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Medical Biostatistics Questions for MD Pharmacology Students

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1. TYPES OF DATA AND SCALES OF MEASUREMENT

• Classify types of data in biostatistics with examples from pharmacology.
• Differentiate between nominal, ordinal, interval, and ratio data with drug examples.
• What is the difference between discrete and continuous data?

• Explain different types of variables used in clinical research. Give examples relevant to drug trials.

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2. MEASURES OF CENTRAL TENDENCY AND DISPERSION

• Define mean, median, and mode. When is each preferred in clinical data?
• Define standard deviation (SD) vs. standard error of mean (SEM). Why is SEM always smaller than SD?
• What is variance? How is it related to SD?
• Define range, interquartile range (IQR), and coefficient of variation (CV).
• When do you use SEM vs. SD in reporting drug trial results?

• In a skewed distribution of drug plasma levels, which measure of central tendency is preferred?
• If the SD of a dataset is 0, what does that mean?

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3. NORMAL DISTRIBUTION AND PROBABILITY

• What is a normal (Gaussian) distribution? State its properties.
• What percentage of values fall within ±1 SD, ±2 SD, ±3 SD of the mean?
• What is a skewed distribution? Positive vs. negative skew.
• Define kurtosis.
• What is the Central Limit Theorem? Why is it important in biostatistics?

• A drug's plasma concentration data shows positive skew. Which statistical test would you apply?

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4. HYPOTHESIS TESTING

• Define null hypothesis and alternative hypothesis. What is a Type I error (alpha error) and Type II error (beta error)? How can each be minimized?
• Explain the concept of statistical significance. What does a p-value of 0.03 mean?

• Difference between one-tailed and two-tailed tests.
• What is the level of significance (alpha)? Why is 0.05 commonly used?
• What is the difference between a p-value and a confidence interval?

• A drug trial shows p = 0.049 for efficacy. How do you interpret this?
• What are the limitations of relying solely on the p-value?

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5. P-VALUE AND CONFIDENCE INTERVALS

• Define p-value. What does p < 0.05 signify?
• Define 95% confidence interval. How do you interpret a CI for an odds ratio that includes 1?
• What is the difference between statistical significance and clinical significance?

• A 95% CI for a relative risk is 0.8 to 1.3. Is this result statistically significant? What does it mean clinically?
• Why might a result with p = 0.001 still not be clinically meaningful?

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6. STATISTICAL TESTS - SELECTION AND APPLICATION

• How do you select an appropriate statistical test? Explain with a flow chart.
• Compare parametric vs. non-parametric tests. When is each used in drug trials?

• Student's t-test: paired vs. unpaired. When is each used?
• ANOVA (Analysis of Variance): purpose and when to use.
• Chi-square test: purpose, when to use, and limitations.
• Fisher's exact test: when is it preferred over chi-square?
• Mann-Whitney U test: when to use instead of unpaired t-test?
• Wilcoxon signed rank test vs. paired t-test.
• Kruskal-Wallis test: non-parametric alternative to ANOVA.
• Pearson's correlation vs. Spearman's rank correlation.

• A researcher compares blood pressure reduction between 2 drugs in 15 patients each. Data is normally distributed. Which test is used? (Unpaired t-test)
• Drug efficacy is tested before and after treatment in the same 20 patients. Which test is used? (Paired t-test)
• Comparing a drug's effect on pain scores across 3 groups; data is non-normal. Which test? (Kruskal-Wallis)

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7. STUDY DESIGNS

• Classify clinical study designs. Describe the hierarchy of evidence.
• Compare randomized controlled trial (RCT), cohort study, case-control study, and cross-sectional study - with advantages and limitations of each.
• What is the difference between a prospective and retrospective study?

• What is a cross-over study? What are its advantages in drug trials?
• What is a case series vs. case report?
• What is an ecological study? What is the ecological fallacy?
• Describe the concept of "intention-to-treat" (ITT) analysis vs. per-protocol analysis.
• What is a pragmatic trial vs. explanatory trial?

• Why is an RCT considered the gold standard for drug efficacy?
• What is a factorial design in clinical trials?
• What is a basket trial / umbrella trial (adaptive design)?

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8. RANDOMIZATION AND BLINDING

• What is randomization? What are the types (simple, block, stratified, cluster)?
• Why is blinding important in drug trials? Differentiate single-blind, double-blind, triple-blind.
• What is allocation concealment? How does it differ from blinding?

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9. PHASES OF CLINICAL TRIALS

• Describe the phases of clinical drug trials (Phase I to Phase IV) with objectives, sample size, and significance of each.

• What is a Phase 0 trial?
• What is a Phase IV (post-marketing surveillance) trial? What is pharmacovigilance?
• What is an Investigational New Drug (IND) application?

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10. MEASURES OF ASSOCIATION AND RISK

• Define and calculate: Relative Risk (RR), Odds Ratio (OR), Attributable Risk (AR), Population Attributable Risk (PAR), and Number Needed to Treat (NNT). Give clinical examples.

• When is odds ratio used instead of relative risk?
• Relative risk reduction (RRR) vs. absolute risk reduction (ARR): which is more clinically useful?
• What is Number Needed to Harm (NNH)?
• What is the significance of NNT = 1?

• RR = [a/(a+b)] / [c/(c+d)]
• OR = (a×d) / (b×c)
• ARR = Risk in control - Risk in intervention
• NNT = 1/ARR
• RRR = 1 - RR

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11. SENSITIVITY, SPECIFICITY, PREDICTIVE VALUES (2x2 TABLE)

• Explain sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) using a 2×2 table. How does disease prevalence affect PPV and NPV?

• Define likelihood ratio (positive and negative).
• What is ROC curve? What does AUC represent?
• What is the difference between sensitivity and specificity? Which is more important for a screening drug/test vs. a confirmatory test?
• Define Youden's index.

• Explain Bayes' theorem and its application to diagnostic testing.
• If the prevalence of a disease drops, what happens to PPV?

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12. SAMPLING METHODS

• Define population vs. sample.
• Types of sampling: simple random, systematic, stratified, cluster, convenience, snowball.
• What is sampling error? What is sampling bias?
• What is the difference between sampling error and non-sampling error?

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13. SAMPLE SIZE CALCULATION

• What factors determine sample size in a drug trial?
• Define alpha error, beta error, power of a study, and effect size. How are they related to sample size?
• Why does increasing the sample size reduce Type II error?

• A clinical trial has 80% power. What does this mean?
• What happens to sample size requirement if alpha is changed from 0.05 to 0.01?

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14. BIAS AND CONFOUNDING

• Define bias. Classify the types of bias in clinical research (selection bias, information bias, observer bias, lead time bias, attrition bias). How can each be minimized?
• What is confounding? How is it controlled (restriction, matching, randomization, multivariable analysis)?

• What is Berkson's bias?
• What is Hawthorne effect?
• What is detection bias vs. recall bias?
• What is channeling bias in pharmacology?

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15. CORRELATION AND REGRESSION

• Define Pearson's correlation coefficient (r). Interpret r = +0.9 and r = -0.1.
• What is linear regression? What is the regression equation?
• What is multiple regression? When is it used?
• Logistic regression: when is it used vs. linear regression?
• What is multicollinearity?

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16. SURVIVAL ANALYSIS

• What is survival analysis? What is a survival curve (Kaplan-Meier curve)?
• What is the log-rank test? When is it used?
• Define hazard ratio. How is it interpreted?
• What is censoring in survival data?

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17. META-ANALYSIS AND SYSTEMATIC REVIEW

• What is a systematic review? How does it differ from a narrative review and a meta-analysis?
• What is a Forest plot? How do you interpret it?
• Define heterogeneity in meta-analysis (I² statistic). What I² value is acceptable?
• What is publication bias? How is it detected (funnel plot)?

• What is a funnel plot? What does an asymmetric funnel plot suggest?
• Fixed-effects vs. random-effects model in meta-analysis.
• What is GRADE (Grading of Recommendations Assessment, Development and Evaluation)?

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18. EVIDENCE-BASED MEDICINE (EBM) AND CLINICAL EPIDEMIOLOGY

• Define Evidence-Based Medicine (EBM). Explain the PICO framework with an example from pharmacology.
• What is the hierarchy of evidence (levels of evidence)? Draw the evidence pyramid.

• What is a clinical practice guideline? How is it developed?
• What is critical appraisal of literature?
• Define internal validity vs. external validity of a study.

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19. MEASURES OF MORBIDITY AND MORTALITY (EPIDEMIOLOGY INTERFACE)

• Define incidence vs. prevalence.
• What is point prevalence vs. period prevalence?
• Define attack rate, case fatality rate, crude death rate.
• What is standardization of rates? Direct vs. indirect standardization.

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20. PHARMACOSTATISTICS / SPECIFIC TO PHARMACOLOGY

• What is dose-response curve? How is EC50 calculated statistically?
• What is bioequivalence? What statistical method is used to prove bioequivalence (TOST - two one-sided test)?
• Define AUC (area under the curve): statistical vs. pharmacokinetic meaning.
• What is inter-individual vs. intra-individual variability in pharmacokinetic studies?
• What is a probit analysis? What is it used for in pharmacology (LD50, ED50)?

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IMPORTANT VIVA / SHORT NOTE DEFINITIONS TO KNOW

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FREQUENTLY ASKED EXAMINATION QUESTIONS (NMC / University Pattern)

1. Write a short note on p-value and confidence interval.
2. Explain Type I and Type II errors with examples in drug trials.
3. Describe the phases of a clinical trial.
4. Write a note on randomized controlled trial - design, merits, and limitations.
5. Define sensitivity and specificity. Construct a 2×2 table.
6. What is NNT? How is it calculated? Give an example.
7. Explain meta-analysis and systematic review. What is a forest plot?
8. Describe the methods to control confounding in clinical research.
9. Write a note on sample size calculation - factors affecting it.
10. Differentiate parametric from non-parametric statistical tests with examples.
11. What is bioequivalence? How is it statistically established?
12. Explain the PICO framework with an example.
13. Write on survival analysis and Kaplan-Meier curves.
14. What is publication bias? How is it detected?
15. Explain relative risk, odds ratio, and attributable risk with formulae.

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COMPLETE ANSWERS: Medical Biostatistics for MD Pharmacology

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SECTION 1: TYPES OF DATA AND SCALES OF MEASUREMENT

Q. Classify types of data in biostatistics with examples from pharmacology.

• Nominal: Categories with no inherent order. Examples: blood group (A, B, AB, O), sex (male/female), type of adverse drug reaction (rash, vomiting, headache).
• Ordinal: Categories with a meaningful order but unequal intervals. Examples: pain score (mild/moderate/severe), drug response (no response/partial/complete), WHO toxicity grading.

• Discrete: Counted values, whole numbers only. Examples: number of tablets taken, number of adverse events per patient.
• Continuous: Measured values, can take any value within a range. Sub-classified as:
  • Interval: Equal intervals, no true zero. Example: temperature in Celsius (°C).
  • Ratio: Equal intervals with a true zero. Examples: drug plasma concentration (mg/L), weight (kg), blood pressure (mmHg), AUC.

Q. Difference between discrete and continuous data.

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SECTION 2: MEASURES OF CENTRAL TENDENCY AND DISPERSION

Q. Define Mean, Median, and Mode. When is each preferred?

• Sum of all values divided by the number of observations.
• Formula: x̄ = Σx / n
• Preferred when: Data is normally distributed (e.g., reporting mean serum drug levels in a symmetric distribution).
• Disadvantage: Affected by extreme values (outliers).

• The middle value when data is arranged in ascending order. If n is even, median = average of the two middle values.
• Preferred when: Data is skewed or has outliers (e.g., income data, duration of hospital stay, serum bilirubin).
• Advantage: Not affected by extreme values.

• The value that occurs most frequently.
• Preferred when: Identifying the most common category (e.g., the most common adverse reaction reported).
• A dataset can be unimodal, bimodal, or multimodal.

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Q. Define Standard Deviation (SD) vs. Standard Error of Mean (SEM). Why is SEM always smaller?

• Measures the spread/variability of individual observations around the mean within a sample.
• Formula: SD = √[Σ(x - x̄)² / (n-1)]
• Describes the distribution of data in the sample.
• Use SD when describing the variability of a dataset.

• Measures how precisely the sample mean estimates the true population mean.
• Formula: SEM = SD / √n
• Describes the precision of the estimate.
• Use SEM when reporting confidence of a mean estimate.

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Q. Define Range, Interquartile Range (IQR), and Coefficient of Variation (CV).

• Range: Difference between the maximum and minimum values. Simple but very sensitive to outliers.
• Interquartile Range (IQR): Difference between the 75th percentile (Q3) and 25th percentile (Q1). IQR = Q3 - Q1. Robust measure of spread, not affected by outliers. Used with median.
• Coefficient of Variation (CV): CV = (SD / Mean) × 100%. A dimensionless measure that allows comparison of variability between datasets with different units or magnitudes. Useful in pharmacokinetics to compare variability of different parameters.

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SECTION 3: NORMAL DISTRIBUTION AND PROBABILITY

Q. What is a Normal (Gaussian) Distribution? State its properties.

1. Symmetric around the mean.
2. Mean = Median = Mode (all three coincide).
3. The curve is bell-shaped and unimodal.
4. Defined by two parameters: mean (μ) and standard deviation (σ).
5. Asymptotic to the x-axis (the curve never touches zero).
6. Total area under the curve = 1 (or 100%).

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

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Q. What is skewed distribution? Positive vs. negative skew.

• Tail pulled toward the right (higher values).
• Mean > Median > Mode.
• Example: serum bilirubin levels, drug concentration in a population where a few patients are rapid metabolizers with very high drug levels.

• Tail pulled toward the left (lower values).
• Mean < Median < Mode.
• Example: age at death in a developed country (most people live long, fewer die young).

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Q. Central Limit Theorem (CLT)

• Allows use of parametric statistics even when population distribution is unknown, provided sample size is large enough (generally n ≥ 30).
• Justifies use of t-tests in drug trials even when the underlying pharmacokinetic parameters are not perfectly normally distributed.

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SECTION 4: HYPOTHESIS TESTING

Q. Define null hypothesis and alternative hypothesis. Explain Type I and Type II errors.

• States that there is no difference between groups (e.g., "Drug A and Drug B have equal antihypertensive efficacy").
• The hypothesis we attempt to reject.

• States that a difference does exist (e.g., "Drug A is more effective than Drug B").
• Can be one-directional (one-tailed) or non-directional (two-tailed).

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• Rejecting the null hypothesis when it is actually TRUE.
• Concluding a drug works when it actually does not.
• Probability = alpha (α), conventionally set at 0.05 (5%).
• Minimized by: lowering alpha (e.g., to 0.01), using Bonferroni correction for multiple comparisons.

• Failing to reject the null hypothesis when it is actually FALSE.
• Concluding a drug does not work when it actually does.
• Probability = beta (β), conventionally accepted at 0.20 (20%).
• Minimized by: increasing sample size, increasing alpha (but this raises Type I error risk).

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Q. One-tailed vs. Two-tailed tests.

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SECTION 5: P-VALUE AND CONFIDENCE INTERVALS

Q. Define p-value. What does p < 0.05 signify?

• p-value does NOT measure the size or clinical importance of the difference.
• p-value does NOT tell you the probability that H₀ is true.
• A small p can arise from a clinically trivial difference if the sample size is very large.
• p = 0.049 and p = 0.051 are statistically very similar, yet one crosses the arbitrary threshold.

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Q. Define 95% Confidence Interval (CI). How do you interpret CI for an odds ratio?

• If the 95% CI for a mean blood pressure reduction is 8-12 mmHg, the true average effect in the population lies between 8 and 12 mmHg with 95% confidence.
• For OR or RR: If the 95% CI includes 1.0, the result is NOT statistically significant (no difference).
  • OR = 2.5 (95% CI: 1.3 - 4.8) → Significant (CI does not include 1).
  • OR = 1.8 (95% CI: 0.9 - 3.6) → NOT significant (CI crosses 1).

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Q. Statistical significance vs. clinical significance.

• Statistical significance: A difference unlikely to have arisen by chance (p < 0.05). Dependent on sample size.
• Clinical significance: A difference large enough to matter in clinical practice. Expressed as effect size (e.g., mean difference, NNT, hazard ratio).

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SECTION 6: STATISTICAL TESTS

Q. How to select a statistical test?

• Compare groups / test association / measure correlation?

• Categorical (nominal/ordinal) or Numerical (continuous/discrete)?

• 2 groups or >2 groups?

• Yes → Parametric; No → Non-parametric.

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Q. Parametric vs. Non-parametric tests.

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Q. Student's t-test: paired vs. unpaired.

• Compares means of two independent groups.
• Example: Compare mean diastolic BP in patients on Drug A (n=30) vs. Drug B (n=30) - two separate groups.
• Assumption: Both groups normally distributed, similar variance.

• Compares means within the same group measured twice (before/after) or matched pairs.
• Example: Compare mean BP before and after giving Drug A in the same 20 patients.
• More powerful than unpaired t-test because within-subject variability is removed.

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Q. ANOVA (Analysis of Variance)

• Used to compare means across three or more independent groups.
• Null hypothesis: All group means are equal.
• Produces an F-statistic. If p < 0.05, at least one group differs.
• Post-hoc tests (Tukey, Bonferroni) needed to identify which specific groups differ.
• Example: Compare mean analgesic effect of Paracetamol vs. Ibuprofen vs. Diclofenac.

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Q. Chi-square test.

• Tests for association between two categorical variables.
• Compares observed frequencies to expected frequencies.
• Example: Is there an association between sex (male/female) and occurrence of an adverse drug reaction (yes/no)?
• Assumptions: Expected cell frequencies ≥ 5 in all cells.
• Fisher's Exact Test: Used when any expected cell frequency < 5 or when n is small.

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SECTION 7: STUDY DESIGNS

Q. Hierarchy of Evidence (Evidence Pyramid)

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 / Animal studies (lowest)

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Q. Compare RCT, Cohort, Case-Control, and Cross-Sectional studies.

• Participants randomly assigned to intervention or control.
• Gold standard for efficacy of interventions.
• Advantages: Eliminates confounding, minimizes bias, establishes causality.
• Disadvantages: Expensive, time-consuming, ethical limitations, not feasible for rare diseases.
• Used for: Testing drug efficacy.

• Subjects grouped by exposure, followed forward in time to measure outcomes.
• Can be prospective or retrospective.
• Measures incidence and relative risk (RR).
• Advantages: Good for common outcomes, can study multiple outcomes.
• Disadvantages: Time-consuming, expensive, loss to follow-up, not ideal for rare diseases.
• Used for: Long-term drug safety, pharmacovigilance.

• Starts with outcome (cases = disease present, controls = disease absent), looks back at exposure.
• Retrospective. Calculates odds ratio (OR).
• Advantages: Ideal for rare diseases, quick and cheap, can study multiple exposures.
• Disadvantages: Subject to recall bias, cannot calculate incidence or RR directly, selection of controls is difficult.
• Used for: Studying rare adverse drug reactions.

• Measures exposure and outcome simultaneously at one point in time.
• Calculates prevalence.
• Advantages: Fast, cheap, good for prevalence estimates.
• Disadvantages: Cannot establish causality (no temporal sequence), prevalence-incidence bias.
• Used for: Drug utilization surveys, prevalence of adverse reactions.

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Q. Intention-to-Treat (ITT) vs. Per-Protocol Analysis.

• Analyzes all participants as originally randomized, regardless of whether they completed the treatment.
• Preferred because it preserves the benefits of randomization.
• Gives a conservative (real-world) estimate of efficacy.
• Minimizes attrition bias.

• Analyzes only patients who completed the treatment as planned.
• Gives a more optimistic (ideal conditions) estimate of efficacy.
• Prone to bias because dropouts may differ systematically from completers.

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Q. Cross-over Study.

• Each subject acts as their own control - eliminates inter-individual variability.
• Requires fewer subjects (more efficient).
• Very useful in pharmacokinetic/pharmacodynamic studies.

• Risk of carryover effect if washout is inadequate.
• Not suitable for diseases that change over time or for curative treatments.

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SECTION 8: RANDOMIZATION AND BLINDING

Q. Types of Randomization.

1. Simple randomization: Like flipping a coin. Suitable for large trials; may result in unequal group sizes in small trials.
2. Block randomization: Participants randomized in blocks to ensure equal group sizes at any point during the trial. E.g., blocks of 4 or 6.
3. Stratified randomization: Randomization within subgroups (strata) defined by important variables (e.g., age, disease severity) to ensure balance. Usually combined with block randomization.
4. Cluster randomization: Entire groups (e.g., hospitals, villages) rather than individuals are randomized. Used in community interventions.

Q. Blinding - Single, Double, Triple.

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SECTION 9: PHASES OF CLINICAL TRIALS

Q. Phases of Clinical Drug Trials (Phase I-IV)

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SECTION 10: MEASURES OF ASSOCIATION AND RISK

The 2×2 Table (Master Table for All Calculations)

                 Disease Present (D+)    Disease Absent (D-)
Exposed (E+)          a                        b
Not Exposed (E-)      c                        d

Q. All Measures of Association - Definitions and Formulas

• Used in RCTs and cohort studies.
• RR = [a/(a+b)] ÷ [c/(c+d)]
• Interpretation: RR = 2 means the exposed group has double the risk of developing the disease compared to unexposed.
• RR = 1: No association. RR > 1: Increased risk. RR < 1: Protective.

• Used in case-control studies (cannot calculate incidence, so cannot calculate RR).
• OR = (a × d) / (b × c)
• When disease is rare, OR approximates RR.
• Interpretation same as RR: OR = 1 means no association.

• RRR = 1 - RR = (Risk in control - Risk in treatment) / Risk in control
• Expressed as percentage. Example: RRR = 40% means the drug reduced the risk by 40% relative to control.

• ARR = Risk in control - Risk in treatment = c/(c+d) - a/(a+b)
• More clinically meaningful than RRR because it accounts for baseline risk.

• NNT = 1 / ARR
• The number of patients you need to treat to prevent one additional adverse outcome.
• NNT = 1: Perfect (every patient treated benefits).
• NNT = 100: You need to treat 100 patients to prevent one outcome.
• Lower NNT = more effective drug.

• NNH = 1 / Absolute Risk Increase
• Number of patients exposed to a drug to cause one additional harmful event.
• Higher NNH = safer drug.

• Same as ARR: AR = [a/(a+b)] - [c/(c+d)]
• The excess risk attributable to the exposure.

• PAR = Total disease rate - Risk in unexposed
• Indicates how much disease in the total population is attributable to the exposure.

• Drug A: 10/100 patients had a heart attack.
• Placebo: 20/100 patients had a heart attack.
• RR = (10/100) ÷ (20/100) = 0.5
• RRR = 1 - 0.5 = 50%
• ARR = 20/100 - 10/100 = 0.10 (10%)
• NNT = 1/0.10 = 10

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SECTION 11: SENSITIVITY, SPECIFICITY, PPV, NPV

Q. Sensitivity, Specificity, PPV, NPV - Complete Answer

              Disease Present    Disease Absent
Test Positive    TP (a)             FP (b)
Test Negative    FN (c)             TN (d)

• = TP / (TP + FN) = a / (a + c)
• Probability of testing positive when disease IS present.
• A highly sensitive test rarely misses disease. Used for screening.
• SnOut: A highly Sensitive test, when Negative, rules OUT disease.

• = TN / (TN + FP) = d / (b + d)
• Probability of testing negative when disease is ABSENT.
• A highly specific test rarely gives false positives. Used for confirmation.
• SpIn: A highly Specific test, when Positive, rules In disease.

• = TP / (TP + FP) = a / (a + b)
• Probability that the patient has disease given a POSITIVE test.
• Depends on prevalence: PPV increases when prevalence is high.

• = TN / (TN + FN) = d / (c + d)
• Probability that the patient does NOT have disease given a NEGATIVE test.
• Depends on prevalence: NPV decreases when prevalence is high.

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Q. Likelihood Ratios.

• LR+ = Sensitivity / (1 - Specificity)
• How much more likely is a positive test in a diseased vs. non-diseased person.
• LR+ > 10 = very strong evidence for disease.

• LR- = (1 - Sensitivity) / Specificity
• LR- < 0.1 = very strong evidence against disease.

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Q. ROC Curve (Receiver Operating Characteristic Curve).

• A graph that plots Sensitivity (y-axis) vs. 1 - Specificity (x-axis) at various threshold values.
• Used to determine the optimal cutoff value for a diagnostic test.
• The optimal cutoff is the point closest to the upper-left corner.
• AUC (Area Under the Curve): Measures overall test accuracy.
  • AUC = 1.0: Perfect test.
  • AUC = 0.5: No better than chance (diagonal line).
  • AUC > 0.8: Good test.
• ROC curves allow comparison of different diagnostic tests on the same graph.

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Q. Bayes' Theorem.

1. The sensitivity (P(T+|D)) of the test.
2. The prior probability / prevalence of disease (P(D)).

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SECTION 12: SAMPLING METHODS

Q. Types of Sampling.

1. Simple Random Sampling: Each individual has an equal chance. Use random number tables or computer-generated random numbers.
2. Systematic Random Sampling: Select every k-th individual from a list (e.g., every 5th patient in a ward register). k = N/n (population size/sample size).
3. Stratified Random Sampling: Divide population into subgroups (strata) based on a characteristic (e.g., age groups), then randomly sample from each stratum. Ensures representation of all subgroups.
4. Cluster Sampling: Naturally occurring groups (clusters, e.g., hospitals, villages) are randomly selected, and all or a random sample within each cluster are studied. Useful when a complete sampling frame is unavailable.

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SECTION 13: SAMPLE SIZE CALCULATION

Q. Factors affecting sample size.

1. Alpha (α): The acceptable Type I error rate. Lower α (e.g., 0.01 vs. 0.05) → larger sample size needed.
2. Beta (β): The acceptable Type II error rate. Lower β → larger sample size.
3. Power (1 - β): Desired probability of detecting a real difference. Higher power (e.g., 90% vs. 80%) → larger sample.
4. Effect size (d): The minimum clinically meaningful difference expected between groups. Smaller effect size → larger sample needed.
5. Variability (SD): Greater variability in the outcome → larger sample needed.
6. Study design: Paired designs require fewer subjects than unpaired designs.
7. Dropout rate: Expected loss to follow-up necessitates inflating the calculated sample.

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Q. What is Power?

• Power = 1 - β = probability of correctly rejecting a false null hypothesis.
• Power = 80% means there is an 80% chance the study will detect a true difference if it exists, and a 20% chance of missing it (Type II error).
• Standard acceptable power = 80% (β = 0.20), but 90% is preferred for pivotal trials.
• Power increases with: larger sample size, larger effect size, lower variability, higher alpha.

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SECTION 14: BIAS AND CONFOUNDING

Q. Define Bias. Classify with examples.

• Berkson's bias: Hospital-based case-control studies over-represent sick individuals in both cases and controls, distorting the OR.
• Healthy worker effect: Workers appear healthier than the general population because severely ill people cannot work.
• Attrition/Dropout bias: Differential loss to follow-up between groups.

• Recall bias: Cases remember past exposures better than controls (common in case-control studies). Example: mothers of malformed infants remember drug exposures more accurately than controls.
• Observer/Interviewer bias: The investigator's knowledge of the subject's exposure status influences how outcomes are assessed. Minimized by blinding.
• Hawthorne effect: Subjects change their behavior because they know they are being studied.
• Detection bias: One group is more closely monitored, so outcomes are detected more often in that group.
• Lead time bias: Early detection of disease makes survival appear longer without actually prolonging life (relevant for screening studies).

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Q. Confounding - Definition and Control.

1. Associated with the exposure.
2. Associated with the outcome.
3. NOT on the causal pathway between exposure and outcome.

1. Randomization: Best method - distributes both known and unknown confounders equally.
2. Restriction: Limit study to subjects within a narrow range of the confounding variable.
3. Matching: Match cases and controls on the confounder variable (used in case-control studies).

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SECTION 15: CORRELATION AND REGRESSION

Q. Pearson's Correlation Coefficient (r).

• Measures the strength and direction of a linear relationship between two continuous normally distributed variables.
• Range: -1 to +1.
• r = +1: Perfect positive linear relationship.
• r = -1: Perfect negative linear relationship.
• r = 0: No linear relationship.
• r = +0.9: Strong positive correlation (e.g., dose and plasma concentration).
• r = -0.1: Very weak negative correlation (essentially no relationship).
• Caution: Correlation does NOT imply causation.

• Non-parametric equivalent.
• Used for ordinal data or when data is not normally distributed.

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Q. Linear Regression.

• Quantifies the relationship between one independent variable (predictor, X) and one continuous dependent variable (outcome, Y).
• Equation: Y = a + bX (a = intercept, b = slope/regression coefficient).
• b = the change in Y for a one-unit change in X.

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SECTION 16: SURVIVAL ANALYSIS

Q. What is Survival Analysis?

• A step-function curve that estimates the probability of surviving beyond each time point.
• Drops at each event (death/relapse).
• Censored observations shown as tick marks on the curve.
• Two curves (treatment vs. control) compared using the log-rank test.

• The ratio of the hazard rate (instantaneous risk of event) in the treatment group vs. the control group.
• HR = 0.6: Treatment reduces the hazard (risk of event) by 40%.
• HR = 1: No difference.
• HR > 1: Treatment increases risk.
• Produced by Cox proportional hazards regression (allows adjustment for covariates).

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SECTION 17: META-ANALYSIS AND SYSTEMATIC REVIEW

Q. Systematic Review vs. Narrative Review vs. Meta-Analysis.

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Q. Forest Plot.

• Each horizontal line = one study. The square is the point estimate (OR, RR, MD); its size reflects the study's weight (usually proportional to sample size).
• The horizontal line through the square = 95% CI. If it crosses the vertical line of no effect (OR=1 or MD=0), that study is not statistically significant.
• The diamond at the bottom = pooled estimate (summary result). Its width = 95% CI.
• A narrow diamond centered away from the null = precise, significant pooled result.

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Q. Heterogeneity - I² Statistic.

• I² = 0%: No heterogeneity.
• I² = 25%: Low heterogeneity (generally acceptable).
• I² = 50%: Moderate heterogeneity (concerning).
• I² = 75-100%: High/substantial heterogeneity (pooling may not be appropriate).

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Q. Publication Bias and Funnel Plot.

• In the absence of bias, studies scatter symmetrically in an inverted funnel shape around the pooled estimate.
• Asymmetric funnel plot suggests publication bias (small studies with negative results are missing from the bottom-left corner).

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SECTION 18: EVIDENCE-BASED MEDICINE (EBM)

Q. Define EBM and PICO Framework.

1. Best available external research evidence.
2. Individual clinical expertise.
3. Patient values and preferences.

• P = Patient / Population / Problem
• I = Intervention (drug, treatment)
• C = Comparison (standard treatment, placebo)
• O = Outcome (primary endpoint)

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Q. Internal Validity vs. External Validity.

• Internal validity: The degree to which the results of a study accurately reflect the true relationship within the study population. Threatened by bias and confounding.
• External validity (generalizability): The degree to which the study results can be applied to populations and settings outside the study. A highly controlled RCT may have high internal but low external validity (pragmatic concern for MD pharmacology).

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SECTION 19: EPIDEMIOLOGY MEASURES

Q. Incidence vs. Prevalence.

• Incidence rate = New cases / Population at risk × Time

• Point prevalence = Existing cases at one time / Total population
• Period prevalence = Cases during a time period / Population

• If a disease is cured quickly, prevalence << incidence.
• If a disease is chronic, prevalence >> incidence.

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Q. Case Fatality Rate (CFR) vs. Crude Death Rate.

• CFR = (Deaths from a specific disease / Total cases of that disease) × 100%. Measures the severity of a disease. Example: CFR of COVID-19 was ~1-2% in many countries.
• Crude Death Rate = Total deaths in a population / Total population × 1000 per year. Affected by age structure. Hence, age-standardization is needed for comparisons.

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SECTION 20: PHARMACOSTATISTICS

Q. Dose-Response Curve and EC50.

• Emax: Maximum achievable effect.
• EC50: The drug concentration producing 50% of Emax. Inverse measure of potency - lower EC50 = more potent.
• Hill coefficient (n): Steepness of the curve. n > 1 = cooperative binding (steep curve). n = 1 = hyperbolic binding.

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Q. Bioequivalence - Statistical Method (TOST).

• The 90% CI for the ratio of PK parameters (AUC and Cmax) of test vs. reference must fall within the 80-125% bioequivalence limits.
• If the entire 90% CI for AUC ratio falls between 0.80 and 1.25, bioequivalence is established.

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Q. Probit Analysis - LD50, ED50.

• ED50 (Effective Dose 50): The dose that produces the desired effect in 50% of a population.
• LD50 (Lethal Dose 50): The dose that kills 50% of an experimental animal population.
• Therapeutic Index (TI) = LD50 / ED50. Higher TI = wider margin of safety.

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FINAL EXAM QUESTION ANSWERS (Quick Reference)

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