Estimating Treatment Benefits for the Elderly: The Effect of Competing Risks

The current practice of encouraging patients to participate in treatment decisions requires that clinicians be facile in communicating the risks and benefits of therapy. Sharing numeric data can foster the process. However, because the format in which data are presented influences their interpretation [1-3], clinicians need to consider which format best describes the outcomes their patients face. Consider the tension between relative and absolute risk reduction. The interpretation of even a large relative risk reduction is highly dependent on the baseline risk for the specific disease. A 50% reduction in mortality with early intervention, for example, appears different when the risk for death from disease is changed from 2 per 1000 to 200 per 1000. When the mortality risk is low, the absolute survival benefit is small0.1% (2/1000 to 1/1000); when the risk is high, the absolute benefit is great10% (200/1000 to 100/1000). In the former scenario, patients might reasonably choose to forego a noxious intervention. In the latter, however, patients might be more likely to accept the morbidity of treatment. Because this distinction between relative and absolute risk reduction is concealed when benefit is expressed in only relative terms, many have argued that relative risk reductions should be anchored by baseline risk so that the absolute benefit of treatment is clear [2, 4, 5] However, an absolute measure of disease risk (or risk reduction from therapy) is not the ultimate outcome of interest to patients. Overall risk is more important. The difference is the risks patients face from other conditionsthat is, competing risks. When competing risks are great, they matter. The importance of even a 10% absolute survival benefit from treatment is markedly diminished for a patient who is at greater risk for death from other causes, regardless of the proposed therapy. Such great competing risks are most prevalent among the elderly. Although physicians intuitively understand the relevance of competing risks, they may be less sure about how to quantify the effect. We provide a framework to help physicians gauge the effect of competing risks in their elderly patients. Methods Overview To quantify the effect of competing risks, we used age-specific mortality data from U.S. vital statistics and the declining exponential approximation for life expectancy (DEALE) to model age-specific expectations for persons faced with a particular disease-related mortality. We sought to determine, for example, how a new disease with a 5-year mortality rate of 25% would affect the life expectancy of an average 70-year-old man. We then considered two refinements: the first, to better adjust for the individual patient (using self-reported health status), and the second, to describe more thoroughly the outcome (by including disabling events). Modeling the Effect of a New Disease on Life Expectancy Life expectancy and mortality are fundamentally related to probability estimates. In the general population, life expectancy decreases with increasing age, and annual mortality increases. Gompertz was the first to describe this complex mathematic relation using an exponential function that now bears his name. As life expectancy decreases, mortality rates become almost constant over time. When this occurs, the relation between survival and mortality rates can be approximated with a much simpler mathematic relation: a declining exponential function (the DEALE). This approximation was first validated and popularized by Beck and colleagues [6, 7] and is particularly suited to calculating the effect that a new risk has in older patients. The fundamental assumption behind this technique is that life expectancy equals the inverse of the annual mortality rate: Equation 1 Because mortality rates are essentially constant probability estimates when assessed over relatively short time horizons, patient-specific mortality rates can be expressed as the sum of the disease-independent mortality rate (also known as age-specific mortality rate) and a disease-related mortality rate (also known as case-fatality or excess mortality rate): Equation 2 Note that when disease-related mortality is zero (that is, when the patient does not have the disease or when the disease has no effect on survival), the patient-specific mortality rate (and thus life expectancy) is determined solely by the patient's age. Calculation of the life expectancy estimates used in Figure 1 and Figure 2 is relatively simple. Because Figure 1 is the central portion of our paper, we now describe it in detail. Normal life expectancy (the top curves) was determined from the most recent data (1991) from the National Center for Health Statistics, U.S. Department of Health and Human Services [8]. On the basis of remaining life expectancy and the DEALE [6, 7], we calculated the age-specific mortality rate for each age cohort from 65 to 85 years of age. Combining the age-specific mortality with the hypothetical disease-related mortality allowed us to calculate the other four curves. The disease-related annual mortality rate can be calculated from 5-year disease-specific survival using the following equation: Equation 3 Figure 1. The effect of selected disease-related mortality rates on the remaining life expectancy of women (left) and men (right) at the time of diagnosis. Figure 2. The effect of age on the distribution of health states in the future. Thus, if the disease-related 5-year mortality rate is 25% (and the 5-year survival rate is 75%), then the disease-related annual mortality rate is 0.06. Equation 4 A 70-year-old man, for example, has a life expectancy of 12.2 years or an annual age-specific mortality rate of 0.08. Equation 5 Given the foregoing disease, the man's all-cause annual mortality rate is 0.14 (= 0.06 + 0.08), and his life expectancy is 7.2 years. Equation 6 Thus, the sum of the age-specific and disease-related mortality rates gives the patient-specific mortality rate, the inverse of which is life expectancy. Normal life expectancy serves as our proxy for disease-independent data. The mortality reflected in this measure is, of course, itself the result of several diseases in the elderlyprimarily cardiovascular disease and cancer. The method we describe produces a valid approximation whenever the disease in question is not a major contributor to the age-specific mortality rate. For example, if the disease in question was all cardiovascular disease or all cancer, then much of the age-specific mortality rate would already account for the mortality from the disease. Completely successful therapy for such a broad category of disease would move a patient well above his or her normal life expectancy by removing the common causes of death. Thus, the method we describe should be applied only when the physician is considering more discrete diagnoses (for example, aortic aneurysm or breast cancer), which make a relatively small contribution to overall mortality. To provide some quantitative data on how great a contributor to all-cause mortality a given disease can be without affecting our method, we did a sensitivity analysis that removed the contribution of a particular disease from normal life expectancy and accordingly revised the estimate of perfect treatment on life expectancy. For example, for a disease that accounts for 40% of all-cause mortality (such as all cardiovascular diagnoses), revised treatment benefit (in years) was three times the benefit estimated by our method. For a disease that accounts for 30% of all-cause mortality (for example, all cancers considered together), the revised benefit was twice as high as the benefit estimated by our method. However, for a disease that constitutes less than 10% of all-cause mortality (this is the case for any individual cancer), the revised benefit is small (for example, less than 20% higher than that estimated by our method). Adjustments for Health Status The adjustments for health status shown in Table 1 are based on data from the East Boston Senior Health Project. All participants were asked the following question: Compared with others your age, would you rate your overall health as excellent, good, fair, or poor? Analyzing the 1437 men and 2332 women separately, we used 5-year follow-up data to calculate, for each health status self-rating, the proportion of patients who died. The ratio of this health status-specific survival to overall survival served as our health status weight. A more precise analysis for men and women, using five age cohorts (ages 65 to 69 years, 70 to 74 years, 75 to 79 years, 80 to 84 years, and 85 years and older) produced essentially the same weights. Table 1. Estimated Physiologic Age of Elderly Patients Adjusted for Their Self-Reported Health Status* Overall, men who described themselves as in excellent health had a lower mortality rate than average (health status weight, 0.52). Men who reported themselves as in good, fair, and poor health had health status weights of 0.89, 1.26, and 1.88, respectively. The analysis for women showed health status weights of 0.64, 0.88, 1.08, and 1.82 for self-reported health status of excellent, good, fair, and poor, respectively. To approximate a physiologic age to reflect health status, we applied the health status weights to four chronologic ages: 65, 70, 75, and 80 years. Using the age-specific annual mortality from U.S. Vital Statistics data [8] and the health status weight, we calculated a health status-adjusted mortality rate as the following: Equation 7 We then returned to the Vital Statistics data to determine the age at which an average person would have this annual mortality rate. These data do not provide annual mortality rates for persons older than 85 years, forcing us to report 85 years and older for the highest mortality rates. The process was done separately for men and women. Future Disabling Events The expectation of future disabling events (Figure 3) is based on cros