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Biostatistics 80/20 - Introduction to Medicine

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1. The 2x2 Contingency Table - Master This First

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2. Diagnostic Test Characteristics

Sensitivity and Specificity

Source: Harrison's 22e, Table 4-1 - "The sensitivity or true-positive rate reflects how well the new test identifies patients with disease... The specificity, or true-negative rate, reflects how well the new test correctly identifies patients without disease."

Predictive Values

• Goldman-Cecil Medicine, Chapter 8

Likelihood Ratios (LRs)

• LR > 10 or LR < 0.1 = large, often conclusive change in probability
• LR 2-5 / 0.2-0.5 = moderate shift
• LR 1-2 / 0.5-1 = small, rarely important shift

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3. Bayes' Theorem in Practice

Post-test odds = Pre-test odds × Likelihood Ratio

• Harrison's 22e, "Measures of Disease Probability and Bayes' Rule"

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4. Measures of Disease Frequency

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5. Measures of Effect (Treatment and Risk)

• Goldman-Cecil Medicine, "From These Data, One Can Also Calculate"

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6. Study Design Hierarchy

1. Systematic Review / Meta-Analysis - Combines data from multiple studies; highest level when well-done
2. Randomized Controlled Trial (RCT) - Gold standard for therapeutic questions; eliminates confounding
3. Cohort Study - Prospective (follow exposed/unexposed forward); measures incidence and RR; good for rare exposures
4. Case-Control Study - Retrospective (identify cases and controls, look backward); measures OR; good for rare diseases, fast and cheap
5. Cross-Sectional Study - Snapshot; measures prevalence; cannot determine causality
6. Case Reports / Case Series - Hypothesis generating only

• Only RCTs can control for unmeasured confounding
• Cohort studies can calculate incidence and RR; case-control studies can only calculate OR
• Cross-sectional studies show association, not causation
• Pediatric Board Review (9780323876988), Table 29.2

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7. Bias - The Big Three

• Recall bias - Awareness of disease alters subject's memory of prior exposure (especially in case-control studies)
• Lead-time bias - Early detection of disease is mistaken for increased survival
• Loss-to-follow-up bias - Patients who drop out are not randomly distributed (e.g., sicker patients drop out more)
• Hawthorne effect - Participants change behavior because they know they are being studied
• Observer-expectancy bias - Researcher's belief in treatment efficacy affects their assessment

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8. Statistical Significance vs. Clinical Significance

• Pediatric Board Review, "Alpha and Beta"

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9. Evidence-Based Medicine (EBM) Steps

1. Formulate the clinical question (PICO: Patient, Intervention, Comparison, Outcome)
2. Search for evidence (PubMed, Cochrane, UpToDate, guidelines)
3. Critically appraise for internal validity (was the study conducted without bias?) and external validity (are results generalizable to your patient?)
4. Apply evidence to the individual patient, incorporating patient preferences

• Was allocation truly random?
• Were patients and assessors blinded?
• Was analysis by intention-to-treat (ITT)? (This is almost always the correct approach - analyze by original group assignment regardless of actual treatment received)
• Was the study adequately powered?
• Were outcomes clinically meaningful, not just surrogate endpoints?
• Harrison's 22e; Pediatric Board Review

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10. Quick-Reference Mnemonics

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Summary Visual: What Each Study Design Measures

Cross-sectional   → Prevalence, association (not causation)
Case-control      → OR (rare diseases, fast, retrospective)
Cohort            → RR, Incidence (rare exposures, prospective)
RCT               → Causation, ARR, NNT (gold standard)
Systematic Review → Pooled effect estimates (highest level)

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BIOSTATISTICS - COMPLETE SUPER NOTES

1st/2nd Year Medical School

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UNIT 1: DATA TYPES AND DESCRIPTIVE STATISTICS

1.1 Types of Data

• Nominal - categories with no order (e.g., blood type, race, tumor type). No meaningful ranking.
• Ordinal - categories with a meaningful order but unequal intervals (e.g., Glasgow Coma Scale, pain score 1-10, cancer stage). You can rank them, but the difference between ranks is not uniform.
• Dichotomous/Binary - a special case of nominal with exactly two options (e.g., alive/dead, disease present/absent, readmission yes/no).

• Continuous - can take any value within a range; theoretically infinite decimal places (e.g., blood pressure, cholesterol, height, weight, temperature). Analyzed with parametric tests when normally distributed.
• Discrete/Count - whole number counts (e.g., number of pregnancies, number of hospital visits per year). Often require non-parametric or Poisson approaches.
• Interval - equal spacing between values but no true zero (e.g., temperature in Celsius). Ratio comparisons are not meaningful.
• Ratio - equal spacing and a true zero, so ratio comparisons are valid (e.g., weight, height, blood glucose).

Key clinical rule: Continuous > Ordinal > Nominal in terms of statistical power. Always collect data at the highest level possible - you can always collapse it down later (e.g., age in years → age group), but you can't go the other direction.

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1.2 Measures of Central Tendency

• Positively skewed (tail to the right, e.g., income, serum creatinine in outpatients): Mean > Median > Mode. The mean gets pulled toward the tail.
• Negatively skewed (tail to the left): Mode > Median > Mean.

The median is the preferred measure of central tendency when data are skewed, because it is not pulled by outliers. For example, median household income is reported instead of mean income because a few billionaires would distort the mean upward.

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1.3 Measures of Dispersion (Spread)

• Use SD to describe the spread of individual measurements in your sample.
• Use SEM to describe how precisely your sample mean estimates the true population mean.
• SEM is always smaller than SD. Using SEM in a graph makes error bars look smaller - a misleading but common technique in publications.

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1.4 The Normal Distribution (Gaussian Distribution)

• Mean ± 1 SD contains 68% of values
• Mean ± 2 SD contains 95% of values
• Mean ± 3 SD contains 99.7% of values

• Z = (individual value - mean) / SD
• Tells you how many standard deviations a value is from the mean
• Allows comparison of values from different distributions

• Poisson distribution - counts of rare events (e.g., number of emergency visits per day)
• Binomial distribution - number of successes in a fixed number of trials (e.g., number of patients who respond to treatment)
• Skewed distributions - income, length of hospital stay, survival times

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UNIT 2: STUDY DESIGNS

2.1 The Hierarchy of Evidence

1. Systematic Review / Meta-Analysis     ← Highest
2. Randomized Controlled Trial (RCT)
3. Cohort Study
4. Case-Control Study
5. Cross-Sectional Study
6. Case Series / Case Report
7. Expert Opinion / Anecdote            ← Lowest

"The major tools used to develop reliable evidence consist of randomized clinical trials supplemented strategically by large, high-quality observational registries." - Goldman-Cecil Medicine

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2.2 Study Design Details

Cross-Sectional Study

• What it is: A snapshot in time. You measure both the exposure (risk factor) AND the outcome (disease) simultaneously in a sample of the population.
• What it measures: Prevalence (existing cases). Does NOT measure incidence.
• What you can calculate: Prevalence odds ratio. Cannot calculate true relative risk.
• Strengths: Fast, cheap, good for prevalence estimates, hypothesis generation.
• Weaknesses: Cannot establish temporal sequence (which came first?). Cannot prove causation. Susceptible to prevalence-incidence bias (misses short-lived cases).
• Example: Survey 1,000 adults today and measure their blood pressure and salt intake simultaneously.

Case-Control Study

• What it is: Start with people who have the disease (cases) and people who do not (controls). Then look backward to compare how often each group had the exposure.
• Direction: Backward (retrospective)
• What you can calculate: Odds Ratio (OR). Cannot directly calculate incidence or relative risk (because you selected cases - you did not follow a population forward).
• Strengths: Great for rare diseases. Faster and cheaper than cohort. Can study multiple exposures simultaneously. Smaller sample size needed.
• Weaknesses: Susceptible to recall bias (cases remember exposures differently from controls). Cannot establish incidence. Selection of appropriate controls is difficult. Only OR can be calculated, not RR (unless disease is rare).
• Example: Take 100 patients with hepatocellular carcinoma (cases) and 100 patients without (controls). Ask both groups how much alcohol they drank per week over the past 10 years.

Cohort Study

• What it is: Start with a group of people without the disease. Divide them into exposed (have the risk factor) and unexposed (do not). Follow them forward over time to see who develops the disease.
• Direction: Forward (prospective). Can also be retrospective (historical cohort) - use existing records to follow a group forward.
• What you can calculate: Incidence (new cases over time), Relative Risk (RR), and Attributable Risk.
• Strengths: Can establish temporal sequence (exposure → disease). Can calculate incidence and RR. Good for rare exposures. Can study multiple outcomes from a single exposure.
• Weaknesses: Very expensive and time-consuming for rare diseases (need large numbers or long follow-up). Susceptible to loss-to-follow-up bias. Confounding by unmeasured variables.
• Example: Enroll 10,000 smokers and 10,000 non-smokers. Follow them for 20 years. Compare the incidence of lung cancer in each group.

Randomized Controlled Trial (RCT)

• What it is: Participants are randomly assigned to receive the intervention (treatment group) or not receive it (control/placebo group). The gold standard for establishing causation.
• Direction: Prospective (forward)
• What you can calculate: ARR, RRR, NNT, and with true randomization, you can establish causation (not just association).
• Why randomization matters: Randomization distributes both known and unknown confounders equally between groups. This is the only design that controls for unmeasured confounding.
• Types of blinding:
  • Single-blind: Patient does not know which group they are in
  • Double-blind: Neither patient nor investigator knows (preferred)
  • Triple-blind: Patient, investigator, AND data analyst are blinded
• Key concepts in RCT analysis:
  • Intention-to-treat (ITT) analysis: Analyze all participants according to their original assigned group, regardless of whether they actually completed the assigned treatment. Preferred method; maintains the benefits of randomization; mirrors real-world practice.
  • Per-protocol (as-treated) analysis: Analyze only those who completed the assigned treatment. Overestimates efficacy; introduces bias because non-completers are often different from completers.
• Strengths: Establishes causation, controls for confounding, internal validity is highest of all designs.
• Weaknesses: Expensive, time-consuming, ethical constraints (cannot randomize to a harmful exposure), strict inclusion/exclusion criteria limit external validity (generalizability), Hawthorne effect.

Crossover Trial

• Same participants receive both the intervention and the control at different time periods, then cross over. Each patient serves as their own control.
• Advantage: Eliminates between-person variability, smaller sample size needed.
• Disadvantage: Carryover effect (first treatment affects the second period). Only valid for conditions that are stable and treatments that are short-acting.

Systematic Review and Meta-Analysis

• Systematic Review: Comprehensive search and critical appraisal of all studies on a question using pre-defined criteria. Synthesizes evidence qualitatively and/or quantitatively.
• Meta-Analysis: Statistical technique that pools data from multiple studies to produce a summary effect estimate with greater precision and power than any single study.
  • Displays results as a forest plot: each study shown as a horizontal line (95% CI) with a box (point estimate) proportional to study weight. The diamond at the bottom = pooled estimate.
  • Key concern: heterogeneity - are the studies similar enough to pool? Measured by I² statistic. I² > 50% suggests substantial heterogeneity.
• Cochrane Database is the main repository for high-quality systematic reviews.
• Limitation: A systematic review cannot compensate for poor-quality primary studies ("garbage in, garbage out"). Quality depends on whether the literature base is adequate and unbiased.

"Systematic reviews should be used with circumspection in conjunction with selective reading of some of the best empirical studies." - Harrison's Principles 22e

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2.3 Study Design Quick-Reference Table

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UNIT 3: MEASURES OF DISEASE FREQUENCY

3.1 Prevalence vs. Incidence

Prevalence ≈ Incidence × Duration

• Prevalence increases if incidence increases, OR if disease duration increases (e.g., better treatment keeps people alive longer - raises prevalence even without more new cases)
• Prevalence decreases if incidence decreases, OR if disease is cured quickly, OR if it kills quickly

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3.2 Attributable Risk (AR) / Risk Difference

• AR = Incidence in exposed - Incidence in unexposed
• Tells you the additional risk attributable specifically to the exposure
• Also called "excess risk" or "absolute risk increase" in the context of harmful exposures

• AR% = AR / Incidence in exposed × 100
• "What percentage of disease in the exposed group is due to this specific exposure?"

• Considers both the AR and the prevalence of exposure in the population
• Relevant for public health: how much disease would be eliminated if the exposure were completely removed from the population?

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UNIT 4: MEASURES OF EFFECT

4.1 The 2x2 Table for Analytic Studies

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4.2 Relative Risk (Risk Ratio) - RR

RR = [a / (a+b)] ÷ [c / (c+d)]

• RR = 1: No association. Exposure does not affect risk.
• RR > 1: Positive association. Exposure INCREASES risk (harmful).
• RR < 1: Negative association. Exposure DECREASES risk (protective).

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4.3 Odds Ratio - OR

OR = (a × d) / (b × c) ← cross-product ratio

• When the disease is rare (prevalence < 5-10%), the OR approximates the RR.
• When the disease is common, OR will overestimate RR if RR > 1, and underestimate RR if RR < 1.

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4.4 Absolute Risk Reduction (ARR) and Number Needed to Treat (NNT)

ARR = Risk in control group - Risk in treatment group

NNT = 1 / ARR

RRR = 1 - RR = ARR / Risk in control group

• Drug A reduces cardiovascular events from 2% to 1% (ARR = 1%, NNT = 100, RRR = 50%)
• Drug B reduces cardiovascular events from 40% to 20% (ARR = 20%, NNT = 5, RRR = 50%)
• Both have the same RRR of 50%, but Drug B is clinically far more impactful.

• NNH = 1 / Absolute Risk Increase (ARI)
• Number of patients who must receive a treatment before one additional patient is harmed
• Compare NNT and NNH to weigh benefits vs. harms

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UNIT 5: HYPOTHESIS TESTING AND STATISTICAL TESTS

5.1 The Hypothesis Framework

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5.2 Errors in Hypothesis Testing

• You conclude there IS a difference when there actually IS NOT
• You reject the null hypothesis falsely
• A "false positive" finding
• Probability = α (significance level), conventionally set at 0.05 (5%)
• Controlled by the significance threshold

• You conclude there IS NO difference when there actually IS one
• You fail to reject the null hypothesis when you should
• A "false negative" finding
• Probability = β, conventionally set at 0.20 (20%)
• More likely to occur with small sample sizes, small effect sizes, and high variability

• The probability of correctly detecting a real difference when it exists
• Conventionally set at ≥ 0.80 (80%)
• Factors that INCREASE power: Larger sample size, larger effect size, lower variance, higher α (but this increases Type I error), one-tailed vs. two-tailed test

"Because falsely concluding that a difference exists is considered a more serious error than the reverse, levels for beta error are set much lower than those for alpha." - Goldman-Cecil Medicine

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5.3 P-value

• P = 0.05 means: if H₀ were true, there is a 5% chance of seeing a difference this large (or larger) by chance alone
• P < 0.05: "statistically significant" - reject H₀
• P ≥ 0.05: "fail to reject H₀" - result is not statistically significant

• A significant p-value does NOT prove the treatment works; it says the result is unlikely to be due to chance
• A non-significant p-value does NOT prove no effect exists; the study may be underpowered
• P-value does NOT tell you about the size or clinical importance of an effect
• With very large sample sizes, trivially small differences will achieve statistical significance - always also assess clinical significance

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5.4 Confidence Intervals (CI)

• If you repeated the study 100 times with different random samples, the CI would contain the true population value 95 of those times
• A narrower CI = more precision (usually larger sample size)
• A wider CI = less precision (smaller sample size or more variability)

• For means: If the 95% CI for the difference includes zero, the result is NOT statistically significant
• For ratios (RR, OR): If the 95% CI includes 1.0, the result is NOT statistically significant (ratio of 1 = no effect)
• This makes intuitive sense: a CI that crosses the "no effect" value means the data are consistent with no difference

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5.5 Sample Size and Power Calculations

1. The minimum clinically meaningful difference you want to detect (effect size)
2. The significance level α (typically 0.05)
3. The desired power 1 - β (typically 0.80)
4. The expected variability (SD for continuous outcomes; baseline event rate for dichotomous)

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5.6 Choosing the Right Statistical Test

• More powerful when assumptions are met
• Required: continuous data, approximately normal distribution, no major outliers

• Used when: ordinal data, non-normal continuous data, small samples, or many outliers

• Ranges from -1 to +1
• r = +1: perfect positive linear association
• r = -1: perfect negative (inverse) linear association
• r = 0: no linear association
• Correlation does NOT imply causation

• Linear regression: Predicts a continuous outcome from one or more continuous predictors
• Logistic regression: Predicts a binary outcome (yes/no) from one or more predictors; outputs odds ratios
• Cox proportional hazards: Used in survival analysis; outputs hazard ratios

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UNIT 6: DIAGNOSTIC TEST PERFORMANCE

6.1 The 2x2 Diagnostic Table

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6.2 Sensitivity and Specificity

Sensitivity = TP / (TP + FN) = a / (a + c)

• Proportion of people WITH disease who test POSITIVE
• A highly sensitive test is rarely negative in true disease
• A negative result with a highly sensitive test effectively rules OUT disease
• Mnemonic: SnNout - high Snsitivity: Negative result rules out disease

Specificity = TN / (TN + FP) = d / (b + d)

• Proportion of people WITHOUT disease who test NEGATIVE
• A highly specific test is rarely positive in the absence of disease
• A positive result with a highly specific test effectively rules IN disease
• Mnemonic: SpPin - high Specificity: Positive result rules in disease

• Prioritize high sensitivity when: missing a case would be dangerous (e.g., HIV screening, cancer screening, dangerous infections). A false negative is the worse error.
• Prioritize high specificity when: false positives lead to significant harm (e.g., chemotherapy, major surgery, stigmatizing diagnoses). A false positive is the worse error.

"A test with a very high sensitivity when negative helps rule out disease (SnNout), and a test with a very high specificity when positive helps rule in disease (SpPin)." - Harrison's Principles 22e

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6.3 Predictive Values

PPV = TP / (TP + FP) = a / (a + b)

• Given a POSITIVE test result, what is the probability that the patient actually HAS the disease?
• PPV increases with increasing prevalence of disease

NPV = TN / (TN + FN) = d / (c + d)

• Given a NEGATIVE test result, what is the probability that the patient actually does NOT have the disease?
• NPV decreases with increasing prevalence of disease

• In a high-prevalence population (50% prevalence): PPV = ~90%
• In a low-prevalence population (1% prevalence): PPV ≈ 8% (only 1 in 12 positive tests is a true positive!)

"Positive and negative predictive values depend on the test characteristics, but importantly they also depend on the prevalence of the disease in this particular population of patients." - Goldman-Cecil Medicine

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6.4 Likelihood Ratios (LR)

1. Are not affected by prevalence
2. Can be used at the bedside with any pre-test probability
3. Can be applied to tests with multiple levels (not just positive/negative)

LR+ = Sensitivity / (1 - Specificity) = True Positive Rate / False Positive Rate

• "How many times more likely is a positive test in a patient WITH disease compared to one WITHOUT?"
• LR+ > 10 = strong positive result, large shift toward disease

LR- = (1 - Sensitivity) / Specificity = False Negative Rate / True Negative Rate

• "How many times more likely is a negative test in a patient WITH disease vs. one WITHOUT?"
• LR- < 0.1 = strong negative result, large shift away from disease

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6.5 Bayes' Theorem (Pre-test → Post-test Probability)

Post-test probability = function of (Pre-test probability + Test result)

1. Convert pre-test probability to pre-test odds: Pre-test odds = p / (1 - p)
2. Multiply: Post-test odds = Pre-test odds × Likelihood Ratio
3. Convert back to probability: Post-test probability = post-test odds / (1 + post-test odds)

• Very low pre-test probability (e.g., 2%): A positive test with LR+ of 10 only raises post-test probability to ~17% - still not high enough to diagnose or treat
• Very high pre-test probability (e.g., 95%): A negative test with LR- of 0.1 only drops post-test probability to ~66% - still too high to rule out disease

"The largest change in diagnostic likelihood following a test result occurs when the clinician is most uncertain (i.e., pretest probability between 30 and 70%)." - Harrison's Principles 22e

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6.6 Receiver Operating Characteristic (ROC) Curve

• Each point on the curve represents a specific threshold value, with its associated sensitivity and specificity
• Moving up the curve → higher sensitivity, lower specificity (more permissive threshold)
• Moving left on the curve → higher specificity, lower sensitivity (stricter threshold)
• The diagonal line (45°) represents a test with no discriminatory ability - equal to random chance (AUC = 0.5)
• A perfect test would be a point at the top-left corner (sensitivity = 1, specificity = 1)

• AUC = 0.5: No discriminatory ability (useless test)
• AUC 0.7 - 0.8: Acceptable
• AUC 0.8 - 0.9: Excellent
• AUC > 0.9: Outstanding

1. Choosing the optimal cut point for a continuous test (based on the clinical cost of false positives vs. false negatives)
2. Comparing the overall accuracy of two or more different tests
3. Demonstrating the sensitivity-specificity trade-off graphically

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UNIT 7: BIAS, CONFOUNDING, AND VALIDITY

7.1 Internal vs. External Validity

High internal validity is a prerequisite for considering external validity. A biased study cannot be generalized.

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7.2 Bias

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7.3 Confounding

1. Is associated with the exposure (risk factor)
2. Is independently associated with the outcome (disease)
3. Is NOT on the causal pathway between exposure and outcome

Confounding is the Achilles heel of observational studies. Randomization is the only method that controls for both measured and unmeasured confounders.

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7.4 Effect Modification (Interaction)

• Effect modification is a biological phenomenon that should be reported, not adjusted away
• Confounding is a bias that should be controlled

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UNIT 8: EVIDENCE-BASED MEDICINE (EBM)

8.1 The Four Steps of EBM

• P - Patient/Population/Problem: Who is the patient? What is their condition?
• I - Intervention: What intervention are you considering?
• C - Comparison: What is the alternative? (placebo, standard of care, another drug)
• O - Outcome: What outcome matters? (mortality, readmission, quality of life, symptom relief)

• Primary sources: PubMed, MEDLINE
• Secondary sources: Cochrane, UpToDate, ClinicalKey, society guidelines

• Internal validity: Was the study conducted without bias?
• External validity: Are results applicable to your patient?
• Assess study design, blinding, randomization, sample size, outcomes

• Integrate study results with your clinical judgment and the patient's values and preferences
• Not all statistically significant findings warrant a change in practice

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8.2 Critical Appraisal of an RCT

1. Was randomization truly random (not just sequential or alternating)?
2. Was allocation concealed until enrollment (to prevent selection bias)?
3. Were patients and investigators blinded?
4. Was the control/comparator appropriate (not a "straw man" comparator)?
5. Was the analysis intention-to-treat (ITT)?
6. Was the study adequately powered? Were power calculations done a priori?
7. Were the outcomes clinically meaningful, or just surrogate endpoints?
8. Were all enrolled patients accounted for at study end?
9. Were groups similar at baseline?

• Surrogate: Lab values, imaging findings (e.g., LDL cholesterol, tumor size). May not correlate with patient outcomes.
• Clinical: Mortality, hospitalization, quality of life, symptom relief. Preferred.

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8.3 Bradford Hill Criteria for Causation

Temporality is the ONLY required criterion - all others add to the likelihood of causation.

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UNIT 9: SCREENING

9.1 Criteria for a Good Screening Test

1. The disease must be an important health problem
2. Treatment for the disease must be available
3. Facilities for diagnosis and treatment must be available
4. There must be a recognizable latent or early symptomatic stage
5. A suitable test or examination must exist
6. The test must be acceptable to the population
7. The natural history must be adequately understood
8. There must be an agreed-upon treatment policy
9. The cost must be economically balanced against expenditure on medical care
10. Case-finding must be a continuous process

• Screening tests prioritize high sensitivity (don't miss cases). False positives are acceptable at this stage.
• Diagnostic tests (confirmatory) prioritize high specificity (confirm the disease before committing to treatment).

9.2 Biases That Affect Screening Studies

• Screening detects disease earlier. Even if survival is no better, patients appear to live longer after diagnosis simply because the diagnosis was made earlier.
• True survival benefit must be measured from birth, not from diagnosis.
• Solution: Compare age-specific mortality rates between screened and unscreened populations (not survival time from diagnosis).

• Screening intervals preferentially detect slowly progressing cases, which are inherently less lethal.
• Fast-progressing (aggressive) tumors are less likely to be caught during a routine screening interval.
• This makes screened cases appear to do better, even without a true survival benefit.

• Screening detects indolent disease that would never have caused symptoms or death. Treating these patients exposes them to harm with no benefit.
• Example: PSA screening for prostate cancer detects many cancers that would never have become clinically significant.

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UNIT 10: SURVIVAL ANALYSIS

10.1 Kaplan-Meier Curves

• The curve drops vertically each time an event occurs
• Censored subjects (lost to follow-up or study ended before their event) are marked with a tick on the curve and then removed from future calculations
• Two groups can be compared visually, and statistically using the log-rank test (p-value for whether the survival curves differ significantly)

10.2 Hazard Ratio (HR)

• Calculated by Cox proportional hazards regression
• The instantaneous rate of event occurrence in one group relative to another at any given time
• HR = 1: No difference
• HR < 1: Event less likely in treatment group (beneficial)
• HR > 1: Event more likely in treatment group (harmful)
• Similar interpretation to RR but appropriate for time-to-event data with censoring

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QUICK-REFERENCE SUMMARY TABLES

Test Metrics at a Glance

Effect Measures and Their Study Designs

Error Types

Bias Types and Prevention

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BIOSTATISTICS STUDY QUESTIONS

1st & 2nd Year Medical School | 40 Questions | MCQ + SAQ

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SECTION A: DATA TYPES & DESCRIPTIVE STATISTICS (Questions 1-6)

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• A) Nominal, ordinal, continuous, ordinal
• B) Ordinal, nominal, continuous, ordinal
• C) Nominal, continuous, ordinal, nominal
• D) Nominal, ordinal, ordinal, continuous
• E) Ordinal, ordinal, continuous, nominal

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• Blood type = nominal (no meaningful order; A, B, AB, O have no ranking)
• Pain score = ordinal (ordered 0-10, but the intervals between scores are not equal - a jump from 1 to 2 may not equal a jump from 7 to 8)
• Serum sodium = continuous (can take any value within a range, with meaningful equal intervals and a true zero)
• Cancer stage = ordinal (I < II < III < IV in severity, but the difference between Stage I and II may not equal the difference between III and IV)

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• A) Mean = Median = Mode
• B) Mean < Median < Mode
• C) Mean > Median > Mode
• D) Median > Mean > Mode
• E) Mode > Mean > Median

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• A) The drug is statistically and clinically significant
• B) The drug is neither statistically nor clinically significant
• C) The drug is statistically significant but may not be clinically significant
• D) The drug is clinically significant but not statistically significant
• E) The confidence interval indicates the result is not significant

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• A) 0.3%
• B) 1%
• C) 2.5%
• D) 5%
• E) 10%

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SECTION B: STUDY DESIGN (Questions 7-15)

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• A) Cross-sectional survey of blood pressure and stroke prevalence
• B) Case-control study matching stroke patients to controls
• C) Prospective cohort study following treated and untreated patients
• D) Randomized double-blind placebo-controlled trial
• E) Systematic review of existing observational studies

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• A) Relative risk
• B) Attributable risk
• C) Odds ratio
• D) Hazard ratio
• E) Incidence rate ratio

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• Directly calculate incidence of colorectal cancer in each group
• Calculate Relative Risk (RR) directly, which is more intuitive than OR
• Study multiple outcomes from a single exposure (e.g., aspirin's effect on MI, GI bleeding, and colorectal cancer simultaneously)
• Avoid recall bias since exposure data are in objective prescription records (not self-report)

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• A) Per-protocol analysis
• B) As-treated analysis
• C) Intention-to-treat (ITT) analysis
• D) Efficacy analysis
• E) Sensitivity analysis

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• A) Alcohol consumption causes elevated liver enzymes
• B) Elevated liver enzymes cause increased alcohol consumption
• C) An association between alcohol intake and elevated liver enzymes exists in this population at this point in time
• D) Alcohol exposure precedes liver enzyme elevation
• E) Randomized trials are now unnecessary to confirm this finding

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• The high I² (68%) raises concerns about whether the pooled result applies uniformly
• Are the studies representative of your patient population? (external validity)
• Was there publication bias (tendency to only publish positive results)?
• What is the NNT? Is the benefit clinically meaningful?
• Are there safety signals in the individual studies?
• Do existing guidelines support this change?

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• A) The randomization failed and the study is invalid
• B) High uric acid is likely a side effect of the new drug
• C) This finding is likely a Type I error due to multiple comparisons
• D) Uric acid is a confounder and must be adjusted for
• E) The alpha level should be reduced for future trials

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• A) Prospective cohort study
• B) Randomized controlled trial
• C) Case-control study
• D) Cross-sectional study
• E) Ecological study

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SECTION C: MEASURES OF EFFECT (Questions 16-21)

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• A) 1.5
• B) 2.67
• C) 4.0
• D) 6.0
• E) 8.0

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• Risk in smokers = 80/400 = 0.20 (20%)
• Risk in non-smokers = 30/600 = 0.05 (5%)
• RR = 0.20 / 0.05 = 4.0

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• A) 4
• B) 8
• C) 12
• D) 25
• E) 33

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• ARR = 12% - 8% = 4% = 0.04
• NNT = 1/ARR = 1/0.04 = 25

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• A) 40% absolute reduction (down to 18%)
• B) 2% absolute reduction (down to 28%)
• C) 12% absolute reduction (down to 18%)
• D) 50% absolute reduction (down to 15%)
• E) The NNT cannot be applied to this patient

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• Stroke rate in treatment group: 1.5%/year
• Stroke rate in control group: 2.5%/year
• Major bleeding rate in treatment group: 3.0%/year
• Major bleeding rate in control group: 2.0%/year

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• ARR = 2.5% - 1.5% = 1.0%/year
• NNT = 1/0.01 = 100 patients treated per year to prevent 1 stroke

• ARI (absolute risk increase) = 3.0% - 2.0% = 1.0%/year
• NNH = 1/0.01 = 100 patients treated per year to cause 1 major bleed

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• A) The study population is very large
• B) The disease under study is rare (< 5% prevalence)
• C) The control group is matched to the case group
• D) The exposure is rare in the population
• E) The study has a long follow-up period

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SECTION D: DIAGNOSTIC TESTS (Questions 22-30)

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• A) 9
• B) 10
• C) 85
• D) 99
• E) 108

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• Disease present = 10 patients; Disease absent = 990 patients
• TP = 85% of 10 = 8.5 ≈ 9
• FP = (1 - specificity) × 990 = 10% × 990 = 99

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• TP = 9 (0.85 × 10), FN = 1, FP = 99 (0.10 × 990), TN = 891

• Disease present = 200; Disease absent = 800
• TP = 170 (0.85 × 200), FN = 30, FP = 80 (0.10 × 800), TN = 720

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• A) High specificity
• B) High sensitivity
• C) High positive predictive value
• D) High negative predictive value
• E) Low likelihood ratio positive

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• A) 30%
• B) 46%
• C) 62%
• D) 80%
• E) 95%

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• LR+ = Sensitivity / (1 - Specificity) = 0.80 / 0.05 = 16
• Pre-test odds = 0.05 / (1 - 0.05) = 0.05/0.95 = 0.0526
• Post-test odds = 0.0526 × 16 = 0.842
• Post-test probability = 0.842 / (1 + 0.842) = 0.842/1.842 = 45.7% ≈ 46%

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• Deciding to initiate broad-spectrum antibiotics in a patient where resistance risk is high
• Confirming HIV before disclosing a positive result to a patient
• Deciding to proceed with a high-risk surgical procedure
• Confirming cancer before starting chemotherapy In these cases, you want near-certainty before acting (SpPin - high specificity, positive result rules in disease).

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• A) It increases to > 90%
• B) It remains at 85%
• C) It drops to approximately 30%
• D) It drops to approximately 17%
• E) It drops to near zero

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• LR- = 0.035
• Pre-test odds = 0.85 / 0.15 = 5.67
• Post-test odds = 5.67 × 0.035 = 0.198
• Post-test probability = 0.198 / 1.198 = 16.5% ≈ 17%

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• A) Sensitivity increases, specificity decreases
• B) Sensitivity decreases, specificity increases
• C) Both sensitivity and specificity increase
• D) Both sensitivity and specificity decrease
• E) PPV decreases, NPV decreases

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• A) The nocebo effect
• B) Berkson's bias
• C) Bayes' theorem
• D) The Bradford Hill criteria
• E) The Hawthorne effect

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• LR+ = Sensitivity / (1 - Specificity) - how much a positive result increases the probability of disease
• LR- = (1 - Sensitivity) / Specificity - how much a negative result decreases the probability of disease

1. Estimate your patient's pre-test probability from clinical context
2. Apply the LR to convert pre-test → post-test probability

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SECTION E: HYPOTHESIS TESTING, BIAS & CONFOUNDING (Questions 31-40)

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• A) The larger trial committed a Type I error
• B) The smaller trial was likely underpowered (Type II error)
• C) The p-value of 0.12 proves no difference exists
• D) The larger trial's result is clinically more significant
• E) Both trials have the same statistical power

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• A) Drug A is significantly better than Drug B
• B) Drug B is significantly better than Drug A
• C) The difference between drugs is not statistically significant
• D) The study was overpowered
• E) The result is clinically significant

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1. Smoking is associated with the exposure (coffee consumption) - smokers tend to drink more coffee
2. Smoking is independently associated with the outcome (Parkinson's disease) - epidemiological studies show smoking appears to reduce Parkinson's risk
3. Smoking is not on the causal pathway between coffee and Parkinson's - it acts as a separate variable, not a mediator

• Restriction: Analyze only non-smokers and assess if the coffee-Parkinson's association persists
• Matching: Match coffee drinkers and non-drinkers on smoking status at study entry
• Stratified analysis: Calculate RR separately for smokers and non-smokers, then compare
• Multivariable (logistic/Cox) regression: Include smoking as a covariate to estimate the coffee effect adjusted for smoking
• Propensity score methods: Create a propensity score for coffee drinking that balances smoking status

• Perform stratified analysis: Calculate the RR for coffee and Parkinson's separately in smokers and non-smokers
• If the RR is the same in both strata → smoking is a confounder (report a single adjusted RR)
• If the RR differs meaningfully between strata → smoking is an effect modifier (the effect of coffee on Parkinson's is different in smokers vs. non-smokers; report stratified results separately)
• Effect modification is a biological reality to be reported; confounding is a bias to be controlled.

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• A) Confounding
• B) Lead-time bias
• C) Recall bias
• D) Selection bias
• E) Observer-expectancy bias

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• A) Recall bias and selection bias
• B) Lead-time bias and length bias
• C) Confounding and information bias
• D) Volunteer bias and observer bias
• E) Hawthorne effect and nocebo effect

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• A) Recall bias
• B) Placebo effect
• C) Confounding
• D) Effect modification
• E) Berkson's bias

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• A) Recall bias
• B) Lead-time bias
• C) Loss-to-follow-up bias (attrition bias)
• D) Length bias
• E) Hawthorne effect

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1. Temporality (required): Children must have been exposed to power lines/EMF before developing leukemia, not after diagnosis. Longitudinal study data showing exposure preceded disease onset is essential.
2. Strength of association: The relative risk or odds ratio should be large and robust. A weak association (e.g., RR = 1.1) is more easily explained by confounding or bias. A strong association (e.g., RR > 3) is harder to explain by chance.
3. Dose-response relationship: Children living closer to power lines, or with higher measured EMF exposure, should have proportionally higher leukemia rates. A clear gradient strengthens causal arguments.
4. Consistency: The association should be replicated across multiple independent studies in different countries, populations, and research groups. A finding unique to one study is less convincing.
5. Biological plausibility: There should be a known or proposed biological mechanism by which EMF could damage DNA or disrupt normal cell cycling to promote leukemia. Without a plausible mechanism, the association remains unexplained.
6. Specificity: EMF exposure should be specifically linked to leukemia (or at least a defined spectrum of malignancies), not associated with every disease simultaneously.
7. Experiment: Animal studies or controlled experiments exposing cells/animals to similar EMF levels should produce leukemia-promoting effects.

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• A) A case-control study is preferred because mortality is a common outcome
• B) A cross-sectional study would be adequate because it measures both exposure and outcome
• C) A double-blind RCT is ideal but an observational cohort could be used if an RCT is impractical
• D) A meta-analysis should be performed first before any primary research is conducted
• E) A case series of Metformin-treated patients would provide sufficient evidence

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ANSWER KEY SUMMARY

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