Interpreting medical evidence

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Critical appraisal and evidence-based medicine involve the practical application of clinical epidemiology concepts in order to guide clinical decision-making. This requires an evaluation of the quality and applicability of existing research studies to individual clinical scenarios. Appropriate interpretation of the results of a research study in the right context requires a basic understanding of the following foundational concepts (found in the “Epidemiology” article): types of epidemiological studies (e.g., observational studies, experimental studies), common study designs (e.g., case series, cohort studies, case-control studies, randomized controlled trials), causal relationships in research studies, and other reasons for observed associations (e.g., random errors, systematic errors, confounding). This article focuses on an approach to critical appraisal, and epidemiological concepts often encountered in studies of clinical interventions, i.e., measures of association (e.g., relative risk, odds ratios, absolute risk reduction, number needed to treat), measures used to evaluate screening and diagnostic test (e.g., sensitivity, specificity, positive predictive value, negative predictive value), precision, and validity.

The following concepts are discussed separately: measures of disease frequency (e.g., incidence rates, prevalence) commonly used in studies of population health, foundational statistical concepts (e.g., measures of central tendency, measures of dispersion, normal distribution, confidence intervals), and guidance on conducting research projects.

See also “Epidemiology,” “Statistical analysis of data,” and “Population health.”

Evidence-based medicine ^[2]

• Definition: The practice of medicine in which the physician uses clinical decision-making methods based on the best available current research from peer-reviewed clinical and epidemiological studies with the aim of producing the most favorable outcome for the patient.
• Application in clinical practice
  • Define the patient's clinical problem (can be formulated as a PICO question).
  • Search for sources of information about the clinical problem.
  • Perform a critical appraisal of relevant research studies.
  • Apply the information
    • Before discussing the research findings with the patient, consider how and to which extent the researched options can improve patient care.
    • Present comprehensive, but synthesized evidence to the patient using clear and understandable language.
  • Engaged in shared decision-making, considering individual patient's risk profile and preferences.

Levels of evidence ^[3][4]

• Definition: a method used in evidence-based medicine to determine the strength of the findings from a clinical and/or epidemiological study
• Methods: Several different systems exist for assigning levels of evidence.

Grades of clinical recommendation ^[5]

A system developed by the US Preventive Task Force (USPSTF) to rate clinical evidence and create guidelines for clinical practice based on medical evidence. ^[3]

Critical appraisal of research studies

Applications

• Clinical practice (evidence-based medicine)
  • Evaluation of the literature relevant to an individual patient's condition
  • Review of updated guidelines on diagnosis and management of medical conditions
  • Clinical decision-making
• Research and academia
  • Gathering background information for a research study
  • Serving as a reviewer for a medical journal
  • Participation in a journal club

Procedure

Perform an overall assessment and an in-depth analysis of the different study sections. ^[6][7]

Reporting guidelines are available for different study types, e.g., CONSORT for randomized trials, STROBE for observational studies, and PRISMA for systematic reviews.

Measures of association can be used to quantify the strength of a relationship between two variables. See also “Measures of disease frequency.”

Two-by-two table

The degree of association between exposure and disease 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.

Risk

• Risk factor: a variable or attribute that increases the probability of developing a disease or injury ^[9]
• Absolute risk: the likelihood of an event occurring under specific conditions ^[3]
  • Commonly expressed as a percentage
  • Equal to the cumulative incidence, which can be calculated as follows: incidence rate × the time of follow-up
  • Aim: to measure the probability of an individual in a study population developing an outcome
  • Used in: cohort studies
  • Formula: (number of new cases)/(total individuals in a study group) = (a + c)/(a + b + c + d)
• Relative risk: See “Estimates of association strength.”
• Attributable risk: See “Estimates of population impact.”

Formulas of common measures of association

• Measures that help quantify the strength of association
  • Relative risk (RR): (a/(a + b))/(c/(c + d))
  • Odds ratio (OR): (a/c)/(b/d) = ad/bc
• Measures that help quantify the impact of an association on a population
  • Attributable risk (AR): a/(a + b) - c/(c + d)
  • Absolute risk reduction (ARR): c/(c + d) – a/(a + b)
  • Relative risk reduction (RRR): 1 - RR
  • Number needed to treat (NNT): 1/ARR
  • Number needed to harm (NNH): 1/AR

Relative risk (RR; risk ratio) ^[3][10]

• Description: : the likelihood of an outcome in one group exposed to a potential risk factor compared to the risk in another group that has not been exposed
• Purpose
  • To measure how strongly a risk factor is associated with an outcome (e.g., death, injury, disease)
  • To help establish disease etiology
• Used in: : cohort studies and randomized controlled trials
• 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.

Odds ratio (OR) ^[11]

• 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
  • Calculated using the two-by-two table
• Purpose: to measure the strength of an association between a risk factor and an outcome
• Used in: : case-control studies
• Formula
  • Odds ratio of exposure: compares the odds of exposure among individuals with an outcome (e.g., disease) against the odds of exposure among individuals without an outcome
    • Odds of exposure in individuals with disease (i.e., case group): (exposure in individuals with disease)/(no exposure in individuals with disease) = a/c
    • Odds of exposure in individuals without disease (i.e., control group): (exposure in individuals without disease)/(no exposure in individuals without disease) = b/d
    • Odds ratio: (odds of exposure in individuals with disease)/(odds of exposure in individuals without disease) = (a/c)/(b/d) = ad/bc = (a/b)/(c/d)
• Interpretation
  • OR = 1: The outcome is equally likely in exposed and unexposed individuals.
  • OR > 1: The outcome is more likely to occur in exposed individuals.
  • OR < 1: The outcome is less likely to occur in exposed individuals.
• Rare disease assumption
  • Case-control studies do not track participants 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.

Hazard ratio (HR)

• Description: : a measure of the effect of an intervention on an outcome at any given point in time during the study period ^[12][13]
• Purpose: to help determine how long it takes for an event to occur in individuals in the case group, compared to individuals in the control group
• Used in: survival analysis
• Formula: (observed number of events in exposed group / expected number of deaths in exposed group) at time (t) / (observed number of events in unexposed group/expected number of deaths in unexposed group) at time (t) ^[13]
• Interpretation
  • 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 is the risk of an event occurring by the end of the study period (i.e., cumulative risk), while the HR is the risk of an event occurring at any point in time during the study period (i.e., instantaneous risk). ^[13]

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

Attributable risk (AR) ^[14]

• 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
• Used in: cohort studies
• Formulas
  • Exposure AR: (incidence risk in exposed group) - (incidence risk in unexposed group) = a/(a + b) - c/(c + d)
  • Population AR: (incidence risk in the study population) - (incidence risk in the unexposed group) = (a + c)/(a + b + c + d) - c/(c + d)

Attributable risk percent (ARP) ^[14]

• Description: the proportion of disease incidence among exposed individuals that can be attributed to the risk factor
• Purpose: to determine the proportion of cases in the exposed population that can be attributed to the risk factor
• Used in: cohort studies and case-control studies
• Formulas: (incidence risk among exposed) - (incidence risk among unexposed)/(incidence risk among exposed) x 100
  • ARP = (RR - 1)/RR x 100
  • The RR cannot be calculated for case-control studies, so the OR (an estimate of the RR) can be used to calculate the attributable risk: ARP = (OR–1)/OR x 100.
  • Alternatively, ARP = AR/(incidence of disease in the exposed group) x 100 = (a/(a + b) – c/(c + d)) / (a/(a + b)) x 100

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
• Used in: cohort studies and cross-sectional studies
• Formulas
  • 1 - RR
  • Alternatively, RRR = ; ((incidence risk/attributable risk in unexposed/control group) - (incidence risk/attributable risk in exposed/treatment group))/(incidence risk/attributable risk of disease in the unexposed/control group) = (ARC - ART)/ARC = (c/(c + d) – a/(a + b)) / (c/(c + d));
• Example: RRR can be used to demonstrate vaccine effectiveness = (risk among unvaccinated – risk among vaccinated)/(risk among unvaccinated) × 100. ^[10]

Absolute risk reduction (ARR; risk difference)

• Description: : the difference between the risk in 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
• Used in: cohort studies, cross-sectional studies, and clinical trials
• 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
• Used in: 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 potential harms of an intervention
• Used in: 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 prevent one death or adverse event ^[15]
• Formula (same as NNT): 1/ARR

Overview

• Before a diagnostic modality (e.g., laboratory study, imaging study, diagnostic criteria) can be used in clinical practice, it needs to be determined how well the modality can distinguish between individuals with the disease and individuals without the disease.
• A test is compared to the gold standard test using a two-by-two table.
• A two-by-two table can be used to calculate a test's sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV).

Example 2 x 2 table of a diagnostic test ^[16]

• Interpretation
  • Sensitivity = TP/(TP + FN) = 800/(800 + 200) = 80%
  • Specificity = 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%
  • PPV = TP/(TP + FP) = 800/(800 + 400) = 66.6 %
  • NPV = TN/(FN + TN) = 3600/(200 + 3600) = 94.7%

Pretest probability

• Description: the probability that a patient has a specific disease before the result of the test is known
• Features
  • The pretest probability of a disease is determined by its prevalence in a particular group.
  • A test subject's pretest probability affects posttest probabilities (i.e., NPV, PPV) but does not affect test characteristics.
    • A higher pretest probability decreases the NPV and increases the PPV.
    • A lower pretest probability increases the NPV and decreases the PPV.
• Relation between pretest probability and odds
  • Pretest probability = pretest odds /(pretest odds + 1)
  • Pretest odds = pretest probability /(1 - pretest probability)

Test characteristics

• Description
  • The intrinsic properties of a test that do not change based on pretest probability
  • Test characteristics include sensitivity, specificity, false positive rate, false negative rate, positive likelihood ratio, and negative likelihood ratio.

Sensitivity and specificity

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

Test efficiency

• Description: the percentage of times that the test gives the correct answer compared to the total number of tests
• Formula: Test efficiency = (TP + TN)/(TP + FN + FP + TN) x 100
  • T = true, F = false, P = positive, N = negative

Likelihood ratio ^[16][17]

• Description
  • A measure used to determine the utility of a diagnostic test in clinical practice
  • Represents the probability of a test result in someone with the disease over the probability of the test result in someone without the disease
• Interpretation
  • Reflects how much more likely a disease is in a person with a given test result compared to their pretest probability
    • A likelihood ratio > 1 is associated with the presence of a disease.
    • A likelihood ratio < 1 is associated with absence of a disease.
    • If the likelihood ratio is 1, the posttest probability is similar to the pretest probability, and therefore the test has poor clinical utility.
  • Likelihood ratio x pretest odds = posttest odds ^[16][17]
  • A nomogram can also be used to convert pretest probability to posttest probability using likelihood ratios.
• Types
  • Positive likelihood ratio (LR⁺)
    • Ratio of the sensitivity rate (true positive rate) to the false positive rate
    • LR⁺ = (TP rate)/(FP rate) = sensitivity/(1 - specificity)
    • A LR⁺ > 10 indicates that the test is excellent at ruling in (confirming) a disease.
  • Negative likelihood ratio (LR^-)
    • Ratio between the false negative rate and the specificity (true negative rate)
    • LR^- = (FN rate)/(TN rate) = (1 - sensitivity)/specificity
    • A LR^- < 0.1 indicates that the test is excellent at ruling out (screening for) a disease.

When comparing diagnostic tests with similar sensitivity or tests with similar specificity, likelihood ratios are used to determine the relative clinical utility.

Posttest probability (predictive value) ^[17][18]

• Description: the probability that a patient has a particular disease after a diagnostic test is carried out, i.e., P(disease status|test result) when expressed as a conditional probability.
• Features
  • Combines pretest probability (e.g., based on disease prevalence) and test characteristics (e.g., sensitivity, specificity, likelihood ratios) to quantify the likelihood of a patient having a disease
  • Can be determined using formulas or nomograms
  • PPV, 1 - PPV, NPV, and 1 - NPV are posttest probabilities.
• Relation between posttest probability and odds
  • Posttest probability = posttest odds /(posttest odds + 1)
  • Posttest odds = posttest probability /(1 – posttest probability)

Positive predictive value (PPV)

• Description: the proportion of individuals who test positive for a disease who actually have the disease, i.e., P(disease|positive test) when expressed as a conditional probability
• Features
  • Directly correlates with pretest probability
  • The PPV increases with increasing prevalence of a disease in the population. ^[19]
• Formula
  • PPV = TP/(TP + FP) (see “Overview of sensitivity and specificity of screening and diagnostic tests”)
  • The probability that an individual who tested positive actually does not have the disease, i.e., P(no disease|positive test) = 1 - PPV
  • PPV can also be calculated using test characteristics and pretest probability or pretest odds of the disease. ^[20]
    • PPV = sensitivity / [sensitivity + ((1 - specificity) / pretest odds)]
    • Alternatively, PPV = LR⁺ / [LR⁺ + (1/pretest odds)]

Negative predictive value (NPV)

• Description: the proportion of individuals who test negative for a disease who actually do not have the disease, i.e., P(no disease|negative test) when expressed as a conditional probability
• Features
  • NPV inversely correlates with pretest probability.
  • NPV decreases with increasing prevalence of the disease.
• Formula
  • NPV = TN/(FN + TN) (see “Overview of sensitivity and specificity of screening and diagnostic tests”)
  • The probability that an individual who tested negative actually has the disease, i.e., P(disease|negative test) = 1 - NPV
  • NPV can also be calculated using test characteristics and pretest probability or pretest odds of the disease. ^[20]
    • NPV = specificity / [specificity + ((1 - sensitivity) x pretest odds)]
    • Alternatively, NPV = LR^- / [1 + (LR^- x pretest odds)]

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

Cutoff values

• Definition: values used in diagnostic and screening tests to categorize results into positive and negative
  • Positive: meets the threshold for diagnosis
  • Negative: does not meet the threshold for diagnosis
• Interpretation: The effects of raising or lowering a cutoff value depends on whether the test’s original cutoff is high (e.g., tumor marker for cancer, lipase for pancreatitis) or low (e.g., serum sodium levels for hyponatremia, leukocyte count for agranulocytosis). Characteristics such as sensitivity, specificity, and the number of true and false positives and negatives are all affected.
  • In tests with a high cutoff value:
    • Lowering the cutoff (i.e., broadening the inclusion criteria): ↓ specificity, ↑ sensitivity, ↓ PPV, ↑ NPV, ↑ FP, ↑ TP, ↓ FN, ↓ TN
    • Raising the cutoff (i.e., narrowing the inclusion criteria): ↑ specificity, ↓ sensitivity, ↑ PPV, ↓ NPV ↓ FP, ↓ TP, ↑ FN, ↑ TN
  • In tests with a low cutoff value:
    • Lowering the cutoff (i.e., narrowing the inclusion criteria): ↑ specificity, ↓ sensitivity, ↑ PPV, ↓ NPV, ↓ FP, ↓ TP, ↑ FN, ↑ TN
    • Raising the cutoff (i.e., broadening the inclusion criteria): ↓ specificity, ↑ sensitivity, ↓ PPV, ↑ NPV, ↑ FP, ↑ TP, ↓ FN, ↓ TN

Receiver operating characteristic curve (ROC curve) ^[16][21]

• Description: a graph that compares the sensitivity and specificity of a diagnostic test
• Features
  • Every diagnostic test generally involves a tradeoff between sensitivity and specificity.
  • Sensitivity and specificity are inversely proportional, meaning that as the sensitivity increases, the specificity decreases, and vice versa.
  • The ROC shows the tradeoff 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 closely the curve follows the y-axis.
    • A test is considered less accurate if the curve is closer to the diagonal.
  • The area under the ROC curve (AUROC) can also be used for test comparison; the larger the AUROC, the more clinically useful the test. ^[22]
    • AUROC close to 1.0 indicates that the test has high combined sensitivity and specificity.
    • AUROC close to 0.5 indicates poor discriminative ability.
  • Cutoff values
    • Normal ROC
      • Low cutoff value: low sensitivity (high FP) and high specificity (low FN)
      • High cutoff value: high sensitivity (low FP) and low specificity (high FN)
    • Inverse ROC
      • Low cutoff value: high sensitivity (low FP) and low specificity (high FN)
      • High cutoff value: low sensitivity (high FP) and high specificity (low FN)

Screening tests

• Used to identify disease in asymptomatic individuals (e.g., mammogram for breast cancer, Pap smear for cervical cancer)
• Should have a low LR^- and a high sensitivity

Confirmatory tests

• 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 LR⁺ and a high specificity

Precision (reliability) ^[3][23]

• Definition: the reproducibility of test results on the same sample under similar conditions
• Features
  • A test with a high precision will have minimal random error.
  • Precision improves with decreased standard deviation and increased power of a statistical test.
• Methods of estimating precision
  • Interrater reliability: the extent to which a test yields the same results when performed by different researchers
  • Parallel test reliability: the extent to which two tests measuring the same concepts with different items or questions yield the same results when repeated on the same subjects
  • Test-retest reliability: the extent to which a test yields the same results when repeated on the same subjects

Validity (accuracy) ^[3]

• Definition: the correspondence between test results and what the test was developed to measure
• Features
  • A test with high validity will have minimal systematic error and bias.
  • Sensitivity and specificity are measures of validity.
• Types
  • Internal validity
    • The extent to which a study is free of error (most often in the form of bias) and the results are therefore true for the study sample
    • High internal validity can be achieved by:
      • Controlling for age, sex, and other characteristics
      • Refining measurement instruments to reduce systematic errors (bias) to a minimum
  • External validity
    • The extent to which 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 different sample groups.
      • High internal validity

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