 Clinical science
Epidemiology
Summary
Classical epidemiology is the study of the distribution and determinants of disease in populations. Clinical epidemiology applies the principles of epidemiology to improve the prevention, detection, and treatment of disease in patients. Descriptive epidemiological studies investigate individual characteristics, places, and/or the time of events in relation to an outcome. They may take the form of case reports, case series, or ecological studies. Analytical epidemiological studies seek to determine the influence of an exposure on an outcome and can be further divided into experimental (e.g., randomized control studies) and observational (e.g., cohort or casecontrol studies) types. There are a number of factors that influence the amount of clinical evidence epidemiological studies contribute. Conclusions drawn from these studies can be made more reliable by limiting bias, confounding, and effect modification.
In epidemiological studies, the strength of the relationship between two events is measured using ratios, rates, and proportion tests. This relationship can be presented in the form of a twobytwo table, which helps to visualize the number of false positive and true positive diagnostic test results, as well as the number of patients who actually have the disease and those who do not (tested with a gold standard test). A diagnostic test is considered precise if the results it yields are reproducible under similar conditions (reliable) and if it measures what it was developed to measure (valid). The higher a test's reliability and validity, the lower the amount of random errors it will generate.
Also see statistical analysis of data.
Introduction to epidemiology
 Classical epidemiology: the study of determinants and distribution of disease in populations
 Clinical epidemiology: the study and application of principles of epidemiology to improve the prevention, detection, and treatment of disease in patients

Population (epidemiology): the total number of people or inhabitants in a country or region from which a sample is drawn for statistical measurement

Population pyramid: a way of illustrating the age and sex distribution of a specific 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 greater percentage of young people (i.e., youthful population); high birth rates and low life expectancy
 Constrictive pyramid: represents a population in which there is a greater percentage of elderly people; low birth and death rates

Population pyramid: a way of illustrating the age and sex distribution of a specific population
 Data (epidemiology): factual information, collected during observation and/or experimentation, that is used as a basis for analysis and discussion
 Sample (epidemiology): a small group of people that are representative of a population
 Control group: A group in a study that does not receive the intervention (e.g., a drug) or did not develop the outcome (e.g., a disease), which is recruited from the same source population as the study group. It is matched for baseline characteristics with the study population to reduce confounding factors.
Definition  Time  Area  Examples  Possible factors  

Endemic  A disease that affects individuals at a relatively constant and expected rate within a specific population/region  Unlimited  Limited 


Epidemic  A disease that affects individuals at an unusually fast or unexpected rate within a specific population/region  Limited  Limited 
 
Pandemic  Worldwide epidemic  Limited  Unlimited 


References: ^{[1]}^{[2]}^{[3]}
Epidemiological studies
Principles of study design
 Study designs should be tailored to the question that needs to be answered.
 A good study design with high levels of evidence increases the strength of conclusions drawn from the results.
Types of epidemiological studies
Description  Example  

Descriptive studies 
 
Analytical studies 


Interpretation
 Epidemiological studies suggest relationships between two events (e.g., exposure and disease).
 This comparison can be measured using rates, proportions, and/or ratios.
 Ratios: comparison of two related or unrelated values
 Proportion: comparison of one part of the population to the whole

Rates: measure of the frequency of an event in a population over a specific period of time
 Crude: rates that apply to the entire population (do not take specific characteristics into account)
 Specific: rates that apply to a population group with specific characteristics taken into account (e.g., sexspecific, agespecific)
 Standardized (adjusted rates): crude rates that have been adjusted to consider specific population characteristics to allow for comparison (e.g., usually used in death rates)
 These measures determine the strength of association between two events and allow us to describe population characteristics (e.g., detect populations at risk) and quantify morbidity/mortality.
 Furthermore, researchers can eventually develop hypotheses about why these groups are at risk.
References: ^{[1]}^{[2]}^{[3]}
Descriptive studies
Case report
 Description: a report of a disease presentation, treatment, and outcome in a single subject or event
 Example: report of a single case of cervical cancer in a 25yearold female subject
Case series report
 Description: a report of a disease course/response to treatment compiled by aggregating several similar patient cases
 Example: collecting and reporting several cases of pericarditis at a local hospital
Ecological study
 Aim: to identify an exposure associated with an outcome (e.g., disease), especially if the outcome is rare
 Study method: assesses aggregated data where at least one variable (e.g., an outcome) is at a population level and not an individual level
 Example: 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)
References: ^{[1]}^{[2]}^{[3]}
Analytical studies
Experimental studies
Randomized controlled trials (RCT; interventional studies)
 Aim: determines the possible effect of a specific intervention on a population of interest
 Study method: patients are randomly allocated as either treatment or control subjects , after which they are monitored and evaluated for the outcome of interest

Special variants

Blinding: the practice of not informing an individual or group about which individuals are a control or treatment candidate; used to minimize bias
 Singleblind study: Only researchers know who is a control or treatment candidate.
 Doubleblind study: Neither the researcher nor the study participants know who is a control or treatment candidate.
 Tripleblind study: The researcher, the study participants, and the person who analyzes the data do not know who is a control or treatment candidate.

Cluster randomized controlled trials
 Different participants are grouped together into clusters and then randomly assigned to the control or intervention groups.
 A cluster RCT is easier to perform than a classical RCT but may have less validity than a classical RCT.

Blinding: the practice of not informing an individual or group about which individuals are a control or treatment candidate; used to minimize bias
Field trials
 Aim: determines the effect of diseasepreventing 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
Clinical drug trials
 Definition: studies involving human subjects to assess new health interventions to provide safe and effective medical care
 Compares the benefits of a single treatment vs. a placebo or between 2 or more drugs
Study population  Research aim  

Preclinical studies  Animals  Determine the effect, dose, and side effects (teratogenic/carcinogenic potential) of the drug 
Phase 0  Small number of healthy individuals  Test subtherapeutic doses of a new drug to determine preliminary pharmacokinetic and/or pharmacodynamic properties of the drug 
Phase I  Small number of healthy individuals  Determine the side effects, toxicity, pharmacokinetics, and pharmacodynamics of the drug 
Phase II  Small number of patients with a specific disease  Determine the efficacy, effective dosing, and side effects of the drug 
Phase III  Randomized control trial with a large number of patients with a specific disease  Compare the new drug with current treatment options or placebo 
Phase IV  Large number of patients with a specific disease after drug approval  Ascertain the effects of longterm therapy and effects on special patient groups (e.g., patients with chronic renal failure); can lead to withdrawal of a drug from the market 
Clinical drug trials assess adverse event rates and drug interactions. They can be used to develop warnings and precautions as well as contraindications for the use of a drug. For example, if the rate of hyperglycemia is significantly higher in the treatment group compared to the control group, it may not be appropriate for use in patients with diabetes mellitus.
Factorial study
 Aim: to test the effect and interactions of two or more factors (e.g., treatments)
 Study method: Individuals are randomly assigned to groups receiving different doses and combinations of drugs.
 Example: In order to study 5 dose levels of a drug X and 2 dose levels of drug Y, 10 different intervention combinations should be examined.
Crossover study
 Aim: to obtain a more efficient comparison of treatments with fewer patients
 Study method: each patient switches from one treatment to another during the trial period and serves as their own control
 Example: Each patient receives both drug X and drug Y or a placebo, but at different time periods during the study.
Observational studies
Crosssectional study (prevalence study)
 Aim: to determine the prevalence of exposure and disease
 Study method: the prevalence of disease and other variables (e.g., risk factors ) are measured simultaneously at a particular point in time (i.e., a snapshot of the population)
 Example: investigating the number of patients with both coronary heart disease as well as hypertension in the year 1998
Casecontrol study
 Aim: to study if an exposure is associated with an outcome (e.g., disease)

Study method
 Researchers begin by selecting patients with the disease (cases) and without the disease (controls) with matching baseline characteristics from the same source population.
 The observer compares the presence of risk factors between these two groups.
 The odds ratio is then determined between these groups.
 Example: determining the link between cervical cancer and human papillomavirus (HPV) exposure by comparing otherwise similar (e.g., same age) patients with and without histologically confirmed cervical cancer
Cohort study
 Aim: to study the incidence rate and whether the exposure is associated with the outcome of interest (e.g., a disease)

Study method and examples

Retrospective cohort study
 The protocol is established and the study begins after the groups develop an outcome of interest.
 The data from a group of individuals who have the outcome selected (e.g., lung cancer) is retrospectively analyzed to identify what proportion has been exposed to a risk factor and what proportion has not.
 Example: a study that aims to identify what proportion of individuals with lung cancer (i.e., the outcome) smoked ≥ 1 pack of cigarettes a day (i.e., the risk factor) in the past 5 years

Prospective cohort study
 The protocol is established and study begins before the groups develop an outcome of interest.
 Starts with individuals who are either exposed or not exposed to a particular risk factor (e.g., smoking)
 These two groups are then followed for a period of time to see if the disease of interest (e.g, lung cancer) develops.
 Example: a study that aims to identify what proportion of individuals who currently smoke ≥ 1 pack of cigarettes a day (i.e, the risk factor) develop lung cancer (i.e., the outcome) over a period of 5 years

Retrospective cohort study
Twin concordance study
 Aim: determines the inheritability of disease vs. environmental risk factors
 Study method: comparing the frequency of disease in twins (monozygotic or dizygotic)
 Example: twins are followed over a 30year period, following the diagnosis of Hodgkin disease in the first twin, to see if the frequency of cancer differed between monozygotic and dizygotic twins
Adoption study
 Aim: determines the inheritability of disease vs. environmental risk factors
 Study method: comparing the frequency of disease in adopted children vs. children who live with their biological parents
 Example: the prevalence of schizophrenia in adopted children and the prevalence of schizophrenia in children who live with their biological parents is compared to determine the influence of genetic and environmental factors on schizophrenia
Randomized controlled trials are considered the gold standard for clinical trials!
A casecontrol study compares a small population group over a short period of time (less costintensive) and determines how multiple exposures lead to one outcome; a cohort study compares a large population over a long period of time (more costintensive) and determines how one exposure leads to multiple outcomes!
In cohort studies, researchers select individuals based on exposure first and then determine if these individuals develop a disease. This is in contrast to casecontrol studies, in which patients with disease (cases) and those without disease (controls) are selected first to determine if they were exposed or not!
References: ^{[1]}^{[2]}^{[3]}
Other types of studies
Survival analysis (prognosis study)
 Survival analysis is used to measure disease prognosis.

Survival analysis is always prospective in nature:
 Timetoevent analysis: Individual follow‑ups are done after the onset of a disease until a chosen endpoint (e.g., death, development of a particular complication) occurs or exposure to a risk factor to onset of disease.
 Fiveyear survival rate: the percentage of patients with a particular disease who have survived for 5 years after the initial diagnosis
 Pitfalls of survival analysis
 No prediction can be made about the average duration of survival in the case of subjects who did not die within the period of observation. (These subjects are called “censored cases”.)
 Patients may drop out or die before the end of the followup period.

KaplanMeier analysis
 Allows survival analysis to be displayed graphically
 Overcomes problems associated with regular survival analysis
 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 even to be estimated when individuals are studied over different time intervals
 The horizontal axis represents the time of followup
 The vertical axis represents the estimated probability of survival (time intervals, called KaplanMeier estimators, that are defined by a specific event)
Metaanalysis
 Data from multiple studies is systematically assessed and processed with statistical methods
 Aims to increase statistical power and to identify differences between and/or common effects in individual studies (more precise results)
 Limiting factors depend on the individual study types; a metaanalysis is only as good as the individual studies used.
Registry study

Brief description: a retrospective study that uses data obtained from disease registries (e.g., cancer registries)
 Criteria for a good quality cancer registry:
 Complete entries
 Low percentage of cases with a DCO (death certificate only)
 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 of descriptive studies:

Incidence study
 Incidence studies are 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.
 Incidence studies are 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.
 Correlation studies help form hypotheses but cannot be used to test them!
 E.g.: a study to look at correlation between consumption of wine and death due to cardiovascular disease.

Incidence study
References: ^{[1]}^{[2]}^{[3]}
Measures of disease frequency
Morbidity, incidence, and prevalence
 Morbidity: the disease burden in a population

Incidence rate
 Description: the number of new cases of disease per unit of time
 Formula: number of new cases/persontime units

Prevalence

Description
 The ratio of all people with a disease to the total number of people in a population at a particular point in time
 Corresponds to disease frequency
 An increased prevalence of disease with a stable incidence can be explained by factors that result in increased survival and prolonged duration of the disease (e.g., improved quality of care of patients)
 Formula: total number of cases/total population at a given point in time

Description

Relationship between prevalence and incidence

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/(1P) = IR × T
OR  IR = (P / (1P)) ÷ T

P/(1P) = IR × T
 If the disease is extremely rare, P ≈ IR × T
 The number of new cases per unit time can be given by the formula: IR × population at risk (population without the disease)

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

Cumulative incidence

Description
 The proportion of new cases of disease (in an initially diseasefree population) over a defined period of time
 The term attack rate, a synonym of cumulative incidence, is usually used during a disease outbreak.
 Formula: number of new cases in a given time period/population at risk in the same time interval

Description
Prevalence is usually greater than the incidence of a longlasting disease: incidence * average duration of disease = prevalence
Birth, fertility, and mortality
 Birth rate: the number of live births during a specific time interval
 Fertility rate: rate of live births among women of childbearing age (15–44 years) in a population during a specific time interval

Mortality: the occurrence of death in a population
 Mortality rate (crude death rate): The total mortality rate from all causes of death for a population in a specific time period (MR = (deaths/population) * 100)

Case fatality rate (lethality): percentage of cases (patients with a specific condition) that result in death within a specific time period
 Case fatality rate = (number of deaths from a specific condition/number of cases with the same specific condition) * 100
Measure  Description  Formula 

Mortality rate (crude death rate) 


Fetal mortality rate 
 
Neonatal mortality rate 


Post neonatal mortality rate 


Infant mortality rate  
Perinatal mortality rate 


Maternal mortality rate 


Case fatality rate (lethality) 


Proportionate mortality rate 


Leading causes of death by age in the US
Leading cause of death by age  1^{st}  2^{nd}  3^{rd} 

< 1 yr  Congenital anomalies  Preterm birth  SIDS 
1–4 yr  Accident  Congenital anomalies  Homicide 
5–14 yr  Accident  Cancer  Suicide 
15–34 yr  Accident  Suicide  Homicide 
35–44 yr  Accident  Cancer  Heart disease 
45–64 yr  Cancer  Heart disease  Accident 
65+ yr  Heart disease  Cancer  Chronic respiratory disease 
References: ^{[1]}^{[2]}^{[3]}
Measures of risk
 Risk factors: variables or attributes that increase the probability of developing a disease or injury
 Types of risk factors are typically calculated with the help of a twobytwo table which compares two variables: presence/absence of disease and history of exposure to a risk factor
 a = disease in those exposed
 b = no disease in those exposed
 c = disease in those unexposed
 d = no disease in those unexposed
Disease  No disease  

Exposure  a  b 
No exposure  c  d 
Absolute risk
 ∼ Incidence rate
 Measures the probability of acquiring disease/injury in a given study population
 Used in cohort studies
 Formula: (number of new cases) / (total individuals at risk of developing disease) = (a + c)/(a + b + c + d)
Relative risk (RR; risk ratio)
 The risk of an outcome (e.g., disease) among one group compared to the risk among another group
 Measures how strongly a risk factor (e.g., death/injury/disease) in exposed individuals is associated with an outcome
 Used in cohort studies
 Considered statistically significant if the corresponding pvalue is < 0.05
 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 or decreases the risk of reaching the defined outcome.
 RR > 1: Exposure increases the risk of reaching the outcome.
 RR < 1: Exposure decreases the risk of reaching the outcome.
Attributable risk (AR)
 The proportion of cases in exposed individuals that can be attributed to the exposure
 Used in cohort studies

Formula
 Population AR: (incidence rate entire study population)  (incidence rate in unexposed group) = ((a + c)/(a + b + c + d))  (c/(c + d))
 Exposure AR: (incidence rate in exposed group)  (incidence rate in unexposed group) = a/(a + b)  c/(c + d)
Attributable risk percent (ARP)
 The percentage of incidence of disease among exposed individuals that can be attributed to the exposure

Formula
 ARP = (RR  1)/RR
 Alternatively, ARP = AR/(incidence of disease in exposed group) * 100
Odds ratio (OR)
 The odds ratio is a measure of the odds of an individual developing a disease on exposure to a risk factor.
 Compares the odds of a disease/injury occurring in those exposed to a risk factor against the odds of the disease/injury occurring in those not exposed to the same risk factor
 Odds: the probability of a disease/event occurring divided by the probability of this disease/event not occurring

Formula: calculated using the 2x2 table (see above)
 Odds ratio = odds of disease in those exposed/odds of disease in those unexposed
 OR = (a/c) / (b/d); or ad/bc

Interpretation
 OR = 1 means the event is equally likely in both groups.
 OR > 1 means the event is more likely to occur in the group exposed to the risk factor.
 OR < 1 means the event is less likely to occur in the group exposed to the risk factor.
 Used in casecontrol studies to measures the strength of the association between a risk factor and a disease/injury

Rare disease assumption
 Since case control studies do not track patients over time, relative risk cannot be calculated.
 However, the assumption can be made that if an outcome is rare (e.g., the prevalence of a disease), the incidence of that outcome is low, and the odds ratio (OR) approximates the relative risk (RR).
Relative risk reduction (RRR)
 The proportion of decreased risk due to an intervention compared to the control group
 Formula: 1  RR
Absolute risk reduction (ARR; risk difference)
 The difference in risk as a result of exposure compared to nonexposure (e.g., risk of death)
 Formula: absolute risk in unexposed (control) group minus absolute risk in exposed (case) group = (c/(c + d)) – (a/(a + b))
Number needed to treat (NNT)
 The number of individuals that must be treated, in a particular time period, for one person to benefit from treatment (i.e., not develop disease/injury)
 Formula: 1/absolute risk reduction (ARR)
Number needed to harm (NNH)
 The number of individuals who need to be exposed to a certain risk factor before one person develops disease/injury
 Formula: 1/attributable risk (AR)
Number needed to screen (NNS)
 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: 1/absolute risk reduction
Hazard ratio
 The measure of an effect of an intervention on an outcome (death/cure) over a period of time
 Used in 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 event (the outcome of interest e.g., death, cure) is more likely to occur in the exposed group
 HR < 1: the event is less likely to occur in the exposed group
 (Incidence of outcome in exposed group)/ (incidence of outcome in unexposed group) = (a/(a + b))/(c/(c + d))
Doseresponse relationship (epidemiology)
 One of the criteria required to establish causality in epidemiological studies
 The other criteria for causality include:
 Consistency (e.g., consistent results between different studies)
 Strong correlation (e.g., a high relative risk)
 Temporality (e.g., the exposure precedes the outcome)
 Experimental evidence (e.g., includes both human and animal studies)
 Biologic plausibility (e.g., a suitable theory: lung cancer can be caused by cigarette smoking, but not by drinking water)
 Biologic coherence (e.g., the suspected causality is fitting with the natural history of the disease)
 Specificity
 Analogy
 Refers to the presence of a doseresponse curve (e.g., the presence of disease increases/decreases in direct proportion with the level of exposure)
 A causal doseresponse relationship assumes that the greater the exposure, the greater the risk of disease
 Can be influenced by confounding
The relative risk, odds ratio, and hazard ratio are usually displayed with a corresponding pvalue. Per convention, they are considered statistically significant, if the related pvalue is < 0.05!
References: ^{[1]}^{[2]}^{[3]}
Bias, confounding, effect modification, and latent period
Bias
 Definition: an error in the study design or way in which it is conducted that causes systematic deviation of findings from the truth
Types of bias  

Bias  Problem  Example  Solution 
Selection bias 



Allocation bias 

 
Recall bias 



Information bias 



Cognitive bias 



Leadtime bias 



Lengthtime bias 



Surveillance bias 



Confounding
 Definition: any third variable that has not been considered in the study but that correlates with the exposure and the outcome
 Example: A confounder can be responsible for the observed relationship between the dependent and independent variables. For instance, while exposure to coal can result in lung cancer in individuals at a mining company, many miners smoke cigarettes, which acts as a third variable that can lead to lung cancer.

Solution
 Perform multiple studies with different populations.
 Randomization
 Crossover study

Restriction (epidemiology)
 The researcher only studies a part of the population that meet certain criteria (e.g., only males with a particular disease are included in a study to avoid the influence of gender on exposure and outcome)
 Problems
 Limits generalizability
 Makes obtaining a large sample group difficult

Matching (epidemiology)
 Commonly used in casecontrol studies
 Cases and controls are grouped into pairs with similar attributes to avoid confounding
 Problems
 Matching; does not completely eliminate confounding
 Can introduce confounding if the investigators match by factors that are not matched in the source population
 Can introduce bias
 Standardization of data (see Zscore)

Stratified analysis
 Study groups are divided into subgroups according to the third variable.
 Measures of association (e.g., the odds ratio) can be calculated for each subgroup (e.g., stratumspecific odds ratios)

In confounding:
 Stratifying participants into subgroups according to the third variable will eliminate the confounder
 The measures of association between subgroups will be similar, but the stratified measure of association is different from the whole population measure of association (e.g., crude odds ratio)

In effect modification:
 Stratifying participants into subgroups according to the third variable will result in a stronger relationship in one subgroup
 The measures of association will differ between subgroups (i.e., there is a strong association in the subgroup in which the effect modifier is present, while there is no association in the subgroup in which the effect modifier is absent)
Effect modification
 Definition: a third variable that positively or negatively influences a study outcome; occurs when the exposure has a different effect between groups; not considered a type of bias in itself
 Example: a certain drug works in children but does not have any effect on adults

Solution: stratified analysis
 Effect modification can be differentiated from confounding by performing a stratified analysis: When the population is stratified according to a factor, different results will be seen if it is a confounder or if it is an effect modifier.
Latency period
 Definition: A seemingly inactive period between the exposure to a risk modifier to the time its effect becoming clinically apparent
 Example: : The incubation period for infectious diseases is often very short, while there may be a very long latency period between pathogenesis of a malignancy and clinical manifestation.
References:^{[4]}
Evidencebased medicine
Levels of evidence
Level  Source of evidence  

I  Ia  Evidence from a metaanalysis of many randomized controlled studies 
Ib  Evidence from at least one highquality randomized controlled study  
II  IIa  Evidence from at least one highquality, nonrandomized controlled study 
IIb  Evidence from a quasiexperimental study or a cohort study  
III  Evidence from a descriptive study  
IV  Expert opinions, case reports, and other forms of anecdotal evidence 
Grades of clinical recommendation (according to EvidenceBased Medicine (EBM) guidelines)
Grade  Level of recommendation  Type of study 

A  Very high 

B  High 

C  Low 

D  Very low 

References: ^{[1]}^{[2]}^{[3]}
Evaluation of diagnostic tests
Sensitivity and specificity

Sensitivity (epidemiology) (true positive rate)
 The proportion of individuals that correctly register as positive in a clinical test designed to identify a 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
 See twobytwo table below for the formula.

Specificity (true negative rate)
 The proportion of individuals without a disease that correctly test negative in a clinical test designed to identify that disease: i.e., true negative results divided by total true negative and false positive results (typically expressed as a percentage)
 A highly specific test will yield a low false positive rate
 Can be used to confirm the diagnosis following a positive screening test
 See twobytwo table below for the formula.
Predictive values

Positive predictive value (PPV)

The proportion of individuals who test positive for a disease that actually have that disease
 On the other hand, the probability that an individual who tested positive actually does not have the disease is calculated as follows: 1 positive predictive value
 The positive predictive value increases with increasing prevalence of disease in the population.
 See twobytwo table below for the formula.

The proportion of individuals who test positive for a disease that actually have that disease

Negative predictive value (NPV)

The probability that an individual who tested negative is actually diseasefree
 On the other hand, the probability that an individual who tested negative actually has the disease is calculated as follows: 1  negative predictive value
 The negative predictive value decreases with increasing prevalence of the disease in the population.
 See twobytwo table below for the formula.

The probability that an individual who tested negative is actually diseasefree

Likelihood ratio
 Determines the utility of a diagnostic test in clinical practice; likelihood ratio is not influenced by disease prevalence

Reflects how much more likely the disease is in a person with a positive (positive likelihood ratio) or negative (negative likelihood ratio) test result compared to the pretest probability.
 If the likelihood ratio is > 1, then it is associated with the disease.
 If the ratio is < 1, then it is associated with absence of the disease.
 If the likelihood ratio is 1, then the posttest probability is similar to the pretest probability, and therefore the test has poor clinical utility.

Positive likelihood ratio
 Ratio of the sensitivity rate (true positive rate) to the false positive rate
 Sensitivity/(1  specificity)

Negative likelihood ratio
 Ratio between the false negative rate and the specificity (true negative rate)
 (1sensitivity)/specificity

Pretest probability
 The probability that a patient with a particular manifestation has a specific disease before the result of the diagnostic test is known
 The pretest probability of a disease is reflected by its prevalence in a particular region

Negative and positive predictive values depend on the test subject's pretest probability of disease (unlike sensitivity and specificity)
 A higher pretest probability will decrease the NPV and increase the PPV of a test
 A lower pretest probability will increase the NPV and decrease the PPV of a test

Cutoff values
 Every diagnostic test involves a tradeoff between sensitivity and specificity.
 In a ROC curve, for example, the sensitivity is plotted against specificity for different cutoff values and ideally, the cutoff point is on a curve in the upper left corner, where sensitivity and specificity are 100%
 Sensitivity, specificity, positive predictive values, and negative predictive values vary according to the criterion or cutoff values of data

What happens when a cutoff value is raised or lowered depends on whether a diagnostic test 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
 ↓ cutoff value (i.e., broadening the inclusion criteria): lower specificity, higher sensitivity, lower positive predictive value, higher negative predictive value
 ↑ cutoff value (i.e., narrowing the inclusion criteria): higher specificity, lower sensitivity, higher positive predictive value, lower negative predictive value

Lowering or raising a cutoff value for a low value test (causes opposite results)
 ↓ cutoff value (i.e., narrowing the inclusion criteria): higher specificity, lower sensitivity, higher positive predictive value (decrease in false positive > decrease in true positives), lower negative predictive value (increase in false negatives > increase in true negatives)
 ↑ cutoff value (i.e., broadening the inclusion criteria): lower specificity, higher sensitivity, lower positive predictive value (increase in true positives > increase in false positives), higher negative predictive value (decrease in false negatives > decrease in true negatives)

Lowering or raising a cutoff value for a high value test
Unlike sensitivity and specificity, which rely solely on the diagnostic test itself, predictive values are also influenced by disease prevalence!
Verifying the presence or absence of a disease

Screening test

Used to identify disease in asymptomatic individuals.
 E.g., mammogram for breast cancer or a Pap smear for cervical cancer
 Should have a high sensitivity

Used to identify disease in asymptomatic individuals.

Confirmatory test

Confirms disease in individuals with signs or symptoms of 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

Confirms disease in individuals with signs or symptoms of disease
Receiving operating characteristic curve (ROC curve)
 A graph that compares the sensitivity and specificity of a diagnostic test
 Used to show the tradeoff between clinical sensitivity and specificity for every possible cutoff value to evaluate the ability of the test to adequately diagnose subjects (e.g., diseased vs. nondiseased)

The yaxis represents the sensitivity (i.e., true positive rate) and the xaxis corresponds to 1  specificity (i.e., false positive rate).
 A test is considered more accurate if the curve follows the yaxis.
 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.
Twobytwo table
 Definition: a type of contingency table that displays the frequency of two categorical variables, often exposure and outcome of disease
Disease  No disease  Total  Interpretation  

Positive test result 
 
Negative test result 
 
Total  
Interpretation 


Example of a twobytwo table
Diagnostic test for tuberculosis (TB)
(The table below is an annotated 2x2 table, with additional columns detailing total amounts and their interpretation.)
Patients with TB  Patients without TB  Total  

Positive test result  800 (true positive) = TP  400 (false positive) = FP  1200 
Negative test result  200 (false negative) = FN  3600 (true negative) = TN  3800 
Total  1000 (TP + FN)  4000 (FP + TN)  5000 

Sensitivity (true positive rate) = TP/(TP + FN)
 800/(800 + 200) = 80%

Specificity (true negative rate) = TN/(FP + TN)
 3600/(400 + 3600) = 90%

False positive rate = FP/(FP + TN)
 400/(400 + 3600) = 10%

False negative rate = FN/(TP + FN)
 200/(800 + 200) = 20%

Positive predictive value= TP/(TP + FP)
 800/(800 + 400) = 66.6̅. %
References:^{[5]}
Random error, precision, and validity
Random error
 Definition: an error that occurs due to chance and/or precision limitations of a test
 Can be reduced by repeated measurements and averaging over a large number of observations
Precision (reliability)
 Definition: the reproducibility of test results on the same sample under similar conditions
 A test with a high precision will have minimal random error.
 Precision improves with a ↓ standard deviation and ↑ power of a statistical test.
 Precision is measured quantitatively with a reliability coefficient between 0 and 1.
 Reliability coefficient = 1 → the variance of the sample mean is equal to the variance of the true measure → the study/test is highly reliable
 If the variance of the sample is very large as a result of an error in measurement, the value of the reliability coefficient will approach 0.
 Methods of estimating precision:
 Interrater reliability: the test yields similar results when performed by different examiners.
 Paralleltest reliability: the reliability of a new test is compared with an established test. The new test determines the reliability of a test in comparison to another test, the reliability of which has already been established. Similar statistical results imply a similar degree of reliability.
 Testretest reliability: the test yields the same results when repeated on the same subjects.
Validity (accuracy)
 Definition: the correspondence between test measurements/results and what the test was developed to measure
 A test with high validity (accuracy) will have minimal systematic error and bias.
 Sensitivity and specificity are measures of validity (i.e., a highly valid test is highly specific and sensitive).
 There are two forms of validity:

Internal validity
 The extent to which a study is free of error (most often in the form of bias) and the results therefore true for the sample of individuals being studied

High internal validity can be achieved by:
 Matching study groups according to age, sex, and other characteristics
 Observing measures to reduce systemic errors (bias) to a minimum

External validity
 Refers to whether study results can be extrapolated from a sample population to the general population (generalizability).
 A study with high external validity has the following characteristics:
 The study results can be reproduced in sample groups
 High internal validity

Internal validity
References: ^{}