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Intellectual Framework

Teaching UnitsEpidemiology initially focused on causes of mortality in England in the seventeenth century. Much epidemiologic work in the eighteenth century involved the recording and analysis of deaths, grouped according to the diagnoses then in use (e.g., dropsy, ague). Although the discipline of epidemiology antedates the discovery of infectious disease agents, in the nineteenth century it was widely applied to the study of epidemics, many of which were subsequently found to be of infectious origin. In the twentieth century, epidemiologists investigated such varied topics as chronic diseases (like heart disease and cancer), vitamin deficiencies, work-related health problems, disasters (like earthquakes and tornados) and the consequences of social inequality. A recent study of house fires in Dallas illustrates the wide applicability of epidemiology and many of its key principles.

Dallas Fire Study

In 2001 Dr. Gregory Istre and his colleagues studied injuries from house fires that had occurred in Dallas, Texas, from 1991 to 1997, in an attempt to learn how to prevent those injuries.1 They found 223 injuries (91 fatal and 132 nonfatal) from 7,190 house fires, for a rate of 5.2 injured people per 100,000 population per year. Rates of injury were higher among blacks (9.7 per 100,000) than nonblacks (3.5 per 100,000) and higher in the elderly (11.3 per 100,000 versus 4.4 per 100,000 in those less than 65 years old). Census tracts with low median incomes had injury rates 8 times as high as those with high median incomes. Injuries were 6.6 times as common from fires in houses built before 1980 as in more recently built houses. When there was a fire, injuries occurred 1.5 times as often in houses without functioning smoke alarms as in houses with one. Houses in census tracts with the lowest median family income had the lowest proportion of functioning smoke alarms. The investigators estimated that, overall, the rate of fire-related injury in houses without a functioning smoke detector was 8.7 times that in houses with a functioning smoke detector. They concluded that control efforts to prevent house fire injuries should target the elderly, minorities, low-income populations and houses without functioning smoke alarms.

Key Principles

Epidemiology is based on the premise that the cause of a phenomenon that affects members of a population results in higher rates of occurrence of that phenomenon in those members of the population who are exposed to that cause than in those who are not exposed. Furthermore, the cause is thought to be discoverable (through a process of induction using the scientific method) by analyzing the patterns of occurrence of that phenomenon in populations. That is, a cause produces risk, which increases the rate of appearance of cases of a phenomenon among those exposed as compared with those unexposed to the cause. Comparison of rates of cases in exposed and unexposed populations points to differences in risk and suggests both the cause or cause(s) and the mechanisms through which the cause creates the risk. Understanding the cause and the mechanism through which it operates allows the design of interventions for prevention, as well as the testing of the effectiveness of those strategies. In the Dallas fire study, the absence of a functioning smoke alarm was one cause that could be inferred for house fire-associated injuries; other contributing causes seemed to relate in some way to old age (perhaps due both to risk of starting a fire and to difficulty in escaping it) and to poverty (including perhaps faulty house wiring).

Understanding the terms in bold is essential to understanding epidemiology. One may begin by defining a case, as cases represent instances of the problem that one wants to study. A precise and unambiguous definition of a case is essential, but the specific criteria will differ greatly depending on the condition and knowledge about it. In the Dallas fire study, an injured person was defined as any person who was transported by emergency medical services or admitted to Parkland Health and Hospital System for a burn or smoke inhalation or who had been identified by the medical examiner as having died of fire-related injuries; a house fire was defined as one reported to the Dallas Fire Department in an inhabited, nonmobile residential structure that contained one or two units.

The population from which the cases come must also be defined, not least because one of the criteria for defining a case is always the population from which it comes. In the Dallas fire study, only house fires in Dallas in 1991-1997 were studied.

The rate of the phenomenon in a population relates to the frequency of cases. That frequency may be measured in several ways, including the incidence (the number of new cases per person per unit of time) and the prevalence (the proportion of the population at a given time that has a case). The severity of a disease is often measured by the case fatality rate, which is actually the ratio of fatal cases to total cases. In the Dallas fire study, the frequency of injuries was measured by their incidence (5.2 injured people per 100,000 population per year) and that of functioning smoke detectors by their prevalence; the case fatality rate was 41% (91/223).

Risk is a complex concept that can be viewed from several perspectives. The statistician sees risk in terms of the probability of a certain outcome under conditions of uncertainty. The biologist sees risk in terms of the biochemical and immunologic systems that promote disease causation or provide immunity or the disease vectors (like mosquitoes) that effectively expose the individual to the agent. The social scientist sees risk in terms of the social structures and history that affect personal decisions and access to resources important for shaping life's events. The epidemiologist embraces all these views, seeing risk as the funnel through which a complex set of causes results (or not) in a given outcome. A cause may be necessary or sufficient (or both). Cause may be unitary or multifactorial. Often, cause must be described in terms of the interaction of the agent, the host and the environment. Commonly, the epidemiologist uses the term risk factor to describe a definable element of exposure that captures at least one part of the pathway by which the cause increases the risk that a member of the population will meet the criteria of a case. In the Dallas fire study, the cause of house fires was found to be multifactorial. Among the identified risk factors were race, age, poverty and nonfunctioning smoke detectors.

Many sciences use experiments, in which the scientist establishes in advance two or more different starting conditions and then observes differences in subsequent outcome, in order to test hypotheses about causes and their mechanisms. Epidemiologists also use experiments (e.g., to test the usefulness of a new vaccine). However, much of epidemiology involves "natural experiments" or other observational studies, in which events occur without the scientist having controlled the starting conditions. In this way, epidemiology resembles the largely observational sciences like geology and astronomy. The Dallas fire study is an example of an observational study.

The randomized controlled trial is the epidemiologist's analogue of the bench scientist's experiment and represents the highest rank of study design in the epidemiologist's tool kit. In the absence of a randomized controlled trial, observational studies are done in several ways, generally in descending order of reliability: the cohort study, in which naturally exposed and unexposed people are followed to determine who develops the condition of interest; case–control study, in which people who have developed the condition of interest (cases) are compared with people who have not developed it (controls) in order to identify differences in their earlier exposures; cross-sectional study, in which people in a population at a given point in time are assessed to determine the association between possible risk factors and the condition in question; and ecologic study, in which the rate of the condition and the prevalence of a given risk factor in one population are compared with those in other populations or across different time periods. Finally, and least reliably, one may examine the characteristics of individual cases or case clusters, without regard to comparisons with people who did not develop the condition. The Dallas fire study was, for the most part, a cohort study of the Dallas population. For the analysis of income levels, however, the investigators did an ecologic study based on census tracts, as they did not have access to information on the income levels of the people in the fires.

Demonstrating an association between a putative risk factor and the condition under study is a crucial step in the epidemiologist's efforts to understand causation. That association may most simply be displayed in a contingency table, in which every person under study is counted according to that person's exposure to the risk factor (either dichotomous [e.g., yes or no] or according to the dose of exposure received) and whether or not the person has the condition under study. If both exposure and disease are dichotomous, the contingency table is commonly described as a 2 x 2 table. The risk factor is said to be associated with the condition if the proportion of cases among those who have the risk factor is larger than the proportion of cases among those who do not have the risk factor -- and if the difference is greater than one would expect to observe by chance alone. A rigorous assessment of what one might expect from chance alone is the province of statistics, although one can often make an intelligent assessment without formal statistical testing. In the Dallas fire study, associations were found between the risk of injury in house fires and race, age, poverty and non-functioning smoke alarms.

An association may be strong or weak. The strength of an association is measured in several ways. The relative risk (or risk ratio) is defined as the ratio of the incidence of the condition in people who have the risk factor to the incidence of the condition in people who do not have it. It is a measure of proportional increase in risk associated with acquiring the risk factor. (Note that the relative risk can be less than 1 [though no less than 0], in which case the risk factor is protective. Vaccination is a typical example of a protective risk factor. The efficacy of a vaccine or other protective intervention is defined as 1 - relative risk.) Closely related is the odds ratio, which is defined as the ratio of the odds of the condition in those with the risk factor to the odds of the condition in those without it. When the condition is rare -- that is, when fewer than about 5% of the population develop the condition -- the odds ratio is a good approximation of the relative risk. The risk difference is the arithmetic difference in the incidence of the disease in those with the risk factor and the incidence of disease in those without it. The attributable fraction is the proportion of cases in a population that can be attributed to the risk factor. The attributable fraction depends on the prevalence of the risk factor as well as the relative risk associated with it. Each of these measures provides important information about the possible contribution of the risk factor to the occurrence of the condition in question. The attributable fraction indicates the proportion of the cases that could be prevented if the risk factor were removed from the population. The relative risk and odds ratio speak to the proportion of an individual's risk that could be eliminated if that person lost the risk factor. The risk difference indicates the absolute decrease in risk that an individual could expect from the loss of the risk factor. In the Dallas fire study, the investigators reported the strength of association in terms of relative risks. For example, they reported that the relative risk of injury associated with homes built before 1980, compared with homes built more recently, was 6.6.

Demonstrating that an association is causal is a challenging and important task of the epidemiologist, because many associations can be the result of causes other than the risk factor that the epidemiologist is studying. The commonly accepted criteria for concluding that an association is causal are temporality (exposure occurring before the outcome); the strength of the association; the existence of an incremental increase in risk associated with increase in degree of exposure to the risk factor (dose response); consistency of the association across various studies; and biological plausibility of the proposed causal link between exposure and outcome. In the Dallas fire study, the investigators displayed evidence of dose response with a graph showing that the incidence rate of injuries decreased progressively with increasing median family income of census tracts. All cited risk factors were present prior to the fire, thus demonstrating temporality. The idea that non-functioning smoke alarms might be a cause of fire-related injuries is biologically plausible.

The extraneous factors that can result in the finding of associations that are not causal include bias and confounding. Bias is defined as an aspect of the design or execution of a study that yields misleading results. That distortion usually arises as a result of the way people are selected for the study or the way information about them is gathered or interpreted. Such distortions are less common in randomized controlled studies, though they can occur (e.g., if the investigators know which persons in the study received treatment and are influenced by this knowledge when making decisions about whether the persons in the study got better or worse). In observational studies, investigators must be particularly careful to try to mimic the even-handed conditions of the randomized controlled trial as much as possible in order to avoid bias. Confounding is the complication of analysis due to the presence of a third factor that is associated with both the putative risk factor and the outcome. For example, the incidence of death (i.e., the mortality rate) is much higher in Florida than in Michigan. But before concluding that Florida is a less wholesome place, one would need to correct for the confounding factor of age, as Florida has a higher proportion of people of retirement age than does Michigan and older people are more likely to die in any given interval of time. One of the epidemiologist's tools for discovering and correcting confounding is stratification, which in the preceding example would have the epidemiologist compare mortality rates in Florida and Michigan separately for people in various age groups. In the Dallas fire study, the investigators pointed out some features of their study that could have created bias or confounding, including the absence of information about alcohol consumption, missing information about smoke detectors in some house fires, and uncertainty in some fires about whether the smoke detector was functioning.

Earlier we stated that a case must be defined explicitly and unambiguously. That should not be assumed to imply that the definition always correctly characterizes people. In fact, the study of uncertainty in categorizing conditions is a fertile area of epidemiologic study and one with wide ramifications in many areas of human activity. All scientists talk about accuracy and precision. The analogues for the epidemiologist are validity and reliability, respectively. Epidemiologists talk also about diagnostic tests or screening tests. The sensitivity of a test is defined as the proportion of people with the condition who have a positive test result. The specificity of a test is the proportion of people without the condition who have a negative test result. The predictive value of a positive (PVP) is the proportion of people with a positive test who actually have the condition. The predictive value of a negative (PVN) is the proportion of people with a negative test who actually do not have the condition. A good test will have high sensitivity and specificity. However, high sensitivity and specificity do not ensure high predictive value, as predictive value depends heavily on the prevalence of the condition in the population in which the test is used. Bayes's theorem (which shows how the probability of a condition given a test result can be deduced from the probability of that test result given the condition) nicely captures these relations in terms of conditional probability. It is important to note that screening and diagnosis are not restricted to health problems. Sensitivity, specificity and predictive value apply equally to such disparate activities as airport security screening and selecting income tax forms for audit. In the Dallas fire study, the investigators used Bayes's theorem (and the results of a telephone survey to assess the prevalence of functioning smoke detectors in Dallas houses) to estimate the overall probabilities of fire-related injury in houses with and without functioning smoke detectors.

As with all scientific investigation, the experiment is one critical element in a larger process of investigation. Before one can design and carry out an experiment (or measure the associations in a natural experiment), one must formulate a hypothesis to be tested. The epidemiologist frequently generates hypotheses on the basis of descriptive epidemiology, the systematic analysis of who has the condition and when and where cases occur (time, place and person). The patterns observed may suggest both the source and, for infectious diseases, the mode of spread. Information about such cases may come from investigations that the epidemiologist does specifically for that inquiry, as when a cluster of cases leads to an epidemic investigation. Commonly, though, the epidemiologist uses information from ongoing surveillance activities (like death registries or disease reporting) or periodic surveys (such as for health and nutrition) to generate hypotheses. In the Dallas fire study, the investigators linked information already collected by Dallas emergency medical services, the Parkland Health and Hospital System, the office of the medical examiner and the Dallas Fire Department.

Each investigation is embedded in a larger context, which very much affects the conduct and use of epidemiology, as illustrated in the Dallas fire study. The choice of problems on which to work is of great importance to those at risk of those problems and is shaped by political and funding forces. There are racial and ethnic disparities in the incidence and prevalence of many conditions. The conduct of investigations involves important issues of ethics, including, but not limited to, informed consent. In many instances investigational findings appropriately lead to public policy change and intervention, but the decision to make those changes goes beyond the narrow confines of the individual experiment. Considerations of cost-benefit and cost-effectiveness contribute to policy decisions by linking epidemiology with economics. Finally, the tools of epidemiology are useful not just for the practicing scientist but for the consumer and responsible citizen who need to understand the basis for policy and practice recommendations for informed personal and political decision making. For that reason, epidemiology can usefully be taught as part of general education.

Clustering and Ordering the Teaching of Key Principles

One can approach the teaching of epidemiology from any of several directions because many of its principles need little prior knowledge to be understood and are applicable to a wide range of disciplines. Thus, one can teach the central concepts of cause, risk, rates, exposure and case definitions from mathematics, biology or social studies. Some understanding of inductive reasoning allows the teaching process to go more quickly, but epidemiology is as good a science as any for introducing the concepts of inductive reasoning to students for whom it is unfamiliar.

Certain clusters of epidemiologic concepts fit logically together. The concept and the measures of association -- including relative risk, odds ratio, risk difference and attributable fraction -- in any given interval fit well with discussion of comparison of rates, contingency tables, risk factors and efficacy. All cluster around the fundamental idea of comparing the frequencies of countable events in different populations.

Causation is a more complicated concept, and one must understand association first. Temporality, dose response, stratification, bias and confounding are concepts that contribute to an understanding of the distinction between causation and association, although bias and confounding are themselves sufficiently complicated that they may require a separate module.

Sensitivity, specificity and predictive value also are appropriately taught together, either without or, for students familiar with concepts of probability, with conditional probability and Bayes's theorem. Although these concepts are broadly applicable, they are not central to understanding much of the rest of epidemiology and so can be taught as a free-standing module.

Study design is essential to understanding hypothesis testing. The randomized controlled trial and the cohort study are readily understood by students, and the comparison of those two designs highlights such varied issues as bias, confounding, informed consent and the ethics of research. A comparison of these designs with the cross-sectional study underlines the importance of time sequence, as a cause must precede its effect. The case–control study is often hard for students to understand, but it is a versatile and powerful tool when used carefully, so it is worth separate focus for students prepared to think creatively. The ecologic study is widely used but often flawed; students should learn to be skeptical of results from such a study.

Epidemic investigation is another specialized area and so can be omitted or taught at almost any time in an epidemiology curriculum. The related concepts include descriptive epidemiology (time, place, person), incubation period and disease transmission. One great value in teaching epidemic investigation is that examples are often dramatic and the investigation process engages students' imagination.

The concepts of decision making about risk and choices by responsible voters or consumers apply to a wide range of topics addressed by epidemiology. They can readily be clustered with considerations of ethics and public policy, or these concepts can be incorporated into almost all epidemiologic modules.

Mapping of Epidemiologic Principles onto Teaching Modules

Modules have been developed for the teaching of selected epidemiologic principles using a variety of examples and disciplines. The following list suggests clusters of modules that might be used in various subjects to teach the key epidemiologic principles.

David W. Fraser
January 6, 2004

Module Clusters/Sequences by Theme and Subject

Math

Frequencies of countable events: Measures in Epidemiology; Cross-sectional Study Design and Data Analysis; Attributable Risk Applications in Epidemiology
Causation: Observational Studies and Bias in Epidemiology; Confounding in Epidemiology; An Outbreak of Legionnaires' Disease
Sensitivity, specificity, predictive value: Screening and Diagnostic Tests
Study design: Study Design; Observational Studies and Bias in Epidemiology; Confounding in Epidemiology; Case–Control Study
Epidemic investigation: Disease Outbreak Investigation; An Outbreak of Legionnaires' Disease
Decision making, ethics and public policy: Screening and Diagnostic Tests; How to Read the Newspaper

Statistics

Frequencies of countable events: Measures in Epidemiology; Cross-sectional Study Design and Data Analysis; Attributable Risk Applications in Epidemiology
Causation: Observational Studies and Bias in Epidemiology; Confounding in Epidemiology; An Outbreak of Legionnaires' Disease
Sensitivity, specificity, predictive value: Screening and Diagnostic Tests
Study design: Study Design; Observational Studies and Bias in Epidemiology; Confounding in Epidemiology; Case–Control Study
Epidemic investigation: Disease Outbreak Investigation; An Outbreak of Legionnaires' Disease
Decision making, ethics and public policy: Screening and Diagnostic Tests; How to Read the Newspaper

Biology

Frequencies of countable events: Descriptive Epidemiology of Births to Teenage Mothers; Measures in Epidemiology; Casualties of War: The Short- and Long-Term Effects of the 1945 Atomic Bomb Attacks on Japan; Cross-sectional Study Design and Data Analysis; Attributable Risk Applications in Epidemiology; Risk Perception
Causation: Alpine Fizz and Male Infertility: A Mock Trial; Observational Studies and Bias in Epidemiology; Confounding in Epidemiology
Study design: Testing Ephedra; Case–Control Study; Study Design; Ecologic Studies
Epidemic investigation: Disease Outbreak Investigation; An Outbreak of Legionnaires' Disease
Decision making, ethics and public policy: Adolescent Suicide: The Role of Epidemiology in Public Health; Risk Perception; Should the Population Be Screened for HIV?; Casualties of War: The Short- and Long-Term Effects of the 1945 Atomic Bomb Attacks on Japan; How to Read the Newspaper

Chemistry

Causation: Alpine Fizz and Male Infertility: A Mock Trial
Epidemic investigation: Outbreak Investigation in a Vermont Community Hospital

Environmental Science

Frequencies of countable events: Measures in Epidemiology; Cross-sectional Study Design and Data Analysis; Attributable Risk Applications in Epidemiology; Casualties of War: The Short- and Long-Term Effects of the 1945 Atomic Bomb Attacks on Japan
Causation: Alpine Fizz and Male Infertility: A Mock Trial; Observational Studies and Bias in Epidemiology; Confounding in Epidemiology
Study design: Study Design; Ecologic Studies; Case Control Study
Case Control Study: Study Design
Epidemic investigation: Disease Outbreak Investigation; Outbreak Investigation in a Vermont Community Hospital; An Outbreak of Legionnaires' Disease
Decision making, ethics and public policy: Casualties of War: The Short- and Long-Term Effects of the 1945 Atomic Bomb Attacks on Japan; Examining the Plague: An Investigation of Epidemic Past and Present; Bicycle Helmet Effectiveness in Preventing Injury and Death; How to Read the Newspaper; Epidemiology and Public Health Policy: Using the Smoking Ban in New York City Bars as a Case Study

Health Education

Frequencies of countable events: Descriptive Epidemiology of Births to Teenage Mothers; Attributable Risk Applications in Epidemiology; Risk Perception
Causation: Alpine Fizz and Male Infertility: A Mock Trial; An Association: TV and Aggressive Acts; Adolescent Suicide: The Role of Epidemiology in Public Health
Sensitivity, specificity, predictive value: Screening and Diagnostic Tests
Study design: Testing Ephedra: Using Epidemiologic Studies to Teach the Scientific Method; Study Design; An Association: TV and Aggressive Acts; Case–Control Study; Adolescent Suicide: The Role of Epidemiology in Public Health
Decision making, ethics and public policy: Adolescent Suicide: The Role of Epidemiology in Public Health; Should the Population Be Screened for HIV?; Bicycle Helmet Effectiveness in Preventing Injury and Death; Risk Perception; How to Read the Newspaper; Epidemiology and Public Health Policy: Using the Smoking Ban in New York City Bars as a Case Study

Social Science

Frequencies of countable events: Descriptive Epidemiology of Births to Teenage Mothers; Casualties of War: The Short- and Long-Term Effects of the 1945 Atomic Bomb Attacks on Japan
Causation: Mortality and the Transatlantic Slave Trade; Alpine Fizz and Male Infertility: A Mock Trial; An Association: TV and Aggressive Acts; Adolescent Suicide: The Role of Epidemiology in Public Health
Study design: An Association: TV and Aggressive Acts; Study Design; Ecologic Studies; Adolescent Suicide: The Role of Epidemiology in Public Health
Epidemic investigation: Disease Outbreak Investigation
Decision making, ethics and public policy: Adolescent Suicide: The Role of Epidemiology in Public Health; Casualties of War: The Short- and Long-Term Effects of the 1945 Atomic Bomb Attacks on Japan; Tuskegee; Mortality and the Transatlantic Slave Trade; Examining the Plague: An Investigation of Epidemic Past and Present; Should the Population Be Screened for HIV?; Public Policy; Bicycle Helmet Effectiveness in Preventing Injury and Death; Risk Perception; How to Read the Newspaper

English

Decision making, ethics and public policy: Public Policy

Reference
  1. Istre GI, McCoy MA, Osborn L, Barnard JJ, Bolton A. Deaths and injuries from house fires. New England Journal of Medicine. 2001;344:1911-1916.
Incidence

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Adolescent Suicide: The Role of Epidemiology in Public Health
Attibutable Risk Applications in Epidemiology
Mortality and the Transatlantic Slave Trade
Measures in Epidemiology
An Association: TV and Aggressive Behavior
Descriptive Epidemiology of Birth's to Teenage Mothers
Casualties of War: The Short and Long-Term Effects of the 1945 Atomic Bomb Attacks on Japan

Case Fatality Rate

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Mortality and the Transatlantic Slave Trade

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Agent

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Disease Outbreak Investigation
An Outbreak of Legionnaires' Disease
Examining the Plague: An Investigation of Epidemic Past and Present

Risk Difference

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Attributable Risk Applications in Epidemiology

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Attributable Fraction

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Measures in Epidemiology
Attributable Risk Applications in Epidemiology

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An Association: TV and Aggressive Acts
Confounding in Epidemiology
Case Control Study

Observational Studies and Bias in Epidemiologic Research

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Confounding in Epidemiology
Observational Studies and Bias in Epidemiologic Research

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Cross-Sectional Study Design and Data Analysis
Testing Ephedra: Using Epidemiological Studies to Teach the Scientific Method

Validity

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Screening and Diagnostic Tests

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Observational Studies and Bias in Epidemiologic Research

Reliability

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Screening and Diagnostic Tests

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Observational Studies and Bias in Epidemiologic Research

Diagnostic Tests

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Diagnostic Tests

Screening Tests
Screening Tests

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Should the Population be Screened for HIV?
Screening and Diagnostic Tests

Sensitivity

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Screening and Diagnostic Tests

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Specificity

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Screening and Diagnostic Tests

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Predictive Value of a Positive

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Screening and Diagnostic Tests

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Predictive Value of a Negative

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Screening and Diagnostic Tests

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Bayes' theorem

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Screening and Diagnostic Tests

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Epidemic Investigation

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An Outbreak of Legionnaires' Disease
Disease Outbreak Investigation
Outbreak Investigation in a Vermont Community Hospital

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N/A

Surveillance

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Ecologic Studies
Casualties of War: The Short and Long-Term Effects of the 1945 Atomic Bomb Attacks on Japan

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Cross-Sectional Study Design and Data Analysis
Descriptive Epidemiology of Birth's to Teenage Mothers
Mortality and the Transatlantic Slave Trade
An Outbreak of Legionnaires' Disease

Racial and Ethnic Disparities

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N/A

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Mortality and the Transatlantic Slave Trade
The Tuskegee Syphilis Study

Ethics

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The Tuskegee Syphilis Study

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Testing Ephedra: Using Epidemiological Studies to Teach the Scientific Method
Should the Population be Screened for HIV?

Cost Benefit

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Attributable Risk Applications in Epidemiology
Bicycle Helmet Effectiveness in Preventing Injury and Death

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N/A

Cost Effectiveness

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Attributable Risk Applications in Epidemiology
Bicycle Helmet Effectiveness in Preventing Injury and Death

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N/A