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Last updated: March 25, 2021

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Classical epidemiology is the study of the distribution and determinants of disease in populations. There are two main types of epidemiological studies: observational and experimental. Observational studies are categorized into descriptive and analytical studies. Descriptive studies (case reports, case series, cross-sectional studies, ecological studies) consider the relationship between a particular outcome and individual characteristics, location, and/or time of events, while analytical studies (e.g., cohort, case-control studies) seek to determine the influence of an exposure on an outcome. In experimental studies (e.g., randomized control trials, noninferiority trials, crossover studies), an experiment is performed to determine the effect of an intervention on diseases in subjects. The conclusions drawn from epidemiological studies can be made more reliable by limiting bias, confounding, and effect modification.

To measure the strength of the relationship between two events, researchers use ratios (e.g., incidence, prevalence), rates (e.g., birth, fertility, mortality), and proportion tests (e.g., relative risk, absolute risk, attributable risk). This relationship can be presented in a two-by-two table, which helps visualize the number of false positive and true positive diagnostic results and, ideally, the number of patients with and without the disease. A diagnostic test is considered accurate if it measures what it was developed to measure (valid) and if the results it yields are reproducible under similar conditions (reliable). The more reliable a test is, the less random errors it will generate.

Clinical epidemiology applies the principles and methods of classical epidemiology to the prevention, detection, and treatment of disease in a clinical setting. Best practice follows evidence-based medicine, in which the physician uses clinical decision-making methods based on the most reliable available research from peer-reviewed clinical and/or epidemiological studies with the aim of producing the most favorable outcome for the patient.

For more information, see “Statistical analysis of data.”

  • Classical epidemiology: the study of the determinants and distribution of disease in populations [1][2]
  • Clinical epidemiology: the study and application of epidemiology principles and methods to the clinical setting
  • Population (epidemiology): the total number of inhabitants in a region from which a sample is drawn for statistical measurement [3]
    • Population pyramid: an illustration of the age and sex distribution of a population
      • Stationary pyramid
        • Represents a population in which age and sex distribution remain constant over time
        • Equal birth and death rates
      • Expansive pyramid
        • Represents a population in which there is a higher percentage of young people (i.e., a youthful population)
        • High birth rates and low life expectancy
      • Constrictive pyramid
        • Represents a population in which there is a higher percentage of elderly people (i.e., an older population)
        • Low birth rate and high life expectancy
  • Data (epidemiology): information, collected during observation and/or experimentation, that is used as a basis for analysis and discussion [4]
  • Sample (epidemiology): a group of people that is representative of a larger population
  • Control group
    • A group, recruited from the same source population as the study group, that does not receive the intervention (e.g., a drug) or did not develop the outcome (e.g., a disease)
    • It is matched for baseline characteristics with the study population to reduce confounding factors.
Types of diseases
Endemic Epidemic Pandemic
Definition [1]
  • A disease is endemic when it affects individuals at a relatively constant rate within a specific population in a given region.
  • A disease that affects individuals at an unusually fast rate within a specific population in a given region
  • A disease that affects a wide geographic area, such as multiple countries or continents
  • Unlimited
  • Limited
  • Limited


  • Limited
  • Limited
  • Unlimited
Possible factors
  • Spread of disease vectors and pathogen reservoirs
  • Geographical conditions
  • Climate
  • Living conditions (e.g., sewage systems, housing, work)
  • Infectivity of a pathogen: increased ability to multiply in a host
  • Living conditions (e.g., living in crowded areas)
  • Spread/introduction of the pathogen to a new geographical area

Principles of study design

  • Study designs should be tailored to the question that needs to be answered.
  • The higher the levels of evidence in a study design, the stronger the conclusions that can be drawn from the results.

Types of epidemiological studies [5]

Observational studies Experimental studies
Descriptive studies Analytical studies
  • Intervention included
  • Usually involves 3 elements:
    • Study participants
    • Treatment (i.e., the procedure applied to the study participants)
    • Response (i.e., the effect of the procedure applied to the experimental subject)
  • The independent variable is manipulated to determine the effect on the dependent variable.
  • To identify individual characteristics (age, sex, occupation), location (e.g., residence, hospital), and/or time of events (e.g., during diagnosis, reporting) in relation to an outcome (e.g., disease)
  • To determine the relationship between an exposure and an outcome
  • To determine the effect of an intervention on subjects or diseases
  • Create hypothesis
  • No comparison group
  • Test hypothesis
  • Always involve a comparison group.
  • Test hypothesis
  • Always involve a comparison group.
  • Informed consent is usually required.

Interpretation [2]

Epidemiological studies suggest relationships between two factors (e.g., exposure and disease). The following measures can be used to compare factors in epidemiological studies:

  • Proportion
    • Comparison of one part of the population to the whole
    • Proportions are usually expressed as percentages.
  • Rate (epidemiology)
    • A measure of the frequency of an event in a population over a specific period of time
    • Rates are usually reported as numbers of cases per 1,000 or 100,000 in a given time unit.
    • Types
      • Crude rate: Rates apply to the entire population (specific characteristics are not taken into account).
      • Specific rate: Rates apply to a population group with specific characteristics (e.g., sex-specific, age-specific).
      • Standardized rate (adjusted rate): crude rates that have been adjusted for specific population characteristics to allow for comparison (e.g., commonly used in death rates)
  • Ratios
    • Comparison of two values or the magnitude of two quantities
    • The numerator and denominator do not necessarily need to be related (e.g., a ratio comparing the number of hospitals in a city and the size of the population living in that city).
    • Ratios are usually expressed as X:Y or X per Y.

These measures are used to determine the strength of association between two factors and to describe population characteristics (e.g., at-risk populations) and to quantify morbidity/mortality. Researchers can use the findings from comparison studies to develop hypotheses about why certain groups are at risk for certain diseases. [6]

  • Causal criteria (Bradford-Hill criteria): a list of criteria that helps to establish causality in epidemiological studies [7]
    • Strength of association (effect size)
      • A quantitative measure of the degree of relationship between two variables
      • The stronger the association between an exposure and its observed outcome, the more likely there is to be a causal relationship between them
    • Dose-response relationship (biological gradient): tests whether greater exposure usually leads to a higher occurrence of the outcome (e.g., the greater the exposure to ionizing radiation, the higher the risk of malignancy)
    • Temporality: tests whether the outcome occurs after the effect within an expected amount of time (e.g., surgical site infection occurs after incision of the skin)
    • Reproducibility (consistency): The strength of association found between two factors increases when similar findings are observed in different studies (e.g., in different places, with different sample sizes).
    • Specificity: It is more likely that a causal relationship exists between a factor and an effect when a specific disease occurs in a specific population at a specific time (e.g., there is an increase in the number of leukemia cases in a small town after a chemical factory is built nearby).
    • Biologic plausibility: The relationship between an exposure and an outcome is usually consistent with current biological and medical knowledge (e.g., carcinogens in cigarettes cause lung cancer, and water molecules do not).
    • Coherence (epidemiology)
      • Tests whether new evidence is in agreement with previously established evidence
      • If there is a contradiction with previously established results, this reflects negatively on the likelihood of a causal relationship between a given set of factors (e.g., an epidemiological study that finds a correlation between higher rates of lung cancer in men while there is no available biological data to support it).
    • Experimental evidence: data drawn from provisional experimentation support the presumed causal relationship between exposure and outcome (e.g., a distance of at least 2 meters between people is correlated with a decrease in the number of COVID-19 cases)
    • Analogy (epidemiology): When there is strong evidence of a causal relationship between an exposure and an outcome, there is a greater likelihood of a causal relationship between another similar exposure and outcome (e.g., when one class of medication is known to produce an effect, it is likely that another agent of that class produces a similar effect).
  • Reverse causality: an association between exposure and outcome that is different than common presumption (e.g., people assume that low socioeconomic status causes schizophrenia, but in fact, schizophrenia causes a decline in socioeconomic status over time) [8]

Descriptive studies
Case report Case series report Ecological study [9] Cross-sectional study (prevalence study) [10]
  • A report of a disease presentation, treatment, and outcome in a single subject or event
  • A report of a disease course or response to treatment that is compiled by aggregating several similar patient cases
  • A study that assesses links between an exposure and an outcome (e.g., disease), typically used if the outcome is rare
  • A study that determines the prevalence of exposure and disease at a specific point in time
Study method
  • An unusual outcome in a single subject is described in detail.
  • Generally, unique findings are reported.
  • It can help in the formulation of a hypothesis.
  • Researchers assess aggregated data of similar patient cases.
  • Typically, they all receive the same intervention.
  • There is no control group.
  • Researchers assess aggregated data where at least one variable (e.g., an outcome) is at a group level and not at an individual level.
  • The observation is an entire country or a large population of people (e.g., the mean, prevalence, incidence, or rate of disease).
  • The prevalence of disease and other variables (e.g., risk factors in relation to demographic data) are measured simultaneously at a particular point in time (a snapshot of the population).
  • It can reveal an association between risk factors and disease.
  • It can help examine the population and eventually support diagnostic tests.
  • Ecological fallacy: making inferences about an individual in a group based on the characteristics of that group
  • It cannot directly measure incidence or risk.
  • It cannot assess causality.
  • Examining a single case of cervical cancer in a 25-year-old female individual
  • Collecting and examining several cases of pericarditis at a local hospital
  • Determining the incidence of cholera deaths based on specific locations (e.g., different parts of a city) to identify the exposure (e.g., water from a single contaminated pump)

Experimental studies

Randomized controlled trials (RCTs; interventional studies)

  • Aim: : to determine the possible effect of a specific intervention on a given population
  • Study method
    • Patients are randomly allocated as either treatment or control subjects.
    • Control subjects can receive a placebo, a treatment used in standard practice, or no intervention at all.
    • Treatment subjects receive the standard practice medication.
  • Advantages
    • Minimizes bias
    • Can demonstrate causality
  • Disadvantages
    • Cannot be used to evaluate rare diseases
    • Cannot be used when treatments have well-known adverse side effects
    • High-cost and time-consuming
  • Special variants
    • Blinding: the practice of not informing an individual or group about which study participants are part of the control group and which are part of the treatment group
      • It is used to reduce bias.
      • Triple-blind study: Neither the researchers, the study participants, nor the data analysts know which study participants are part of the control group and which are part of the treatment group. The purpose of triple-blinding is to reduce assessment bias and to increase the accuracy and objectivity of the outcome (such studies are typically difficult to conduct).
      • Double-blind study: Neither the researchers nor the study participants know which study participants are part of the control group and which are part of the treatment group. Double blinding is the gold standard when studying treatment outcomes. [11]
      • Single-blind study: Only the researchers know which study participants are part of the control group and which are part of the treatment group.
    • Cluster randomized controlled trials
      • Participants are grouped together into clusters and then these clusters are randomly assigned to the control or intervention groups.
      • A cluster RCT is easier to perform than a classical RCT but may have less validity.

Randomized controlled trials are considered the gold standard for clinical trials.

Field trials

  • Aim: determines the effect of disease-preventing interventions in noninstitutionalized individuals
  • Example: following subjects who have received the Salk vaccine for prevention of poliomyelitis

Community trials

  • Aim: similar to field trials, but follows entire communities instead
  • Example: following communities who implement lifestyle changes to prevent cardiovascular disease

Noninferiority trials [12]

  • Aim: to demonstrate that the effect of a new treatment is not inferior to that of an existing treatment by more than a certain margin
  • Study method
    • Studies in which the use of a placebo group would be unethical
    • A noninferiority margin is used to quantify the amount of treatment efficacy difference allowed.
      • The margin is typically chosen with reference to the effect of the active control in previous placebo-controlled trials.
      • It is specified based on clinical and statistical reasoning.
      • It guides the conclusion of the trial and the final clinical decision-making.
    • Performed using both intention-to-treat analysis and per-protocol analysis
    • If both approaches show noninferiority, the trial is considered positive.
  • Disadvantages
    • The difficulty of setting an appropriate noninferiority margin
    • In some cases, blinding does not protect against bias.

Clinical drug trials [13][14]

  • Definition: studies that involve human subjects and assess new health interventions to provide safe and effective medical care
  • Aim: to compare the benefits of a single treatment to a placebo or between two or more treatments
  • Study method: Study participants are randomly assigned to groups that receive different doses and combinations of drugs.
  • Study variant: factorial study [14]
  • Example

Crossover study [14]

  • Aim: : to obtain an efficient comparison of two or more treatments with fewer patients
  • Study method
    • Each patient switches from one treatment to another during the trial period, with a washout period between two treatments.
    • Patients serve as their own control.
    • The order of treatments is randomized.
  • Example: Each patient receives both drug X and drug Y or a placebo, but at different time periods during the study.

Observational studies

Case-control study [2]

  • Aim: : to study if an exposure (i.e., a risk factor) is associated with an outcome (i.e., disease)
  • Study method
    • Researchers begin by selecting patients with the disease (cases) and without the disease (controls) that have otherwise matching characteristics (e.g., gender, age) from the same source population.
    • The data from a group of individuals who have the outcome in question (e.g., lung cancer) is analyzed to identify what proportion has been exposed to a risk factor and what proportion has not.
    • The odds ratio is then determined between these groups.
    • Example: A study that aims to identify what proportion of individuals with lung cancer smoked ≥ 1 pack of cigarettes a day (the risk factor) in the past 5 years compared to individuals without lung cancer.
  • Advantages
    • Helps determine whether patients with a disease are more likely to have been exposed to a risk factor than patients without that disease.
    • Cost-efficient
    • Can be used in rare diseases
    • Can be used in diseases with long latent periods
  • Disadvantages
    • Recall and/or survivorship bias occurs in retrospective studies.
    • Cannot be used to determine prevalence or incidence
  • Example: determining the link between cervical cancer and human papillomavirus (HPV) exposure by comparing otherwise similar patients with and without histologically confirmed cervical cancer

Cohort study [2]

  • Aim: to study the incidence rate and whether the exposure is associated with the outcome of interest
  • Study method
    • The researchers gather a group of study participants who have common characteristics.
    • Participants are then classified into groups according to their exposure or lack of exposure.
    • The incidence of the outcome of interest is compared between the two groups.
  • Types
    • Prospective cohort study
      • The protocol is established and the study begins before the groups develop an outcome of interest.
      • Study participants are categorized into an exposure group and a nonexposure group.
      • These two groups are followed for a period of time and then compared to see how the outcome of interest (e.g., lung cancer) develops among them.
      • Example: a study that compares the proportion of individuals who currently smoke ≥ 1 pack of cigarettes a day (the risk factor) who develop lung cancer in the next 5 years (the outcome) to the proportion of nonsmokers who develop lung cancer in the same period
    • Retrospective cohort study
      • The protocol is established and the study begins after the exposure and outcome have already occurred.
      • Study participants are categorized into a group that was previously exposed to a given risk factor (e.g., smoking) and a group that was not.
      • These two groups are then compared to see if the outcome of interest (e.g., lung cancer) developed equally in both groups or if there is an association with the risk factor (i.e., if the disease is more frequently seen in either the exposure or nonexposure group).
      • Example: a study that compares the proportion of individuals with a smoking history of ≥ 1 pack of cigarettes a day (e.g., the risk factor) 5 years ago compared to individuals who were nonsmokers 5 years ago and developed lung cancer (e.g., the outcome)
  • Advantages
    • Helps determine whether a given exposure plays a role in the development of a disease
    • Allows for the calculation of relative risk (see “Measures of risk” below)
    • Helps determine incidence
  • Disadvantages
    • High-cost and time-consuming
    • Only assesses the exposures determined at the beginning of the study
    • Requires a large study group

A case-control study examines a small population group over a short period of time (less cost-intensive) and determines how multiple exposures lead to one outcome. A cohort study examines a large population over a long period of time (more cost-intensive) and determines how one exposure leads to multiple outcomes.

In cohort studies, the study group is selected based on whether they were exposed to a risk factor. In case-control studies, the study group is selected according to having a disease or not, and then it is determined which participants were exposed to a risk factor.

Twin concordance study

  • Aim: to determine the influence of genetic and environmental risk factors on the development of a disease
  • Study method: comparing the frequency of a given disease in twins (monozygotic or dizygotic)
  • Example: Twins, one of which is diagnosed with Hodgkin diseases, are studied over a 30-year period, following the diagnosis of Hodgkin disease in the first twin, to see if the frequency of cancer differs between them.

Adoption study

  • Aim: to determine the influence of genetic and environmental risk factors on the development of a disease
  • Study method: comparing the frequency of disease in adopted children to the frequency in children who live with their biological parents
  • Example: Two groups of adults that are the same age and grew up in the same area are studied. Individuals in one group were adopted, and individuals in the other were raised by their biological parents. The prevalence of schizophrenia is compared between the two groups.

Survival analysis (prognosis study) [2]

  • Description
    • Determines the average time to a given outcome identified on follow-up
    • Always prospective in nature
      • Time-to-event analysis: Individual follow‑ups are performed from the onset of a disease to a chosen endpoint (e.g., death, development of a particular complication), or after exposure to a risk factor until the onset of a disease.
      • Five-year survival rate: the percentage of patients with a particular disease who have survived for 5 years after the initial diagnosis
  • Aim: : to measure disease prognosis
  • Disadvantages
    • In studies where the endpoint is death, no prediction can be made for subjects who do not die within the period of observation (these subjects are called “censored cases”).
    • Patients may drop out or die before the end of the follow-up period.
  • Kaplan-Meier analysis
    • Allows survival analysis to be displayed graphically
    • Used to analyze incomplete survival data
      • Ideal for a small number of cases and to describe the survival of a cohort
      • Allows survival over time to be estimated even when individuals are studied over different time intervals
      • The horizontal axis represents the time of follow-up.
    • The vertical axis represents the estimated probability of survival.
    • Time intervals, called Kaplan-Meier estimators, are defined by specific events.

Meta-analysis [15]

  • Aim: : to increase statistical power and achieve more precise results
  • Study method
    • Data from multiple studies is systematically assessed and processed with statistical methods.
    • Identify similarities and/or differences between individual studies
  • Advantages
    • More precise than individual studies
    • Allows generalization of study findings
  • Disadvantages
    • Unable to eliminate limiting factors that depend on the individual study types
    • Only as good as the individual studies used
    • Susceptible to publication bias

Systematic Review [2][16]

  • Aim: to answer a defined research question
  • Study method
    • Researchers collect and summarize evidence that fits established criteria.
    • Uses a systematic approach to the request question
    • Quality assessment of the study is achieved by methods such as the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement.
    • Generally, it does not involve statistical analysis of the reviewed data.
  • Advantages: can improve evidence-based clinical decision-making
  • Disadvantages

Registry study

  • Description: a retrospective study that uses data obtained from disease registries (e.g., cancer registries)
    • Criteria for a good quality cancer registry:

Descriptive studies

  • Characteristics: no intervention
    • Instead, patients are observed and the clinical course of the disease is studied.
    • The observations are used to form a hypothesis.
  • Examples
    • Incidence study
      • Used to determine the incidence of a particular event in a population during a certain time period (usually a year). If the event in consideration is death, the study is called a mortality study
      • Usually performed as cohort studies in order to compare the incidence of an event (e.g., disease) between two groups
    • Correlation study
      • The unit of analysis is the entire population.
      • Any conclusions that are drawn from the correlation study can only be applied to the entire population and not to an individual.
      • Helps to form hypotheses but cannot be used to test them
      • E.g., a study to look at the correlation between consumption of wine and death due to cardiovascular disease


  • Description: number of new cases [2]
  • Measures
Measures of incidence
Incidence rate Cumulative incidence
  • The number of new cases of a disease per unit of time
  • The proportion of new cases of disease (in an initially disease-free population) over a defined period of time
  • Measures risk of disease
  • Expressed as a proportion
  • In the setting of disease outbreaks, cumulative incidence is referred to as attack rate: the proportion of people who become ill in relation to the total number of people exposed.
  • Number of new cases/person-time units
    • Population at risk: the group of people, healthy or sick, that are at risk of developing the condition being studied
    • Person-time units: record “person-days”, where the period of time an individual is observed is a factor in the unit
  • Number of new cases in a specific time period for a given population at risk


  • Description: number of new and preexisting cases
  • Formula: total number of cases/total population
    • The time period can refer to:
    • For example, if a survey in a town with a population of 120,000 reveals that 451 people have lung cancer, the prevalence of lung cancer in that town would be 451 per 120,000, which would be expressed as 375.8 per 100,000.
  • Relationship between prevalence and incidence
    • Prevalence is usually greater than the incidence in a long-lasting disease, while it usually overlaps for a short-lasting disease: (incidence) x (average duration of disease) = prevalence
    • An increased prevalence of the disease with a stable incidence can be explained by factors that result in increased survival and/or prolonged duration of the disease (e.g., improved quality of care of patients).
    • A decreased prevalence of the disease with a stable incidence can be the result of increased mortality and/or faster healing time.
    • Extensive vaccine administration and/or the removal of risk factors can cause prevalence and incidence to decrease together.
    • If the population is in a steady state, the relationship between incidence rate (IR), prevalence (P), and the average duration of the disease (T) can be described mathematically as:
      • P/(1 - P) = IR × T
      • IR = (P/(1 - P))/T
    • If the disease is extremely rare, P ≈ IR × T
    • Number of new cases per unit time = IR × (population at risk)

Other measures

  • Birth rate: the number of live births within a specific time interval [17]
  • Fertility rate: the rate of live births among women of childbearing age (15–44 years) in a population within a specific time interval
  • Morbidity: the number of individuals in a population with a disease at a specific point in time (i.e., the disease burden in a population)
  • Mortality: the number of deaths in a population within a specific time interval
Overview of other measures of disease frequency
Measure Description Formula
Mortality rate (crude death rate)
  • The total number of deaths in a population within a specific time interval
  • MR = (deaths)/(population) × 100
  • Typically measured for one year and expressed as the number of deaths per 1000 individuals/year.
Case fatality rate (lethality)
  • Percentage of cases (patients with a specific condition) that result in death within a specific time interval
  • CFR = (number of deaths from a specific condition)/(number of cases with the same specific condition) × 100
Proportionate mortality rate
  • Percentage of deaths due to a specific cause within a specific time interval
  • PMR = (number of deaths from a specific cause in a year)/(total deaths from all causes in a year) × 10
Fetal mortality rate
  • Yearly rate of fetal deaths
  • FMR = (number of infant deaths during the first 24 hours after birth)/(total number of live births) × 1,000
Neonatal mortality rate
  • Yearly rate of neonatal deaths
  • NMR = (number of infant deaths during the first 28 days of life)/(total number of live births) × 1,000
Post neonatal mortality rate
  • Yearly rate of post-neonatal deaths (from 28 days up to, but not including, 1 year of age)
  • PNMR = (number of infant deaths between 28 and 365 days of age)/(total number of live births) × 1,000
Infant mortality rate
  • Yearly rate of total infant deaths (from birth to 1 year of age) [17]
  • IMR = (number of infant deaths during the first year after birth)/(total number of live births) × 1,000
Perinatal mortality rate
  • The yearly rate of fetal deaths (stillbirths) and early neonatal deaths [17]
  • PMR = ((number of stillbirths) + (number of infant deaths during the first week after birth))/(total number of births × 1,000
Maternal mortality rate
  • Maternal death is the pregnancy-related death of a woman.
  • The number of maternal deaths per 100,000 live births in the same year.
  • MMR = (maternal deaths)/(live childbirths) × 100,000

Leading causes of death by age in the US [18]


1st 2nd 3rd
< 1 y.o.
  • Congenital anomalies
  • Maternal complications
1–4 y.o.
  • Accident
  • Congenital anomalies
  • Homicide
5–14 y.o.
  • Accident
  • Cancer
15–34 y.o.
  • Accident
  • Homicide
35–44 y.o.
  • Accident
  • Cancer
45–64 y.o.
  • Cancer
  • Accident
65+ y.o.
  • Cancer
  • Chronic respiratory disease

Risk factor

  • Definition: a variable or attribute that increases the probability of developing a disease or injury [19]
  • Calculation: The strength of a given risk factor is typically evaluated using a two-by-two table, which compares the presence/absence of disease with the history of exposure to a risk factor.

No disease

Exposure a b
No exposure c d

Absolute risk [2]

  • Description: the likelihood of an event occurring under specific conditions
    • Commonly expressed as a percentage
    • Approximately equal to the incidence rate
  • Purpose: to measure the probability of an individual in a study population developing an outcome
  • Usage: cohort studies
  • Formula: : Using the variables for disease exposure in the two-by-two table, (number of new cases)/(total individuals in a study group) = (a + c)/(a + b + c + d)

Relative risk (RR; risk ratio) [2][17]

  • Description: : the likelihood of an outcome in one group exposed to a risk factor compared to the risk in another group that has not been exposed
  • Purpose
    • To measure how strongly a risk factor in exposed individuals is associated with an outcome (e.g., death, injury, disease)
    • To help establish disease etiology
  • Usage: cohort studies
  • Formula: (incidence of disease in exposed group)/(incidence of disease in unexposed group) = (a/(a + b))/(c/(c + d))
  • Interpretation
    • RR = 1: Exposure neither increases nor decreases the risk of the defined outcome.
    • RR > 1: Exposure increases the risk of the outcome.
    • RR < 1: Exposure decreases the risk of the outcome.

Attributable risk (AR) [20]

  • Description: the absolute difference between the risk of an outcome occurring in exposed individuals and unexposed individuals
  • Purpose: to measure the excess risk of an outcome that can be attributed to the exposure
  • Usage: used in cohort studies
  • Formulas

Attributable risk percent (ARP) [20]

Odds ratio (OR) [21]

  • Description
    • Comparison of the odds of an event occurring in one group against the odds of an event occurring in another group
    • Odds: the probability of an event occurring divided by the probability of this event not occurring
  • Purpose: to measure the strength of an association between two events (e.g., a risk factor and an outcome)
  • Usage: : case-control studies
  • Formula
    • Calculated using the two-by-two table
    • Odds ratio of exposure
      • Odds of exposure in individuals with disease (i.e. case group) = (exposure in individuals with disease)/(no exposure in individuals with disease) (i.e., a/c)
      • Odds of exposure in individuals without disease (i.e. control group) = (exposure in individuals without disease)/(no exposure in individuals without disease) (i.e., b/d)
      • Odds ratio = (odds of exposure in individuals with disease)/(odds of exposure in individuals without disease) = (a/c)/(b/d) or ad/bc or (a/b)/(c/d)
    • Odds ratio of disease
      • Odds of disease in exposed individuals = (disease in exposed individuals)/(no disease in exposed individuals) (i.e., a/b)
      • Odds of disease in unexposed individuals = (disease in unexposed individuals)/(no disease in unexposed individuals) (i.e., c/d)
      • Odds ratio = (odds of disease in exposed individuals)/(odds of disease in unexposed individuals) = (a/b)/(c/d) or ad/bc or (a/c)/(b/d)
  • Interpretation
    • OR = 1: The event is equally likely in exposed and unexposed individuals.
    • OR > 1: The event is more likely to occur in exposed individuals.
    • OR < 1: The event is less likely to occur in exposed individuals.
  • Rare disease assumption
    • Case-control studies do not track patients over time, so they cannot be used to calculate relative risk.
    • However, the assumption can be made that if an outcome (e.g., disease prevalence) is rare, the incidence of that outcome is low and the OR is approximately the same as the RR.

Relative risk reduction (RRR)

  • Description: : the proportion of risk in the exposure group after an intervention compared to the risk in the nonexposure group
  • Purpose: to determine how much the treatment reduces the risk of negative outcomes
  • Usage: cohort studies and cross-sectional studies
  • Formula: : 1 - RR

Absolute risk reduction (ARR; risk difference)

  • Description: : the difference in risk between the exposure group after an intervention and the risk in the nonexposure group (e.g., risk of death)
  • Purpose: to show the risk without treatment as well as the risk reduction associated with treatment
  • Usage: cohort studies and cross-sectional studies
  • Formula: : (absolute risk in the unexposed group) - (absolute risk in the exposed group) = c/(c + d) – a/(a + b)

Number needed to treat (NNT)

  • Description
    • The number of individuals that must be treated, in a particular time period, for one person to benefit from treatment (i.e., to not develop the disease)
    • Inversely related to the effectiveness of a treatment
  • Purpose: to compare the effectiveness of different treatments
  • Usage: clinical trials
  • Formula: : 1/ARR

Number needed to harm (NNH)

  • Description
    • The number of individuals who need to be exposed to a certain risk factor before one person develops an outcome
    • Directly correlates to the safety of the exposure
  • Purpose: to determine the effectiveness of an intervention
  • Usage: clinical trials
  • Formula: : 1/AR

Number needed to screen (NNS)

  • Description: the number of individuals who need to be screened in a particular time period in order to detect a single case of the disease
  • Formula: same as NNT (1/ARR)

Hazard ratio

  • Description: : the measure of the effect of an intervention on an outcome over a period of time
  • Purpose: to help determine how long it takes for an event to occur
  • Usage: survival analysis
  • Formula
    • Incidence of outcome in exposed group/incidence of outcome in unexposed group = (a/(a + b))/(c/(c + d))
      • HR = 1: no relationship
      • HR > 1: The outcome of interest is more likely to occur in exposed individuals.
      • HR < 1: The outcome of interest is less likely to occur in exposed individuals.

The RR, OR, and hazard ratio are usually displayed with a corresponding p-value. They are considered statistically significant if the p-value is < 0.05.

Bias (systematic error) [22]

  • Definition: an error in the study design or way in which the study is conducted that causes systematic deviation of findings from the true value

Selection bias

  • Description: The individuals in a sample group are not representative of the population from which the sample is drawn because the sampling or the treatment allocation is not random.
  • Types
    • Berkson bias: Individuals in sample groups drawn from a hospital population are more likely to be ill than individuals in the general population.
    • Sampling bias (ascertainment bias)
      • Occurs when certain individuals are more likely to be selected for a study group, resulting in a nonrandomized sample
      • This can lead to incorrect conclusions being drawn about the relationship between exposures and outcomes.
      • Limits generalizability
      • Types of sampling bias
        • Nonresponse bias: Nonresponder characteristics differ significantly from responder characteristics because nonresponders do not return information during a study (e.g., subjects do not return a call).
        • Healthy worker effect: The working population is healthier on average than the general population.
        • Volunteer bias: Individuals who volunteer to participate in a study have different characteristics than the general population.
    • Attrition bias
      • Selective loss of participants to follow up
      • Most commonly seen in prospective studies
      • Risk that the remaining participants differ significantly from those lost to follow up
    • Susceptibility bias: One disease predisposes affected individuals to another disease, and the treatment for the first disease is mistakenly interpreted as a predisposing factor for the second disease.
    • Survival bias
      • Also known as prevalence-incidence bias and Neyman bias
      • When observed subjects have more or less severe manifestations than the standard exposed individual
        • If individuals with severe disease die before the moment of observation, those with less severe disease are more likely to be observed.
        • If individuals with less severe disease have a resolution of their disease before the moment of observation, those with more severe disease are more likely to be observed.
        • Most commonly occurs in case-control and cross-sectional studies.
  • Solutions
    • Randomization
    • Ensure the sample is representative of the population of interest (e.g., in case-control studies).
    • Ensure the correct reference group is chosen for comparison.
    • Collect as much data on the characteristics of the participants as possible.
    • Nonresponder characteristics should not be assumed. Instead, undisclosed characteristics of nonresponders should be recorded as unknown.
    • See “Intention-to-treat analysis” below.

Allocation bias

  • Description: a systematic difference in the way that participants are assigned to treatment and control groups
  • Example: assigning all female patients to one group and all male patients to another group
  • Solution: randomization

Recall bias

  • Description
    • Awareness of a condition by subjects changes their recall of related risk factors (recall a certain exposure)
    • Common in retrospective studies
  • Example: After claims that the MMR vaccine caused autism became public, parents of children diagnosed with autism were more likely to recall the start of autism being soon after their child was vaccinated, as compared with parents of children who were diagnosed with autism prior to these claims becoming public.
  • Solution: reducing time to follow up in retrospective studies (e.g., retrospective cohort studies or case-control studies)

Information bias

  • Description: Incorrect data collection, measurement, or interpretation that leads to misclassification of groups or exposure
    • Information is gathered differently between the treatment and control groups.
    • Insufficient information about exposure and disease frequency among subjects
  • Types of information bias
    • Measurement bias: any systematic error that occurs when measuring the outcome
    • Reporting bias: a distortion of the information from research due to the selective disclosure or suppression of information by the individuals involved in the study
      • Can involve the study, design, analysis, and/or findings
      • Results in underreporting or overreporting of exposure or outcome
    • Interviewer bias: Different interviewing approaches prompt different responses by interviewees, which results in researchers finding differences between groups when there are none.
  • Solution: standardize data collection

Cognitive bias

  • Description: : The personal beliefs of the subjects and/or investigators
  • Types of cognitive bias
    • Response bias: Study participants do not respond truthfully or accurately because of the manner in which questions are phrased (e.g., leading questions) and/or because subjects interpret certain answer options to be more socially acceptable than others.
    • Observer bias (experimenter-expectancy effect or Pygmalion effect): The measurement of a variable or classification of subjects is influenced by the researcher's knowledge or expectations.
    • Confirmation bias: The researcher includes only those results that support their hypothesis and ignores other results.
    • Placebo and nocebo effects: A placebo or nocebo affects subjects' preconceptions/beliefs about the outcome.
  • Solutions
    • Use of a placebo
    • Blinding
    • Prolong the time of observation to monitor long-term effects.

Lead-time bias

  • Description
    • Early detection of disease is misinterpreted as increased survival.
    • Lead time: the average length of time between the detection of a disease and the expected outcome
    • Often discussed in the context of cancer screening
    • Lead-time bias occurs when survival times are chosen as an endpoint of screening tests.
  • Example: The use of a CT scan rather than the conventional x-ray results in earlier detection of a malignant tumor. However, early treatment of this tumor does not improve survival. Therefore, any apparent improvement in 5-year survival rates in patients diagnosed using CT scan in comparison to patients diagnosed using x-rays is the result of lead-time bias.
  • Solutions

Length-time bias

  • Description
    • An apparent improvement in the duration of survival for a terminal disease with a long clinical course (e.g., slow-growing tumor)
    • Often discussed in the context of cancer screening
  • Example: Slow-growing tumors tend to be less aggressive and remain asymptomatic for a longer period, so they are more likely to be identified on screening and are associated with improved survival.
  • Solutions
    • Arrange patients according to the severity of the disease.
    • Use a randomized controlled trial to allocate subjects into control and treatment groups.

Surveillance bias

  • Description
    • An outcome is diagnosed more frequently in a sample group than in the general population because of increased testing and monitoring.
    • Results in misleadingly high incidence and prevalence rates
  • Example: Endometrial cancer is more frequently detected in postmenopausal patients exposed to estrogen therapy than in those not exposed to estrogen therapy. Estrogen therapy increases the risk of bleeding, leading to more frequent screening.
  • Solutions
    • Compare the treatment group to an unexposed control group with a similar likelihood of screening.
    • Select an outcome that is possible in both the exposed and unexposed groups.

Performance bias

  • Description: Researchers provide different levels of attention/care to different groups, or subjects change their responses when they become aware of which group they are allocated to.
  • Examples
    • Hawthorne effect
      • Subjects change their behavior once they are aware that they are being observed.
      • Especially relevant in psychiatric research
      • This type of bias is difficult to eliminate.
    • Procedure bias: When patients or investigators decide on the assignment of treatment and this affects the findings. The investigator may consciously or subconsciously assign particular treatments to specific types of patients (e.g., one group receives a higher quality of treatment).
  • Solution: blinding


  • Definition
    • Any third variable that has not been considered in the study but that correlates with the exposure and the outcome
    • A confounder can be responsible for the observed relationship between the dependent and independent variables.
  • Example: Exposure to coal can cause lung cancer in mine workers. Many miners also smoke cigarettes, which can lead to lung cancer as well.
  • Solutions
    • Perform multiple studies with different populations.
    • Randomization (randomised controlled trials)
    • Crossover study design
    • Restriction (epidemiology)
      • Definition: a study design in which only individuals who meet certain criteria are included in the study sample (e.g., only male individuals with a particular disease are included in a study to avoid the influence of gender on the exposure and outcome)
      • Disadvantages
    • Matching (epidemiology)
      • Definition
      • Disadvantages
        • Does not completely eliminate confounding
        • Can introduce confounding if the effect of the matching factor on disease occurrence cannot be studied anymore
        • Can introduce bias
      • Example: in a study on the relationship between hypertension and end-stage renal disease, obesity is a potential confounder because it is associated with both diseases. By matching through BMI, the group of patients exposed to hypertension and the unexposed group would be matched according to an average BMI.
    • Stratified analysis
    • Standardization of data (see “Z-score” in “Statistical analysis of data.”)

Effect modification

  • Definition: A third variable influences the effect of an exposure on an outcome.
    • Occurs when the exposure has a different effect on the control and treatment groups
    • Not considered a type of bias in itself, but rather a biological phenomenon (i.e., the exposure has a different impact in different circumstances)
  • Example: A certain drug works in children, but does not have any effect on adults.
  • Solution: stratified analysis

Latency period

  • Definition: a seemingly inactive period between the exposure to a risk modifier and when its effect becomes clinically apparent
  • Example: The incubation period for infectious diseases is often very short, while there may be a very long latency period between the pathogenesis and clinical manifestation of malignancy.


Intention-to-treat analysis

  • Description: All patients who initially enrolled in the study, including drop-outs, are included in the analysis of study data.
  • Advantage
    • Allows the investigator or reader of the study to draw accurate conclusions regarding the effectiveness of an intervention
    • Helps to reduce selection bias: Participants who are randomized are included in the analysis and analyzed according to the group they were originally assigned to.
    • Preserves randomization
  • Disadvantages
    • Noncompliance can lead to a conservative estimate of the treatment effect.
    • Heterogeneity might be introduced (e.g., noncompliant, drop-out, and compliant subjects are analyzed together).
    • Susceptible to type II error

Per-protocol analysis [23][24]

  • Definition: Treatment and control groups are compared using data from only those study participants who adhered to the study protocol.
  • Advantages
    • Improves the estimate of the real effect of treatment under optimal conditions
    • Can be used in noninferiority trials, phase 1 trials, and phase 2 trials
  • Disadvantages
    • Loss of randomization (increased selection bias)
    • Overestimates the effects of the tested treatments
    • Possibly a significant reduction in sample size
    • Increases risk of bias
    • Excludes participants that did not adhere to the protocol or were lost to follow up

Stratified analysis

  • Description
    • Stratifying participants into subgroups according to a third variable to eliminate confounding (e.g., by age, gender, race)
    • Evaluation of the association between exposure and disease is performed within each stratum (e.g., crude odds ratio).
    • Crude odds ratio or relative risk, as well as their confidence intervals, are used to measures the strength of the association (how different they are)
    • Eliminates confounding
  • Example: evaluating the association between obesity and cardiovascular disease after stratifying by age

Sensitivity and specificity [25]

  • Every diagnostic test generally involves a trade-off between sensitivity and specificity.
  • Sensitivity and specificity are inversely proportional, meaning that as the sensitivity increases, the specificity decreases, and vice versa.
  • The goal is to maximize both. However, this is dependent on the cut‐off level chosen for a positive diagnosis.
  • Predictive values will also help determine how useful a test is once the test results are known.
Sensitivity (epidemiology) (true positive rate) Specificity (epidemiology) (true negative rate)
  • The proportion of individuals that correctly register as positive in a clinical test designed to identify a disease
  • The proportion of individuals that correctly test negative in a clinical test designed to identify that disease
  • A test with a high sensitivity will yield a low false negative rate.
  • A test with a high sensitivity (i.e., few false negatives) but low specificity for a disease with low prevalence will yield a high false positive rate.
  • Can be used for screening purposes
  • High sensitivity is usually achieved at the expense of specificity.
  • If a highly sensitive test yields a negative result, the disease can be ruled out.

A highly sensitive test can rule out a disease if negative, and a highly specific test can rule in the disease if positive.

Predictive values [26]

Pre-test probability

Positive predictive value (PPV)

  • Description: the proportion of individuals who test positive for a disease that actually have that disease
  • Features
  • Formula

Negative predictive value (NPV)

Likelihood ratio

Cutoff values [27]

  • Definition: dividing points on measuring scales where the test results are divided into different categories
    • Positive: has the condition of interest
    • Negative: does not have the condition of interest
  • Features
    • Sensitivity, specificity, PPVs, and NPVs vary according to the criterion and/or the cutoff values of the data.
    • In an ROC curve, for example, the sensitivity is plotted against specificity for different cutoff values. Ideally, the cutoff point is on a curve in the upper left corner, where sensitivity and specificity are 100%.
  • Interpretation: What happens when a cutoff value is raised or lowered depends on whether the test in question requires a high value (e.g., tumor marker for cancer, lipase for pancreatitis) or a low value (e.g., hyponatremia, agranulocytosis).
    • Lowering or raising a cutoff value for a high value test:
      • Decreased cutoff value (i.e., broadening the inclusion criteria): lower specificity, higher sensitivity, lower PPV, higher NPV
      • Increased cutoff value (i.e., narrowing the inclusion criteria): higher specificity, lower sensitivity, higher PPV, lower NPV
    • Lowering or raising a cutoff value for a low value test:
      • Decreased cutoff value (i.e., narrowed inclusion criteria): higher specificity, lower sensitivity, higher PPV (decrease in false positives > decrease in true positives), lower NPV (increase in false negatives > increase in true negatives)
      • Increased cutoff value (i.e., broadened inclusion criteria): lower specificity, higher sensitivity, lower PPV (increase in true positives > increase in false positives), higher NPV (decrease in false negatives > decrease in true negatives)

Unlike sensitivity and specificity, which are determined solely by the diagnostic test itself, predictive values are also influenced by disease prevalence.

Verifying the presence or absence of a disease

  • Screening test
  • Confirmatory test
    • Confirms disease in individuals with signs or symptoms of the disease (e.g., biopsy for breast cancer or cervical cancer)
    • Usually performed after a screening test to confirm a diagnosis
    • Should have a high specificity

Receiving operating characteristic curve (ROC curve) [28][29]

  • Description: a graph that compares the sensitivity and specificity of a diagnostic test
  • Features
    • Shows the trade-off between clinical sensitivity and specificity for every possible cutoff value, to evaluate the ability of the test to correctly diagnose subjects
    • The y-axis represents the sensitivity (i.e., true positive rate) and the x-axis corresponds to 1 - specificity (i.e., the false positive rate).
      • A test is considered more accurate the more the curve follows the y-axis.
      • A test is considered less accurate if the curve is closer to the diagonal.
    • The area under the curve also allows the usefulness of tests to be compared: The larger the area under the ROC curve, the higher the validity of the test.

Two-by-two table

  • Definition: a type of contingency table that displays the frequency of two categorical variables, often exposure and outcome
Fetaures of a two-by-two table
Disease No disease Interpretation
Positive test result
  • True positive (TP)
  • False positive (FP)
  • All subjects with positive test results (TP + FP)
  • PPV = TP/(TP + FP)
Negative test result
  • False negative (FN)
  • True negative (TN)
  • All subjects with negative test results (FN + TN)
  • NPV = TN/(FN + TN)
  • Example [29]

Diagnostic test for tuberculosis (TB)
Patients with TB Patients without TB Total
Positive test result 800 (TP) 400 (FP) 1200
Negative test result 200 (FN) 3600 (TN) 3800
Total 1000 (TP + FN) 4000 (FP + TN) 5000