Chapter 2. Epidemiologic Measures

• A variety of measures are employed in epidemiology, each of which has a specific definition and use.
• When characterizing the likelihood of developing a disease within a specified period of time, the appropriate measure is risk.
•  Prevalence is used to describe the proportion of a population that is affected by a disease.
• When measuring the rate of new occurrences of a disease, incidence is the appropriate measure.
•  Case fatality is used to describe the natural history of a disease and corresponds to the proportion of affected persons who die from that illness. Conversely, survival is the likelihood of escaping death from that illness.

Acute myelogenous leukemia (AML), also known as acute nonlymphocytic leukemia, is a heterogeneous group of disorders involving uncontrolled proliferation of primitive blood-forming cells. AML accounts for almost one third of all leukemias, with over 9000 patients newly diagnosed in the United States each year. This disease tends to occur in later life, with a median age at onset of 65 years. Males are at a slightly higher risk than females.

Although for most patients the cause of AML is unknown, a number of risk factors have been identified, including exposure to ionizing radiation, benzene, certain drugs, and perhaps cigarette smoke. This disease also occurs with unusual frequency among patients with certain congenital disorders—such as Down syndrome.

Patients with AML may present with a variety of symptoms, including weakness, fatigue, unexplained weight loss, infection, and bleeding. On physical examination, these patients often are pale, have multiple bruises, and have fevers, with evidence of localized infections. In some instances, enlargement of the lymph nodes, spleen, or liver may be found. Examination of blood specimens reveals anemia, low platelet counts, and markedly elevated leukocyte counts, with immature granulocytes abnormally appearing in the circulating blood. The bone marrow of these patients tends to be packed densely with cells, including a high proportion of immature cells.

The clinical management of AML involves an attempt to induce remission with chemotherapy. The likelihood of achieving remission is reduced for patients who are older, are obese, have impaired renal function, or have preexisting medical conditions, particularly prior disorders of the bone marrow. Remissions may be induced in two thirds or more of patients, with remission failures most commonly attributable to infection or hemorrhage leading to death. Even among patients in remission, about 75% will eventually relapse, and only one fifth of patients can be expected to live 5 years beyond the time of diagnosis.

The complications of infection and bleeding among these patients are directly related to chemotherapy-induced suppression of the bone marrow, with consequent reductions in the circulating levels of neutrophils and platelets. Very low neutrophil counts increase susceptibility to a wide variety of infections, with clinical or microbiologic evidence of infection in about 30–40% of patients. Among the most common types of infection are those involving in-dwelling catheters, the urinary tract, and the soft tissues. The leading bacterial pathogens are S aureus, Staphylococcus epidermidis, Viridans streptococci, Escherichia coli, Enterobacter, Pseudomonas, and Klebsiella species. Candida albicans and other fungi can also cause infections among these patients. Treatment with broad-spectrum antibiotics has reduced the risk of life-threatening infections in these individuals. An evolving area of therapy is the use of so-called growth factors to stimulate the patient’s ability to produce replacement neutrophils. The use of these growth factors can lower the rate of infection and the need for antibiotics, but it is unclear whether the ultimate prognosis of the disease is affected.

In about half of the instances of fever among neutropenic patients, an infection cannot be documented either clinically or microbiologically. These episodes, therefore, are referred to as unexplained fever. Even in the absence of an identified specific infectious agent, fever is an ominous sign in a neutropenic patient and is associated with a high risk of adverse outcomes, including death. It has become standard practice to treat febrile neutropenic patients with combinations of antibiotics that are effective against a wide range of infectious agents. The selection of a regimen of antibiotic treatment on the basis of likely infectious agents, in the absence of documentation of those agents, is referred to as empiric treatment. Evidence about the likely pathogens is derived from experience in managing other febrile neutropenic patients in whom responsible infectious agents were identified.

The importance of risk assessment is evident in the Patient Profile. Antibiotics were administered to the patient even before an infectious cause of fever was identified. In this situation, the attending physician concluded that the potential risk of complications from delayed antibiotic treatment outweighed the likelihood of harm from treatment administered before the cause of the fever was determined. Virtually every treatment decision involves a counterbalancing of risks and benefits. In this chapter, emphasis will be placed on how epidemiologic measures can be used to assess outcomes and thereby guide decision making.

Risk

All members of the population, or cohort, are free of disease at the start of observation. Risk, which has no units, lies between 0 (when no new occurrences arise) and 1 (when, at the other extreme, the entire population becomes affected during the risk period). Alternatively, risk can be expressed as a percentage by multiplying the proportion by 100.

In Figure 2–1 a hypothetical study of six subjects illustrates the calculation of risk. This study began in 1995 and concluded in 2004. Individual subjects entered the study at various times, were all free of the disease of interest at the time of enrollment, and were followed up for at least 2 years. For example, Patient A was enrolled in 1995, was diagnosed with the disease just prior to 1997, and was followed up until death in 2002. Patient B was enrolled in 1997, was followed up until 1999 without developing the disease, and then discontinued participation in the study. Patient C was enrolled in 1999, was diagnosed with the disease just prior to 2002, and survived through the end of the observation period in 2004. Patients D, E, and F entered the study in 1997, 2002, and 1998, respectively; each patient was followed through 2004 without developing the disease.

Of the six subjects under observation (N = 6), only one (A = 1) developed the disease within 2 years of entry into the study. The 2-year risk of disease, therefore, is estimated by

These same data are also summarized in Figure 2–2, where the time scale on the horizontal axis represents the duration of observation for each subject. In other words, observation of a particular individual begins at time zero and continues until that person dies or is lost from the study or until the study is concluded. The format used in Figure 2–2 is sometimes preferred as a matter of convenience, because it may be easier to visualize the actual lengths of observation for individual subjects. The following example further illustrates the use of risks and how they are estimated.

Example 1. In deciding whether to treat the patient in the Patient Profile with antibiotics prior to determining the cause of the fever, the clinician had to address this key question: How likely is it that the patient has a bacterial infection? The answer can be based on experience with similar patients. For example, to estimate a cancer patient’s risk of acquiring an infection in the hospital (a nosocomial infection), a study was conducted of 5031 patients admitted to a comprehensive cancer center. The investigators carefully defined a nosocomial infection as an infection that (1) is documented by cultures, (2) was not incubating at admission, (3) occurred at least 48 hours after admission, and (4) occurred no more than 48 hours following discharge (somewhat longer for surgical wound infections). Of the 5031 patients, 596 developed an infection that met these criteria. The risk was

In this example, the risk period for each patient began 48 hours after hospitalization and ended 48 hours after discharge. This equation indicates that about 12% of cancer patients similar to those studied will develop a nosocomial infection during or soon after hospitalization. The risk is greater than would be expected for the average hospitalized patient, suggesting that cancer patients are at an unusually high risk of developing a hospital-acquired infection.

A broad range of hospitalized cancer patients were involved in this study. The woman in the Patient Profile, however, had a fever and a low granulocyte count. A more refined estimate of the likelihood of infection could be derived from a study of patients with similar conditions. In one such study, 1022 cancer patients with fever and granulocytopenia were studied according to a defined protocol. Of these patients, 530 had a clinically or microbiologically documented bacterial infection. Thus, the risk of infection in granulocytopenic, febrile cancer patients is estimated to be

This result suggests that patients similar to the one described in the Patient Profile have a very high risk of a bacterial infection, thus supporting the decision to treat the patient with antibiotics even before an infection is diagnosed.

Prevalence

Prevalence, like risk, ranges between 0 and 1 and has no units. The calculation of prevalence can be illustrated using the data summarized in Figure 2–1. For example, to calculate the prevalence of the disease of interest in 2001, it is necessary to know (1) the number of persons under observation in 2001 and (2) the number of individuals affected at that time. First, four persons are under observation in 2001 (Patients A, C, D, and F) (N = 4). Second, at that time one of these persons (Patient A) is affected (C = 1). Thus, the prevalence in 2001 is

Example 2. An important question in deciding whether to administer antibiotics to the patient described in the Patient Profile is the type of infection involved. As indicated earlier, individuals with low neutrophil counts are susceptible to a wide variety of bacterial infections. Therefore, broad-spectrum antibiotics are used empirically in these patients until the specific infecting organism is identified.

These bacteria often can be cultured from persons without symptomatic illness. For example, the prevalence of skin colonization with S aureus was estimated among 96 people attending an outpatient clinic for the first time. Patients with skin infections were excluded from the study. S aureus was cultured from specimens from 62 patients. The prevalence of colonization with S aureus in this group was

From this equation, it is estimated that in a group of patients similar to the patients studied, the prevalence of skin colonization with S aureus is about 65%.

Incidence Rate

To illustrate calculation of person-time and incidence rate, consider the small hypothetical cohort illustrated schematically in Figure 2–2. Patient A developed the disease 2 years after entry into the study. Because subjects contribute person-time only while eligible to develop the disease, the person-time for Patient A was 2 years. Similarly, Patients B, C, D, E, and F contributed 2, 3, 7, 2, and 6 years, respectively. Patients A and C developed disease. Thus, A (the number of new cases of disease in the population) = 2, the total PT = 2 + 2 + 3 + 7 + 2 + 6 = 22 person-years, and the incidence rate is

Note that the total person-years of observation is obtained simply by addition of the years contributed by each subject. Alternatively, this rate can be expressed as 9 cases/100 person-years by multiplying the numerator and denominator by 100. Although these two expressions are equivalent, the latter might be preferred since it does not require use of decimal points.

Example 3. Returning to the study cited in Example 1, the incidence rate of nosocomial infections can be calculated from additional data reported in that investigation. The 5031 patients remained under observation for a total of 127,859 patient-days (or an average length of stay of 127,859/5031 = 25.4 days). Since 596 patients developed an infection that met the definition for a hospital-acquired infection, the incidence rate can be estimated as

This means that among patients similar to those studied, on average, about 0.47% of patients would be expected to develop a nosocomial infection per day.

Calculation of incidence rates for a large population, such as that in a city, by separately enumerating the person-years at risk for each individual, as described above, would require a tremendous amount of work. Fortunately, person-time for a large population can often be calculated by multiplying the average size of the population at risk by the length of time the population is observed:

In many instances, relatively few people in the population develop the disease, and the population undergoes no major demographic shifts during the time period of observation. In such situations, the average size of the population at risk can be estimated by the size of the entire population, using census or other data. The person-time of a large, stable population can often be estimated by

Example 4 illustrates calculation of incidence rates using this alternative approach to estimating person-time.

Example 4. In the United States, the National Cancer Institute maintains a network of registries that collect information on all new occurrences of cancer within populations residing in specific geographic areas. Collectively, these registries cover about 14% of the population of the United States, and between 1996 and 2000, 2957 females were newly diagnosed with acute myelocytic leukemia in these areas. An estimated 19,185,836 females lived in these combined areas on average during this 5-year period. Thus, the number of woman-years of observation for this population was 19,185,836 women × 5 years = 95,929,180 woman-years. Therefore, the average annual incidence rate of acute myelocytic leukemia among females was 3.1 cases for every 100,000 woman-years of observation in these specific study areas.

As summarized in Table 2–1, risk, prevalence, and incidence rates differ in at least three important ways. First, the measures have different units. Incidence rates are expressed as units of newly diagnosed patients per unit of person-time, whereas risk and prevalence have no units. Second, these measures reflect different aspects of disease. Incidence rates and risk describe occurrence of new disease, whereas prevalence reflects already existing disease. Third, these measures are calculated differently. As shown in Figure 2–1, in 2001 the prevalence was 25%, the 2-year risk was 17%, and the incidence rate was 9 cases per 100 person-years. These differences indicate that the three measures cannot be compared directly with one another.

In view of these inherent differences, the measures have different applications. Risk is most useful if interest centers on the proportion of a population that will become ill over a specified period of time. Risk also can be used to estimate the probability that a particular individual within a population will become ill over a specified period of time. Incidence rates are preferred if interest centers on the rapidity with which new cases arise in a population (the time period may be long or unspecified). Prevalence is preferred if interest centers on the number of existing cases within a population or the proportion of cases of a given type. Example 5 illustrates some of the differences among these measures.

Example 5. The use of an antibiotic, norfloxacin, was studied for prevention of gram-negative bacterial infections in patients with acute leukemia who had treatment-related low neutrophil counts. All 35 patients who received norfloxacin developed fever. The 35 patients were observed for a total of 220.5 person-days before first developing fever; each day, on average, about 28% of the patients had a fever. Thus, the risk of developing a fever was 35/35 = 1 in this group of patients, the incidence rate was 35/220.5 = 0.16 cases/person-day = 16 cases/100 person-days, and the average prevalence was 28%.

A risk of 1 suggests that treatment with norfloxacin does not ultimately prevent infectious fevers or reduce the risk of developing fever. On the other hand, the incidence rate in the norfloxacin-treated group was lower than that in a group of similar patients who did not receive norfloxacin, suggesting that treatment slowed or delayed the onset of fever. Furthermore, prevalence of fever was lower in the norfloxacin-treated group, which indicates that patients treated with norfloxacin are less likely to be febrile on an average day.

Survival is the probability of remaining alive for a specific length of time. For a chronic disease such as cancer, 1-year survival and 5-year survival rates are often used as indicators of the severity of disease and the prognosis. For example, the 5-year survival for acute myelocytic leukemia is about 0.19, indicating that only 19% of patients with acute myelocytic leukemia survive at least 5 years after diagnosis.

In simple situations, survival (S) is estimated as

where D is the number of deaths observed in a specified period of time and A is the number of newly diagnosed patients under observation. Survival for at least 2 years after diagnosis can be determined from the data in Figure 2–3. Observation of each patient begins at diagnosis (time = 0), and continues until one of the following outcomes occurs: death, survival for 5 years, or follow-up ceases (the subject is “censored”). A patient is censored when follow-up ends prior to death or completion of a full period of observation. Follow-up could end for one of several reasons: (1) the patient decides to discontinue participation, (2) the patient is “lost” to follow-up, or (3) the study ends. Five of the six people under observation (N = 6) in Figure 2–3 survive at least 2 years. Thus, the 2-year survival is

Calculation of survival indicates the probability of surviving a specified length of time and is inversely related to the risk of death. Survival estimates provide a useful way to summarize prognosis, as illustrated in Example 6.

Example 6. The patient described in the Patient Profile has acute myelogenous leukemia. Data collected by the National Cancer Institute for patients diagnosed with this disease in the United States between 1992 and 1999 indicate that only about 19% of patients survived for at least 5 years from the time of diagnosis. For persons who were under 65 years of age at diagnosis, the 5-year survival rate (31%) was higher than for persons who were 65 years or older at diagnosis (4%). Nevertheless, it can be concluded from these data that, regardless of age, patients with acute myelogenous leukemia as a group have an extremely poor prognosis. The group experience also serves as the best indicator of prognosis for individual patients with this diagnosis. For example, a patient with acute myelogenous leukemia who is under 65 years of age would be expected to have a 1-in-3 chance of surviving at least 5 years from the time of diagnosis. For a patient 65 years or older with the same diagnosis, the chance of surviving at least 5 years from diagnosis is reduced to 1 in 25.

Life Table & Other Survival Analyses

When studying survival and risk, problems may arise if the investigator cannot follow some subjects for the entire risk period, either because the subjects move away or miss a follow-up appointment. In Figure 2–3, for example, observation of Patients B and E stopped after 2 years (censored). In determining the survival for a 5-year period, observation of Patients B and E is incomplete; we have less than 5 years of observation on these individuals. It is known only that these individuals survived for at least 2 years, not if they survived a full 5 years. It might seem, therefore, that these patients do not contribute any useful information toward the estimation of a 5-year survival probability. In the absence of information about what happened to these patients over the full observation period, we might consider two extreme scenarios. In the first scenario, both Patients B and E survive the full 5 years. The overall 5-year survival estimate in this situation would be

In the second scenario, neither Patient B nor E survives for the full 5 years. The overall 5-year survival estimate in this situation would be

Clearly, these two extreme assumptions lead to very different estimates of the 5-year probability of survival. Since the observations are incomplete, we do not know which, if either, of these two extreme situations is closer to the correct answer. In this case, the inability to estimate survival probabilities indicates the need for analytic methods to handle censored observations.

Statisticians have developed special techniques, called survival analyses, to account for such incomplete observations. Two particularly useful methods of survival analysis are life table analysis and Kaplan-Meier analysis. Life table and Kaplan-Meier analyses allow calculation of risk even if some of the observations are incomplete. Descriptions of these and other methods of survival analysis can be found in Dawson and Trapp (2004), Basic and Clinical Biostatistics.

The results of a survival analysis can be presented graphically, as shown in Figure 2–4. The information portrayed in this graph relates to the survival experience of patients diagnosed in the United States during 1995 with any type of leukemia. The horizontal axis plots time in years since diagnosis (0 = time of diagnosis) and the vertical axis plots the percentage of patients who are alive. The survival curve begins at the time of diagnosis, when 100% of patients are alive. During the first year following diagnosis, 32% of the patients die (or equivalently, 100% – 32% = 68% survive). During the next year, another 10% of patients die (cumulative survival = 68% – 10% = 58%). The process of attrition to death continues each year through the end of the 5-year observation period.

The survival curve can be used to determine basic summary measures about the prognosis of leukemia in adults, for example, the percentage of patients who survive to some fixed period of time following diagnosis. Typically, cancer prognosis is assessed by determining the percentage of patients who survive for at least 5 years after diagnosis. The approach to estimating this percentage is depicted in Figure 2–5. Beginning on the horizontal axis at 5 years, a line is drawn to the survival curve (Step A). From the point of intersection with the survival curve, a line is drawn across to the vertical axis (Step B). The percentage of survivors (47%) is then read from the vertical axis.

Another summary measure of prognosis is the median survival time, which is the time following diagnosis at which one half of the patients remain alive. The approach to estimating the median survival time is shown in Figure 2–6. Beginning on the vertical axis at the 50% (median) survival level, a line is drawn across to the survival curve (Step A). From the point of intersection with the survival curve, a line is drawn down to the horizontal axis (Step B). The median survival time in this example is estimated to be between 3.5 and 4.5 years, with a best estimate around 4 years. That is to say on average, patients with leukemia diagnosed in the United States during 1995 tended to survive about 4 years from the time of diagnosis. For any individual patient out of this population, 4 years serves as an estimate of the likely survival time. As noted in Chapter 1: Introduction to Epidemiology, additional prognostic factors often can be identified that help to refine the predictions for groups of patients or individuals with those characteristics.

Case Fatality

The resulting estimate can be left as a proportion or multiplied by 100 to convert it to a percentage. Note that this equation is analogous in structure to the equation previously described for risk, or cumulative incidence. The difference between these two measures is the phase of illness to which they are applied. Risk of disease refers to the initial development of the condition, and case fatality refers to the likelihood of death among persons in whom the disease is diagnosed. Case fatality can be thought of as the risk of death among those who have been just diagnosed with the disease. Both measures require specification of some time period over which events are counted.

The relationship between risk and case fatality is depicted schematically in Figure 2–7. The initial population at risk of disease consists of 15 women (N = 15), five of whom develop the condition of interest (A = 5). Risk, or cumulative incidence, therefore, is

Only two (D = 2) of the affected women (A = 5) subsequently die from the condition. The case fatality, therefore, is

The case fatality can range from 0, when no patients die from the disease, to 1 (or 100%), when all patients die from the disease. Since the case fatality represents the proportion of persons affected with a disease who die from it, the case fatality may be thought of as the complement to survival. In other words, for a given period of observation, the case fatality and survival should sum to 100%. Returning to Figure 2–7, survival is

Thus, the case fatality (CF = 40%) and the survival (S = 60%) total 100%.

Five of the basic descriptive measures used in epidemiology have been introduced in this chapter. Although other indicators of disease frequency and prognosis exist, the following five measures are central to the descriptive function of epidemiology.

• 1. Risk, or cumulative incidence, is the proportion of unaffected persons within a population that develops the disease of interest in a specified period of time.
• 2.Prevalence is the proportion of a population affected by the disease of interest at a particular time.
• 3.Incidence rate measures the rapidity with which unaffected persons within a population develop a particular disease.
• 4. Survival is the proportion of persons affected by the disease of interest that lives for at least a specified period of time.
• 5.Case fatality is the proportion of persons within a population affected by a particular disease that dies from the disease within a specified period of time.

Survival and case fatality represent mutually exclusive outcomes. Together they must account for all individuals affected with the disease who have known vital status.

Application of these measures to the questions raised by the Patient Profile results in the following conclusions:

• 1. Hospitalized cancer patients have a substantial risk (R = 0.12, or 12%) of developing an infection during hospitalization.
• 2. The agents (eg, S aureus) that cause infections in the bloodstream of cancer patients are commonly cultured from the skin of healthy persons (prevalence [P] = 0.65, or 65%).
• 3. The incidence rate of infection among hospitalized cancer patients is appreciable (IR = 4.7 cases per 1000 patient-days), but the corresponding incidence rate among patients with impaired immune systems is more than 30 times greater (IR = 160 cases per 1000 patient-days).
• 4. The 5-year survival for adult patients with acute myelogenous leukemia is extremely low (S = 0.19, or 19%).
• 5. Based on the survival data, it can be concluded that 81% of patients with acute myelogenous leukemia die from this disease or its complications within 5 years of diagnosis.

With this information in mind, the physician in the Patient Profile can conclude that the patient is at an unusually high risk for a life-threatening nosocomial bacterial infection. Rapid initiation of broad-spectrum antibiotic therapy is warranted, even before the results of culture specimens are known. When the results of pretreatment cultures and antibiotic susceptibilities become available, the antibiotic regimen can be modified, if necessary. By appropriate use and interpretation of standard epidemiologic measures such as risk and incidence rate, the physician can make informed and potentially life-saving treatment decisions.