Diagnostic and Screening Tests

Learning Objectives

• Understanding the difference between screening and diagnostic tests.
• Defining and calculating the measures of validity for screening and diagnostic tests.
• Comparing and understanding the relationship between sensitivity and specificity, positive and negative predictive values, and likelihood ratios.
• Understanding the benefits and differences of multiple testing (sequential and simultaneous).

Dichotomous vs. Continuous Variables

• Dichotomous Variable:
  • Examples: Male/Female, 1/0
• Continuous Variable:
  • Examples: Height, Weight, Distance, Time

Distribution of LDL-C Levels

• Distribution of achieved low-density lipoprotein cholesterol (LDL-C) in participants of a clinical trial.
• The median LDL-C level was 56 mg/dL (interquartile range, 43-70 mg/dL).
• To convert LDL-C to millimoles per liter, multiply by 0.0259.
• LDL-C levels:
  • <30 mg/dL: n = 971 (6.4%)
  • 30-49 mg/dL: n = 4,780 (31%)
  • 50-69 mg/dL: n = 5,504 (36%)
  • ≥70 mg/dL: n = 4,026 (26%)

Distribution of Neutralizing Titers Against SARS-CoV-2 Variants

• Long COVID vs. Healthy Control
• pNT50 Wu-1 (D614)
• pNT50 BA.1

Screening vs. Diagnostic Tests

• Course of Disease:
  • Biological onset of exposure.
  • Preclinical phase (screening test).
  • Symptom onset.
  • Clinical phase (diagnostic test).
• Outcome:
  • Cured, living with disease, deteriorated, or died.

Screening Tests

• A screening test identifies individuals who may have a certain disease or condition but do not yet exhibit any symptoms.
• The purpose is to detect the presence of a disease or condition early when treatment is likely to be more effective.
• Examples:
  • Mammography: Detects early signs of breast cancer in women who have no symptoms.
  • Pap test: Detects early signs of cervical cancer in women who have no symptoms.
  • Colonoscopy: Detects early signs of colon cancer in people who have no symptoms.
  • Prostate-specific antigen (PSA) test: Detects early signs of prostate cancer in men who have no symptoms.
  • Blood pressure measurement: Detects high blood pressure in people who have no symptoms.
  • Skin cancer screening: Detects early signs of skin cancer in people who have no symptoms.
  • HIV screening: Detects the presence of HIV in people who have no symptoms.

Diagnostic Tests

• A diagnostic test determines the presence or absence of a specific disease or condition in a person who is exhibiting symptoms.
• It confirms or rules out a suspected diagnosis based on a patient's symptoms and medical history.
• Examples:
  • Blood tests: Diagnose conditions such as anemia, infections, liver or kidney disease.
  • X-rays: Diagnose conditions such as broken bones, lung infections, or certain types of cancer.
  • Magnetic resonance imaging (MRI): Diagnose conditions such as brain or spinal cord injuries, certain types of cancer, or abnormalities in organs such as the heart or liver.
  • Computed tomography (CT) scan: Diagnose conditions such as injuries, infections, or certain types of cancer.
  • Biopsy: Diagnose conditions such as cancer or infections.
  • Electrocardiogram (ECG): Diagnose conditions such as heart attacks or abnormal heart rhythms.
  • Colonoscopy: Diagnose conditions such as colon cancer or inflammatory bowel disease.

Validity/Accuracy of Tests

• Sensitivity: The ability of the test to identify correctly those who HAVE the disease.
• Specificity: The ability of the test to identify correctly those who do NOT have the disease.

Assessing Validity

• Must have a 'gold standard' to compare to.
• Considered best test available.
• Often invasive or expensive.

Sensitivity vs. Specificity Example 1

• Low blood sugar cut point.
• Sensitivity = $17 / (17+ 3) = 85$.
• Specificity = $6/(6+14) = 30$.

Sensitivity vs. Specificity Example 2

• High blood sugar cut point
• Sensitivity = $5/(5+15)= 25$.
• Specificity = $18 / (18+2) = 90$.

Sensitivity vs. Specificity relationship

• A 100% sensitivity: TRUE POSITIVE
• B most accurate
• C 100% specificity: TRUE NEGATIVE

Dichotomous Test Results

• True Positive (TP): Have the disease and test positive.
• False Negative (FN): Have the disease but test negative.
• False Positive (FP): Do not have the disease but test positive.
• True Negative (TN): Do not have the disease and test negative.
• Sensitivity: $TP / (TP + FN)$
• Specificity: $TN / (TN + FP)$

Sensitivity and Specificity Example

• Population: 1,000 people, 100 with the disease, 900 without.
• Positive test results: 80 with the disease, 100 without.
• Negative test results: 20 with the disease, 800 without.
• Sensitivity: $80 / 100 = 80$. Specificity: $800 / 900 = 89$.

Multiple Testing Scenarios

• Sequential or serial: One test followed by another test.
  • Net sensitivity decreases.
  • Net specificity increases.
• Simultaneous or parallel: Two tests given at the same time with 'or'.
  • Net gain in sensitivity.
  • Net loss in specificity.

Sequential Testing

• Less expensive/invasive test first; if positive, a second more invasive/expensive test will be performed.
• Reduces false positives.
• Net sensitivity (test 1 ‘and’ test 2): Decreases.
• Net specificity (test 1 ‘and’ test 2): Increases.

Sequential Testing (Two-Stage)

• First test: simpler, inexpensive, or high-sensitive test used for the entire population.
• Second test: More specific test for those who tested positive in the first test.
• Net result: Lower sensitivity and higher specificity.

Sequential Testing Example

TEST 1 (Blood Sugar)

• Sensitivity = 70%
• Specificity = 80%
  TEST 2 (Glucose Tolerance Test)
• Sensitivity= 90%
• Specificity =90%

Calculating Net Sensitivity and Specificity in Sequential Testing

• Net sensitivity: 315/500 = 63%
• Net specificity: 9,310/9,500 = 98%
• Sequential testing results in decreased sensitivity and increased specificity.

Simultaneous Testing

• Two different tests are administered at the same time, and a person is considered positive if either one or both tests are positive.
• Good method for finding all who have the disease.

Example of Simultaneous Testing

• Test A: Sensitivity of 80%, specificity of 60%.
• Test B: Sensitivity of 90%, specificity of 90%.

Calculating Positives on both tests:

• Number of people who tested positive on Test A multiplied by the sensitivity of Test B: 160 x 0.90 = 144 people who tested positive on both tests.

Calculate the net sensitivity and specificity

• 160 – 144 = 16 people who tested positive only in Test A
• 180 – 144 = 36 people who tested positive only in Test B
• Total # of people that tested positive in both tests
• Total number of people who have the disease
• Parallel testing results in increase sensitivity and decrease in specificity

Cut Point Considerations

• High penalty for missing a case: Maximize true positives, use a cut point with high sensitivity.
• Ineffective treatment or slow disease progression: Minimize false positives, use a cut point with high specificity.
• Balance severity of false positives against false negatives.

Improving Reliability

• Fluctuations in Parameters: Standardize fluctuating variables.
• Variability of Test Chemicals: Use standards in laboratory tests, run multiple samples.
• Observer/Rater Variation: Extensive training of observers, use multiple observers.

Sensitivity and Specificity Limitations

• Sensitivity and specificity have limited impact in translating the implications of those characteristics to the endpoint user, the patient.

Predictive Values

• Positive Predictive Value (PPV): Probability that a patient who tests positive actually has the disease.
• Negative Predictive Value (NPV): Probability that a patient who tests negative does not have the disease.

Predictive Value Calculation

• Positive predictive value = $80/180 = 44$%
• Negative predictive value = $800/820 = 98$

Relationship of Disease Prevalence to Positive Predictive Value

• EXAMPLE: Sensitivity = 99%, Specificity = 95%
• Disease Prevalence: 1%
  • Positive Predictive Value = $99 / 594 = 17$%
• Disease Prevalence: 5%
  • Positive Predictive Value = $495 / 970 =51$%

Example Prevalence Calculation (1%)

• 99% Sensitivity: $0.99 = x /100$
• 95% Specificity: $0.95 = y / 9,900$
• x = 99 , y = 9,405
• $99 / 594 = 0.167 x 100 = 16.7$%

Example Prevalence Calculation (5%)

• 99% Sensitivity: $0.99 = x / 500$
• 95% Specificity: $0.95 = y / 9,500$
• x = 495 , y = 9,025
• $495 / 970 = 0.510 x 100 = 51.0$%

Predictive Value and Prevalence

• The higher the prevalence, the higher the predictive value.

Practice Question 1

• Screening to prevent transmission of a preventable disease (i.e., HIV in blood donors) that is expensive and difficult to treat: Optimize sensitivity.

Practice Question 2

• Screening to prevent the progression of prostate cancer, which is slow-growing: Optimize specificity.

Screening Programs Considerations

• Screening tests with low sensitivity, when used in people not at high risk for disease or when testing for very rare diseases, can be problematic.
• Compliance and access are critical for effective screening programs.

Screening Bias

• Screening can lead to biases that overestimate survival duration.
  • Lead-time bias: Overestimation of survival duration due to earlier detection.
  • Length-time bias: Overestimation of survival duration due to the relative excess of cases detected that are slowly progressing.

Lead-Time Bias

• Cancer detected through screening leads to perceived longer survival time.
  *Cancer detected through symptoms

Lead-Time Bias Example

• Without Screening: A man develops prostate cancer at age 67 and is diagnosed due to symptoms at age 70. He dies at age 75, so his observed survival time from diagnosis is 5 years.
• With Screening: The same man undergoes a PSA test at age 60, leading to an early diagnosis of the same cancer. He still dies at age 75, but his observed survival from diagnosis is now 15 years instead of 5.

Length-Biased

• Screening test detects more slow-growers than fast-growers.
• People whose cancer is detected by screening do better, even if there is no real benefit to catching the cancer earlier.
• This gives an impression that detecting disease such as cancers by screening can lead to better prognosis – even if it does not.

Mammography and Tumor Detection

• Mammography tends to detect slow-growing tumors more frequently than aggressive ones.
• Screened populations appear to have more survivors, but this may not be due to screening saving lives.

CRC Diagnostic Test Example

• A novel method to diagnose colorectal cancer (CRC) was recently developed.
• Two-hundred fifty people, of which 68 have CRC, were tested using this new diagnostic.
• Sensitivity of this test was 88.2%, while the specificity was 67.5%.

CRC Prevalence Calculation

$\frac{68}{250} = 0.272 x 100 = 27.2$

Constructing a 2 x 2 Table

Sensitivity = 88.2%

• $68 x 0.882 = 60$
• Specificity = 67.5%
• $182 x 0.676 = 123$

Calculating Predictive Values

• PPV = $60/119 = 50.4$% probability that the individual has CRC
• PNV = $123/131 = 93.8$% probability that the individual does not have CRC