Epidemiological Values of Diagnostic Tests

Overview of Screening Tests

Screening Screening Preoperative Care tests

Screening Screening Preoperative Care tests are used to identify people in the early stages of a disease and enable early intervention with the goal of reducing morbidity Morbidity The proportion of patients with a particular disease during a given year per given unit of population. Measures of Health Status and mortality Mortality All deaths reported in a given population. Measures of Health Status.

Screening Screening Preoperative Care tests do not provide a definitive diagnosis:

• Screening Screening Preoperative Care tests don’t “prove” that a person has a disease, but only provide suspicion.
• A positive screening Screening Preoperative Care test is followed up by another diagnostic test, which (ideally) can definitively verify the suspicion (e.g., a biopsy Biopsy Removal and pathologic examination of specimens from the living body. Ewing Sarcoma).

The usefulness of screening Screening Preoperative Care tests requires assessment of:

• Frequency of overdiagnosis: How often does a test suggest a patient has a disease when in fact they do not?
• Frequency of misdiagnosis
• Adverse effects of the test: Is the test painful or otherwise damaging?
• Screening Screening Preoperative Care for diseases for which early intervention has shown no benefit

Contingency tables used in evaluating screening Screening Preoperative Care tests

Contingency tables are commonly used in the statistical analysis of multiple variables. To evaluate the epidemiologic value of a screening Screening Preoperative Care test, a table similar to that presented below can be used to determine the relative frequencies of individuals with different combinations of screening Screening Preoperative Care test results (positive or negative) and true disease state (truly have or do not have the disease).

It is important that the table is set up in a standard fashion in order for standard formulas to be applicable. The standard table is presented below (with screening Screening Preoperative Care test results on the left, true disease state on top, and “yes” answers before “no” answers).

In this table:

• A represents true positives (TPs): people with a positive screening Screening Preoperative Care test and actually having the disease
• B represents false positives (FPs): people with a positive screening Screening Preoperative Care test but not actually having the disease
• C represents false negatives (FNs): people with a negative screening Screening Preoperative Care test but actually having the disease
• D represents true negatives (TNs): people with a negative screening Screening Preoperative Care test and not having the disease

False Positives and False Negatives

False positive

• An FP test result indicates that a person has the disease when they do not. 
• Known as a type I error Error Refers to any act of commission (doing something wrong) or omission (failing to do something right) that exposes patients to potentially hazardous situations. Disclosure of Information:
  • An error Error Refers to any act of commission (doing something wrong) or omission (failing to do something right) that exposes patients to potentially hazardous situations. Disclosure of Information in which a test result incorrectly indicates the presence of a condition when the condition is not truly present
  • A rejection of a true null hypothesis Null hypothesis The null hypothesis (H0) states that there is no difference between the populations being studied (or put another way, there is no relationship between the variables being tested). Statistical Tests and Data Representation
• Effects of FP results:
  • Can lead to unneeded testing and medications
  • Burden on the healthcare system Healthcare System The complexity of health systems and the delivery of healthcare has resulted in the growing field of health systems science, which has now joined basic and clinical sciences as the 3rd pillar of medical education. Health systems science allows for an understanding of the framework in which care providers practice, and in comprehension of the interconnected components of care delivery. Healthcare System
  • Anxiety Anxiety Feelings or emotions of dread, apprehension, and impending disaster but not disabling as with anxiety disorders. Generalized Anxiety Disorder for patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship

False negative

• An FN test result indicates a person does not have the disease when, in fact, they do.
• Known as a type II error Error Refers to any act of commission (doing something wrong) or omission (failing to do something right) that exposes patients to potentially hazardous situations. Disclosure of Information:
  • An error Error Refers to any act of commission (doing something wrong) or omission (failing to do something right) that exposes patients to potentially hazardous situations. Disclosure of Information where the test result incorrectly fails to detect the presence of a condition when, in fact, the condition is present
  • Nonrejection of a false null hypothesis Null hypothesis The null hypothesis (H0) states that there is no difference between the populations being studied (or put another way, there is no relationship between the variables being tested). Statistical Tests and Data Representation
• Effects of FN results:
  • People with the disease are not promptly diagnosed.
  • Leads to a delay in management plan and a possible ↑ in morbidity Morbidity The proportion of patients with a particular disease during a given year per given unit of population. Measures of Health Status or mortality Mortality All deaths reported in a given population. Measures of Health Status

Sensitivity and Specificity

Sensitivity and specificity are measures used to assess the performance of screening Screening Preoperative Care and diagnostic tests.

Sensitivity

Definition:

• Probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability of a test in accurately diagnosing a person who has the disease
• The proportion of diseased people that test positive
• A measure of the inclusivity of a diagnostic test: Does it identify everyone who actually has the disease?

Calculations:

To calculate sensitivity, a 2×2 contingency table Contingency table A contingency table lists the frequency distributions of variables from a study and is a convenient way to look at any relationships between variables. Measures of Risk should be set up:

Sensitivity is the proportion of people who test positive on the screening Screening Preoperative Care test and have the disease (TPs, found in square A) divided by all the people who are truly diseased regardless of their screening Screening Preoperative Care test results (TPs and FNs, A + C). Sensitivity is represented by the following equation:

Example: A new diagnostic test is evaluated on a group of patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship: 100 patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship are known to have the disease, and another 100 patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship are known to be disease free in a control group. Among them, 90 patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship with the disease and 20 individuals in the control group show a positive result. What is the sensitivity of the new test?

Answer: In this case, there were 100 patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship who were known to have the disease. Sensitivity is the proportion of these patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship who were correctly identified based on the positive test. Set up a contingency table Contingency table A contingency table lists the frequency distributions of variables from a study and is a convenient way to look at any relationships between variables. Measures of Risk as follows:

Importance of sensitivity:

• Tests with high sensitivity are important when it is crucial that you miss as few cases as humanly possible.
• Tests with high sensitivity are good screening Screening Preoperative Care tests.
• Example: HIV HIV Anti-HIV Drugs screening Screening Preoperative Care tests. For the 1st screening Screening Preoperative Care test, you want to cast a wide net and catch all positive cases. You will likely end up with a higher number of FPs (which can be identified on later confirmatory testing) by not having missed anyone during your initial screening Screening Preoperative Care test.

Specificity

Definition:

• Probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability of a test in correctly rejecting a person who does not have the disease
• The proportion of healthy people that test negative
• A measure of the exclusivity of a diagnostic test

Calculation:

Specificity is also calculated using a similar contingency table Contingency table A contingency table lists the frequency distributions of variables from a study and is a convenient way to look at any relationships between variables. Measures of Risk:

Specificity is the proportion of people who are truly negative and have a negative screening Screening Preoperative Care test (TNs, found in square D) divided by all people who are truly negative, regardless of their screening Screening Preoperative Care test results (TNs and FPs, B + D). Specificity is represented by the following equations:

where TN = true negatives and FP= false positives

Example: A new diagnostic test is tested on a group of patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship: 100 patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship are known to have the disease, and another 100 patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship are known to be disease free in a control group. Among them, 90 patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship with the disease and 20 individuals in the control group show a positive result. What is the specificity of the new test?

Answer: In this case, all patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship in the control group are known to be disease free. Specificity is the proportion of these patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship who were correctly identified based on the negative test. Set up a contingency table Contingency table A contingency table lists the frequency distributions of variables from a study and is a convenient way to look at any relationships between variables. Measures of Risk as follows:

Importance of specificity:

• Tests with high specificity are important when it is crucial that you exclude everyone who is truly healthy.
• Tests with high specificity are good confirmatory/diagnostic tests.
• Example: HIV-confirmation tests. We did not want to exclude anyone in the initial screening Screening Preoperative Care tests; thus, we accepted a high FP rate to make sure no one with HIV HIV Anti-HIV Drugs was excluded. Before beginning lifelong treatment with antiretrovirals, however, it is important to exclude all FP cases to ensure that only those individuals who are truly HIV HIV Anti-HIV Drugs positive receive treatment.

Positive and Negative Predictive Values

Predictive values are also called “precision rates.”

Positive predictive value

Definition:

The positive predictive value is the percentage of people with a positive test result who actually have the disease among all people with a positive result (A), regardless of whether or not they have the disease (A+B).

Calculation:

The positive predictive value is calculated using the equation:

where A = true positives and B = false positives

Example: A new diagnostic test is tested on a group of patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship: 100 patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship are known to have the disease, and another 100 patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship are known to be disease free in a control group. Among them, 90 patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship with the disease and 20 individuals in the control group show a positive result. What is the positive predictive value of the new test?

Answer: The positive predictive value is asking about the proportion of TP cases out of all positive cases (TP + FP). Set up a contingency table Contingency table A contingency table lists the frequency distributions of variables from a study and is a convenient way to look at any relationships between variables. Measures of Risk as follows:

Difference between positive predictive value and sensitivity:

• Positive predictive value considers all patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship with a positive test, including those who truly have and do not have the disease.
• Sensitivity considers all patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship who truly have the disease, including those with positive and negative tests.

Negative predictive value (NPV)

Definition:

The NPV is the percentage of people with a negative test result who are actually disease free (D), among all people with a negative result (regardless of whether or not they have the disease, C + D).

Calculation:

The NPV is calculated using the following equation:

where D = true negatives and C = false negatives

Example: A new diagnostic test is tested on a group of patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship: 100 patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship are known to have the disease, and another 100 patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship are known to be disease free in a control group. Among them, 90 patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship with the disease and 20 individuals in the control group show a positive result. What is the NPV of the new test?

Answer: The NPV is asking about the proportion of TN cases out of all negative cases (TN + FN). Set up a contingency table Contingency table A contingency table lists the frequency distributions of variables from a study and is a convenient way to look at any relationships between variables. Measures of Risk as follows:

Difference between NPV and specificity:

• NPV is looking at all patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship with a negative test, including those who truly have and do not have the disease.
• Specificity is looking at all patients Patients Individuals participating in the health care system for the purpose of receiving therapeutic, diagnostic, or preventive procedures. Clinician–Patient Relationship who are truly disease free, including those with both positive and negative tests.

Summary Example: Sensitivity, Specificity, Positive Predictive Value, and NPV

Pregnancy Pregnancy The status during which female mammals carry their developing young (embryos or fetuses) in utero before birth, beginning from fertilization to birth. Pregnancy: Diagnosis, Physiology, and Care example:

In a study, 4,810 women take a home urine pregnancy Pregnancy The status during which female mammals carry their developing young (embryos or fetuses) in utero before birth, beginning from fertilization to birth. Pregnancy: Diagnosis, Physiology, and Care test. All of them undergo an ultrasound to confirm whether or not they are truly pregnant. Among them, 9 women have a positive urine pregnancy Pregnancy The status during which female mammals carry their developing young (embryos or fetuses) in utero before birth, beginning from fertilization to birth. Pregnancy: Diagnosis, Physiology, and Care test result and are actually found to be pregnant on ultrasound; 1 woman has a negative urine pregnancy Pregnancy The status during which female mammals carry their developing young (embryos or fetuses) in utero before birth, beginning from fertilization to birth. Pregnancy: Diagnosis, Physiology, and Care test result but is actually pregnant; 351 women have positive urine pregnancy Pregnancy The status during which female mammals carry their developing young (embryos or fetuses) in utero before birth, beginning from fertilization to birth. Pregnancy: Diagnosis, Physiology, and Care test results and are found to not be pregnant; 4,449 women have negative urine pregnancy Pregnancy The status during which female mammals carry their developing young (embryos or fetuses) in utero before birth, beginning from fertilization to birth. Pregnancy: Diagnosis, Physiology, and Care test results and ultrasound results confirm that they are not pregnant. (Note: This is sample data and does not represent real values.)

In this example, the home pregnancy Pregnancy The status during which female mammals carry their developing young (embryos or fetuses) in utero before birth, beginning from fertilization to birth. Pregnancy: Diagnosis, Physiology, and Care test is the screening Screening Preoperative Care test, and “ pregnancy Pregnancy The status during which female mammals carry their developing young (embryos or fetuses) in utero before birth, beginning from fertilization to birth. Pregnancy: Diagnosis, Physiology, and Care” is the “disease” state.

The contingency table Contingency table A contingency table lists the frequency distributions of variables from a study and is a convenient way to look at any relationships between variables. Measures of Risk is as follows:

Likelihood Ratios

Definition

• Likelihood ratios (LRs) are ORs that indicate the likelihood that a given test result is expected in a patient with the disease compared with the likelihood that that same result would be expected in a patient without the disease.
• The LRs tell us by how much we should shift our suspicion that a person has a condition based on their test result.
• Interpretation:
  • LR > 1: 
    • The test is associated with presence of the disease.
    • A high LR (typically and arbitrarily defined as > 5 or > 10) indicates a strong suspicion that a person has the disease if they test positive.
  • LR < 1: 
    • The test is associated with absence of the disease.
    • A low LR indicates a strong suspicion that a person does not have the disease if they test negative.
• In practice, we usually only use the positive LR (LR+).

Positive likelihood ratio

• Definition: the probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability of a positive test result for a person who really has the disease (TPs) divided by the probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability of a positive test result for someone who does not really have the disease (FPs)
• Equations:
  • LR+ = probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability of TPs / probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability of FPs
  • LR+ = P(TP) / P(FP) 
  • Can be expressed as a function of sensitivity and specificity:

Negative likelihood ratio (LR‒)

• Definition: the probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability of a negative test result for a person who really is healthy (TNs) divided by the probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability of a negative test result for someone who actually has the disease (FNs)
• Equations:
  • LR‒ = probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability of TNs / probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability of FNs
  • LR‒ = P(TN) / P(FN)
  • Can be expressed as a function of sensitivity and specificity:

Example and interpretation of LRs

Using the same pregnancy Pregnancy The status during which female mammals carry their developing young (embryos or fetuses) in utero before birth, beginning from fertilization to birth. Pregnancy: Diagnosis, Physiology, and Care example in the section above, and knowing that the sensitivity was 90% and the specificity was 92.7%, the LR+ and LR‒ can be computed as follows:

LR+ = 0.9 / (1 ‒ 0.927) = 12.3 = 1,230%

LR‒ = (1 ‒ 0.9) / 0.927 = 0.11 = 11%

Interpretation: There is a 12-fold greater likelihood that a woman who tests positive is truly pregnant. A negative test result reduces the odds of being pregnant by 89%.

Pre-test and Post-test Probabilities

Pre-test probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability

• Probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability of a screened person of having the disease
• Determining the pre-test probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability:
  • Can be determined using published epidemiological data: typically the prevalence Prevalence The total number of cases of a given disease in a specified population at a designated time. It is differentiated from incidence, which refers to the number of new cases in the population at a given time. Measures of Disease Frequency of a disease in the population
  • Clinical criteria scales Scales Dry or greasy masses of keratin that represent thickened stratum corneum. Secondary Skin Lesions can also be used to calculate the pre-test probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability (e.g., Well’s deep vein thrombosis Thrombosis Formation and development of a thrombus or blood clot in the blood vessel. Epidemic Typhus ( DVT DVT Deep vein thrombosis (DVT) usually occurs in the deep veins of the lower extremities. The affected veins include the femoral, popliteal, iliofemoral, and pelvic veins. Proximal DVT is more likely to cause a pulmonary embolism (PE) and is generally considered more serious. Deep Vein Thrombosis) criteria for clinically determining the pre-test probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability of DVT DVT Deep vein thrombosis (DVT) usually occurs in the deep veins of the lower extremities. The affected veins include the femoral, popliteal, iliofemoral, and pelvic veins. Proximal DVT is more likely to cause a pulmonary embolism (PE) and is generally considered more serious. Deep Vein Thrombosis))
• Clinical uses: 
  • To calculate post-test probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability (see below)
  • If high enough, can be used to validate at the beginning of treatment without testing
  • If low enough, can be used to reject the diagnosis as unlikely

Post-test probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability

• Probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability of a person having the disease after getting the results of a test
• Calculations:
  • Typically calculated using online calculators in clinical studies
  • Involves the following variables:
    • Pre-test probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability
    • Sensitivity of the test
    • Specificity of the test
• Post-test probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability of a positive result: probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability that the disease is present when the test result is positive
• Post-test probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability of a negative result: probability Probability Probability is a mathematical tool used to study randomness and provide predictions about the likelihood of something happening. There are several basic rules of probability that can be used to help determine the probability of multiple events happening together, separately, or sequentially. Basics of Probability that the disease is present when the test result is negative