraction and reoperative status are important predictors of outcome in the cardiac surgical population but are not routinely measured or not directly relevant to other population groups.²² If the independent variable is dichotomous (yes/no, male/female), a two-by-two table can be constructed to examine the odds ratio and a chi-square test performed to assess significance (Table 222-1). If multiple variables are being considered, the level of significance is generally set smaller than P = .05, using a multiple comparison (e.g., Bonferroni) correction²³ to determine a more appropriate P value.

TABLE 222-1 Two-by-Two Contingency Table Examining Relationship of MOF After Open Heart Surgery (Outcome) to a History of CHF (Predictor) in 3830 Patients*

CHF, congestive heart failure; MOF, multiple organ failure.

* The odds ratio is defined by cross-multiplication (121 × 2697) ÷ (846 × 166). The odds ratio of 2.3 indicates patients with CHF are 2.3 times as likely to develop postoperative organ system failure as those without prior CHF. This univariate relationship can then be tested by chi-square for statistical significance.

If the independent variable under consideration is a continuous variable (e.g., age) a Student’s t-test is one appropriate choice for statistical comparison. With continuous variables, consideration must be given to the possibility that the relationship of the variable to outcome is not linear. Figure 222-1 demonstrates the relationship of ICU admission serum bicarbonate to mortality outcome in cardiac surgical patients,²⁴ where the data points have been averaged with adjacent values to produce a locally weighted smoothing scatterplot graph.²⁵ Serum bicarbonate values above 22 mmol/L at ICU admission imply a relatively constant risk. Below this value, the risk of death rises sharply. Analysis of this locally weighted smoothing scatterplot graph suggests two ways for dealing with the impact of serum bicarbonate on mortality. One would be to make admission bicarbonate a dichotomous variable (i.e., >22 mEq or <22 mEq). The other would be to transform the data via a logarithmic equation to make the relationship more linear. Cubic splines analysis,²⁶ another statistical smoothing technique, may also be used to assign weight to physiologic variables.

Figure 222-1 A locally weighted smoothing scatterplot (LOWESS) analysis of the relationship between ICU admission bicarbonate level (x-axis) and mortality (y-axis). Individual patient data are grouped and averaged with surrounding data to produce a smooth plot. In this instance, the mortality rate appears to be stable with admission serum bicarbonate levels of 22 mmol/L and above but rises rapidly with lower values. Admission bicarbonate level of less than 21 mmol/L was given prognostic weight in the model that used these data.

(Data from Higgins TL, Estafanous FG, Loop FD et al. ICU admission score for predicting morbidity and mortality risk after coronary artery bypass grafting. Ann Thorac Surg 1997;64:1050-8.)

Univariate analysis assesses the forecasting ability of variables without regard to possible correlations or interactions between variables. Linear discriminant and logistic regression techniques can evaluate and correct for overlapping influences on outcome. For example, a history of heart failure and depressed left ventricular ejection fraction are both empirical predictors of poor outcome in patients presenting for cardiac surgery.²⁷ As might be expected, there is considerable overlap between the population with systolic heart failure and those with low ejection fraction. The multivariate analysis in this specific instance eliminates history of heart failure as a variable and retains only measured ejection fraction in the final equation.

Because linear discriminant techniques require certain assumptions about data, logistic techniques are more commonly utilized.⁴ Subjecting the data to multiple logistic regression will produce an equation with a constant, a β coefficient and standard error, and an odds ratio that represents each term’s effect on outcome. Table 222-2 displays the results of the logistic regression used in the Mortality Probability Model III ICU admission model (MPM₀ III). There are 17 variable terms, and a constant term, each with a β value that when multiplied by presence or absence of a factor, becomes part of the calculation of mortality probability using a logistic regression equation. The odds ratios reflect the relative risk of mortality if a factor is present. The challenge in building a model is to include sufficient terms to deliver reliable prediction while keeping the model from being cumbersome to use or too closely fitted to its unique development population. Generally accepted practice is to limit the number of terms in the logistic regression model to 10% of the number of patients having the outcome of interest to avoid “overfitting” the model to the developmental dataset. It is important to identify interaction between variables that may be additive, subtractive (canceling), or synergistic and thus require additional terms in the final model. In the earlier example, seven interaction items were added to reflect important observations in elderly patients,²⁸ who frequently have better outcomes than expected.

TABLE 222-2 Variables in the MPM₀ III Logistic Regression Model

Odds ratios for variables with an asterisk (*) are also affected by the associated interaction terms.

The patient’s diagnosis is an important determinant of outcome,¹⁷ but conflicting philosophies exist on how disease status should be addressed by a severity adjustment model. One approach is to define principal diagnostic categories and add a weighted term to the logistic regression equation for each illness. This approach acknowledges the different impact of physiologic derangement by diagnosis. For example, patients with diabetic ketoacidosis have markedly altered physiology but a low expected mortality; a patient with an expanding abdominal aneurysm may show little physiologic abnormality and yet be at high risk for death or morbidity. Too many diagnostic categories, however, may result in too few patients in each category to allow statistical analysis for a typical ICU, and such systems are difficult to use without sophisticated (and often proprietary) software.

The other approach is to ignore disease status and assume that factors such as age, chronic health status, and altered physiology will suffice to explain outcome in large groups of patients. This method avoids issues with inaccurate labeling of illness in patients with multiple problems and the need for lengthy lists of coefficients but could result in a model that is more dependent on having an “average” case mix.^29,30 Regardless of the specific approach, age and comorbidities (metastatic or hematologic cancer, immunosuppression, and cirrhosis) are given weight in nearly all ICU models to help account for the patient’s physiologic reserve or ability to recover from acute illness.

Validation and Testing Model Performance

Models may be validated on an independent dataset or by using the development set with methods such as jackknife or bootstrap validation.³¹ Two criteria are essential in assessing model performance: calibration and discrimination. Calibration refers to how well the model tracks outcomes across its relevant range. A model may be very good at predicting good outcome in healthy patients and poor outcomes in very sick patients yet unable to distinguish outcome for patients in the middle range. The Hosmer-Lemeshow goodness-of-fit test³² assesses calibration by stratifying the data into categories (usually deciles) of risk. The number of patients with an observed outcome is compared with the number of predicted outcomes at each risk level. If the observed and expected outcomes are very close at each level across the range of the model, the sum of chi-squares will be low, indicating good calibration. The P value for the Hosmer-Lemeshow goodness-of-fit increases with better calibration and should be nonsignificant (i.e., >.05). Special precautions apply to using the Hosmer-Lemeshow tests with very large databases.³³

The second measurement of model performance is discrimination, or how well the model predicts the correct outcome. A classification table (Table 222-3) displays four possible outcomes that define sensitivity and specificity of a model with a binary (died/survived) prediction and outcome. Sensitivity (the true-positive rate) and specificity (the true-negative rate, or 1—the false-positive rate) are measures of discrimination but will vary according to the decision point chosen to distinguish between outcomes when a model produces a continuous range of possibilities. The sensitivity and specificity of a model when using 50% as the decision point will differ from that using 95% as the decision point. The classification table can be recalculated for a range of outcomes by choosing various decision points: for example, 10%, 25%, 50%, 75%, and 95% mortality risk. At each decision point, the true-positive rate (proportion of observed deaths predicted correctly) and the false-negative (proportion of survivors incorrectly predicted to die) and overall correct classification rate can be presented. The C-statistic, or area under a receiver-operating characteristic (ROC) curve, is a convenient way to summarize sensitivity and specificity at all possible decision points. A graph of the true-positive proportion (sensitivity) against the false-positive proportion (1—specificity) across the range of the model produces the ROC curve (Figure 222-2). A model with equal probability of producing the correct or incorrect result (e.g., flipping a coin) will produce a straight line at a 45-degree angle that encompasses half of the area (0.5) under the “curve.” Models with better discrimination will incorporate increasingly more area under the curve to a theoretical maximum of 1.0. Most ICU models have ROC areas of 0.8 to 0.9 in the development set, although the ROC area usually decreases when models are applied prospectively to new datasets. The ROC analysis is valid only if the model has first been shown to calibrate well.

TABLE 222-3 Classification Table

Figure 222-2 Relative operating characteristic (ROC) curves. A coin toss gives an ROC of 0.5. In models that discriminate outcome, an increasing area under the curve, also called the C-statistic, is enclosed.

(From Swets JA. Measuring the accuracy of diagnostic systems. Science 1988;240:1285-94.)

A model may discriminate and calibrate well on its development dataset yet fail when applied to a new population. Discrepancies in performance can relate to differences in surveillance strategies and definitions³⁴ and can occur when a population is skewed by an unusual number of patients having certain risk factors, as could be seen in a specialized ICU.²⁹ Large numbers of low-risk ICU admissions will result in poor predictive accuracy for the entire ICU population.³⁵ The use of sampling techniques (i.e., choosing to collect data randomly on 50% of patients rather than all patients) also appears to bias results.³⁶ Models can also deteriorate over time, owing to changes in populations and medical practice. These explanations should be considered before concluding that quality of care is different between the original and later applications of a model.³⁷

Standardized Mortality Ratio

Application of a severity-of-illness scoring system involves comparison of observed outcomes with those predicted by the model. The standardized mortality ratio is defined as observed divided by expected mortality and is generally expressed as a mean value ± 95% confidence intervals (CIs), which will depend on the number of patients in the sample. Standardized mortality ratio values of 1.0 (± the CI) indicate that the mortality rate, adjusted for presenting illness, is at the expected level. Standardized mortality ratio values significantly lower than 1.0 indicate performance better than expected. Small differences in scores, as could be caused by consistent errors in scoring elements, timing of data collection, or sampling rate, have been shown to cause important changes in the standardized mortality ratio.^36,38

Models Based on Physiologic Derangement

Three widely utilized general-purpose ICU outcome systems are based on changes in patient physiology: the Acute Physiology and Chronic Health Evaluation (APACHE II,³⁹ APACHE III,⁴⁰ APACHE IV⁴¹), the Mortality Probability Models (MPM I,⁴² MPM II,⁴³ MPM₂₄,⁴⁴ MPM₀ III⁴⁵), and the Simplified Acute Physiology Score (SAPS I,⁴⁶ SAPS II,⁴⁷ SAPS III^48,49). These models are all based on the premise that as illness increases, patients will exhibit greater deviation from physiologic normal for a variety of common parameters such as heart rate, blood pressure, neurologic status, and laboratory values. Risk is also assigned for advanced age and chronic illness.