Ch 3: Biomedical Decision Making : Probabilistic Clinical Reasoning

• Medical decision-making is central to clinical practice but is inherently uncertain due to imperfect data and unpredictable treatment outcomes.
• Understanding probability and updating it with new information are crucial for clinical decision-support systems.
• Probabilistic medical reasoning is valuable for handling uncertainty but unsuitable for all cases.
• Good medicine involves understanding probabilities and possibilities to determine which tests will provide valuable information.

Clinical Decisions

• Probabilistic medical reasoning is a valuable approach but unsuitable for all cases.
• Imperfect associations between symptoms and diseases lead to uncertainty.
• Clinical data are imperfect, and uncertainty is always present in diagnosis and treatment.
• Probability and risk analysis can help determine when treatment is justified.

Examples of Uncertainty

• Polymerase chain reaction (PCR) test for detecting HIV in blood donors shows uncertainty, as positive results don't guarantee HIV presence.
• A 66-year-old woman with coronary artery disease needs a third coronary artery bypass graft (CABG) surgery, she faces uncertainty in choosing between surgery and facing a high risk of heart attack.
• A 33-year-old woman with a history of blood clots experiences leg pain and swelling causing uncertainty whether she is experiencing deep vein thrombosis (DVT) or not.

Probability and Uncertainty

• Applying probability-based expressions in medicine can help reduce ambiguity and improve clarity in communication about the likelihood of diseases and treatment outcomes.
• Clinicians often use ambiguous language to describe a patient's condition, this can lead to miscommunication in medical decision-making.
• Medical decisions based on probabilities are necessary but also perilous.

Diagnostic Process

• The hypothetico-deductive approach to diagnosis involves initial judgment, hypothesis generation, and probability estimation.
• Initial Judgment involves the clinician forming an intuitive belief about the likelihood of a disease, based on experience or medical knowledge.
• Observations lead to a working diagnosis, which is refined as new information is gathered during Hypothesis Generation.
• The clinician can make an explicit estimate of disease probability before conducting further tests, which is known as pretest (prior) probability.
• The diagnostic examples demonstrate the process of pretest probability estimation, diagnostic testing, and post-test probability calculation to improve decision-making accuracy.
• The structured process of the hypothetico-deductive approach helps refine diagnoses and improve decision-making accuracy in medical practice.

Probability Assessment

• Clinicians estimate pretest probability to express uncertainty before ordering tests.
• Probability (p) represents the likelihood of an event occurring on a scale from 0 to 1, where 0 means impossible and 1 means certain.
• For independent events (A & B), the joint probability is p[A] × p[B].
• Flipping heads twice has a probability of 0.5 x 0.5 = 0.25
• Conditional probability is the likelihood of an event (A) given that another event (B) has occurred, denoted as p[A|B].
• If 30% of patients with a swollen leg have a blood clot, then p[blood clot | swollen leg] = 0.3.
• Probability estimates can be derived using subjective or objective methods, each with strengths and limitations in clinical decision-making.
• Before observing swelling, the pretest probability is based on general prevalence in the population.

Diagnostic Process Example

• A 60-year-old man complains of pressure-like chest pain during quick walks.
• This leads the clinician to believe there is a high chance that he has heart disease.
• The clinician assesses likelihood of heart disease based on symptoms, history, experience
• The estimated pretest probability is 50% (1:1 odds).
• An exercise stress test is performed to reduce uncertainty, where abnormal ECG results support the presence of heart disease.
• Using Bayes’ theorem, the clinician updates the probability of disease based on the test results.
• Post-test probability helps determine the next steps in diagnosis and treatment, which ensures more accurate decision-making in diagnosing heart disease.

Subjective Probability Estimation

• Clinicians estimate disease probability based on personal experience, comparing cases to previous encounters.
• This relies on cognitive heuristics, mental shortcuts that can introduce systematic errors.
• Three key heuristics influence probability estimation: representativeness, availability, and anchoring and adjustment.
• Representativeness Heuristic means clinicians judge probability based on how closely a patient resembles their mental image of a disease.
• Errors occur for Representativeness Heuristic when the disease is rare, previous experiences are atypical, or the patient’s presentation is unusual for the disease.
• The Availability Heuristic means probability estimation is influenced by how easily similar cases come to mind.
• Dramatic or emotional cases are remembered more vividly, leading to overestimation of their frequency due to the Availability Heuristic.
• Anchoring and Adjustment Heuristic means clinicians start with an initial estimate (anchor) and adjust based on new information, but adjustments are often insufficient.

Subjective Probability - Heuristics Example

• Representativeness Heuristic example: A patient resembles a mental image of a disease.
• Availability Heuristic example: A clinician recalls a fatal blood clot case, which may overestimate the likelihood of thrombosis in patients with a swollen leg.
• Anchoring and Adjustment Heuristic example: A clinician estimates a 50% probability of heart disease but, after learning about a strong family history, only increases the probability to 60% instead of 80%.

Objective Probability Estimates

• Uses published research, disease prevalence, and clinical prediction rules to provide more accurate assessments of disease probability.
• Prevalence (frequency of a disease in a population) serves as an anchor for probability estimation.
• The prevalence of prostate cancer in 50-year-old men (5–14%) helps estimate individual risk, adjusted based on symptoms (e.g., difficulty urinating, prostate nodule).
• Clinical Prediction Rules are systematic methods to refine probability estimates by placing patients into subgroups with known disease probabilities.
• Clinical Prediction Rules are developed using statistical analysis of symptoms and signs.
• For cardiac complications, a clinical predication rule/scoring system assigns diagnostic weights to risk factors (e.g., recent heart attack, arrhythmia).
• A total score as part of a clinical predication rule predicts complication risk (e.g., 27% for a high-risk patient).
• Referral Bias means studies often overestimate disease probability because they are based on patients already referred to specialists, who see a higher-risk population.
• Early studies on microhematuria (blood in urine) suggested a high cancer risk, leading to unnecessary testing which demonstrates Referral Bias.
• Later studies found only a 2% risk in asymptomatic patients, revealing the impact of referral bias for microhematuria.
• Clinicians start with objective data (prevalence, prediction rules) and refine it using patient-specific factors, while avoiding anchoring errors.
• If the prevalence of heart disease in men with typical angina is 90%, a clinician might adjust it upward based on a strong family history.
• Avoid anchoring errors, where adjustments stay too close to the initial estimate when combining Objective and Subjective Estimates.

Diagnostic Tests

• Assessing a diagnostic test involves determining criteria for classifying results as normal or abnormal and evaluating test performance.
• Many biological measurements follow a normal distribution (bell curve).
• Laboratories often define the upper limit of normal as two standard deviations above the mean (e.g., cholesterol >220 mg/dl is considered high)
• The statistical cutoff may not always have biological significance.
• The distributions of healthy and diseased individuals often overlap, leading to misclassification (True Positive, True Negative, False Positive, False Negative)
• Adjusting the cutoff point affects test accuracy, that means higher cutoff gives more false negatives (FNs) but fewer false positives (FPs) and lower cutoff has the opposite effect.
• Columns in a contingency table are Diseased (TP + FN) vs. Non-Diseased (FP + TN), and rows are Positive test (TP + FP) vs. Negative test (FN + TN).
• A perfect test has zero FP and FN results, but real-world tests always involve some error.
• Contingency tables and statistical measures help clinicians evaluate and improve the accuracy of diagnostic tests.

Measures of Test Performance

• Assessed using concordance (agreement) and discordance (disagreement) measures derived from a 2 × 2 contingency table.
• Sensitivity (True Positive Rate - TPR) is the probability that a diseased patient tests positive, calculated as TPR = TP / (TP + FN).
• Specificity (True Negative Rate - TNR) is the probability that a non-diseased patient tests negative, calculated as TNR = TN / (TN + FP)
• False Negative Rate (FNR) is the probability that a diseased patient receives a negative result, calculated as FNR = FN / (TP + FN), and TPR + FNR = 1.
• False Positive Rate (FPR) is the probability that a non-diseased patient receives a positive result, calculated as FPR = FP / (TN + FP), and TNR + FPR = 1.
• The cutoff value used to define abnormal results affects a test's sensitivity and specificity.
• Higher specificity, lower sensitivity occurs when increasing the cutoff (higher threshold for abnormality) which reduces false positives (FPs) but increases false negatives (FNs)
• Higher sensitivity, lower specificity happens when lowering the cutoff (more inclusive definition of abnormality) reduces FNs but increases FPs.
• For serious diseases with effective treatment, minimize FNs (increase sensitivity).
• For less serious diseases or risky treatments, minimize FPs (increase specificity).
• Sensitivity and specificity are not inherent properties of a test but rather depend on the selected threshold.
• A test’s range of performance across different cutoffs is best visualized using a receiver-operating characteristic (ROC) curve.
• ROC curves plot sensitivity (TPR) vs. 1 - specificity (FPR) across different cutoff values.
• Higher ROC curves indicate better test performance (lower FPR for the same TPR).
• If Test B's curve lies above Test A's, Test B has greater discriminative power.
• Factors like cost, risk, discomfort, and time also influence test selection.
• Ideally choose the test with the highest sensitivity and specificity, provided other factors (cost, risk) are equal.
• A more accurate test reduces diagnostic uncertainty and improves decision-making.

HIV Antibody Test Performance Example

• Hypothetical data: 98 True Positives (TP), 2 False Negatives (FN), 297 True Negatives (TN), 3 False Positives (FP)
• Sensitivity (TPR): 98 / (98 + 2) = 0.98 , Meaning the test correctly identifies 98% of HIV-positive patients.
• Specificity (TNR): 297 / (297 + 3) = 0.991 , Meaning the test correctly identifies 99.1% of HIV-negative patients.
• False Negative Rate (FNR): 2% of HIV-positive patients are incorrectly classified as negative.
• False Positive Rate (FPR): 0.9% of HIV-negative patients are incorrectly classified as positive.

Test Performance Evaluation

• Relies on classifying results as true positive (TP), true negative (TN), false positive (FP), or false negative (FN).
• The gold-standard test provides a definitive diagnosis (e.g., biopsy, surgery).
• The index test is the test being evaluated for its accuracy in comparison to the gold standard.
• The gold-standard test is often more expensive, invasive, or difficult, making the index test a practical alternative.
• The study population is a selected group where the test's accuracy is measured.
• The clinically relevant population is the broader group where the test will be applied in real-world settings.
• A test may perform differently in study populations versus in the clinically relevant population, affecting its generalizability.

Bias Measurement

• Disease prevalence in study populations may not match the clinically relevant population, leading to inaccurate test sensitivity and specificity.
• A CEA blood test for colon cancer initially appeared highly accurate but later proved ineffective due to differences in study and real-world populations.
• Spectrum Bias means early studies may include only severely ill patients and healthy volunteers, making detection easier.
• This lowers the false-negative rate (FNR) and inflates sensitivity (TPR) in study results for Spectrum Bias.
• Specificity (TNR) is also overestimated because healthy volunteers are unlikely to have conditions that cause false positives for Spectrum Bias.
• Test-Referral Bias occurs when only patients with positive index test results undergo the gold standard test.
• This excludes TN and FN cases, leading to an overestimated sensitivity (TPR) and underestimated specificity (TNR) in the Test-Referral Bias study results.
• Test-Interpretation Bias means if the interpretation of the index test influences the interpretation of the gold standard test (or vice versa), the two tests appear to agree more than they should.
• This artificially increases both sensitivity and specificity for Test-Interpretation Bias..
• Adjustments for bias lead to an overestimated TPR (sensitivity), so it should be adjusted downward when applied to new populations.
• The real-world specificity lowers for Spectrum & Interpretation Bias, which means you should adjust downward.
• The real-world specificity is higher for Test-Referral Bias; adjust upward.