Here is the complete, exam-focused viva Q&A set:
Viva Questions & Answers: Statistical Analysis in Research Methodology
MD Pharmacology Exam Preparation
SECTION A: Foundations of Statistical Inference
Q1. What is the difference between a statistic and a parameter?
| Statistic | Parameter |
|---|
| Definition | A numerical value calculated from sample data | A numerical value describing the entire population |
| Source | Sample | Population (usually unknown; estimated from sample) |
| Notation | x̄ (sample mean), s (sample SD), p̂ (sample proportion) | μ (population mean), σ (population SD), π (population proportion) |
| Certainty | Known (calculated) | Unknown (estimated) |
Standard error (SE): Measures how much the sample statistic varies from the true population parameter. SE = SD / √n. As n increases, SE decreases (estimates become more precise).
Q2. What is a sampling distribution? Why does it matter?
The sampling distribution is the probability distribution of a statistic (e.g., the sample mean) calculated from all possible samples of the same size drawn from a population.
Central Limit Theorem (CLT): Regardless of the shape of the population distribution, the sampling distribution of the mean approaches a normal distribution as the sample size increases (typically n ≥ 30). This is the mathematical justification for using normal-theory statistical tests even when the original data are not perfectly normally distributed.
Why it matters: All parametric hypothesis tests and confidence intervals are based on the sampling distribution of the test statistic. The CLT makes these tests valid for reasonably large samples even when the raw data deviate from normality.
Q3. What is a confidence interval? How do you construct and interpret a 95% CI?
A 95% CI is a range of values constructed from sample data such that, in 95% of all possible samples, the interval would contain the true population parameter.
Construction: For a mean: CI = x̄ ± (Z or t) × SE
- For large samples (n > 30): 95% CI = x̄ ± 1.96 × SE
- For small samples (n ≤ 30, normal data): 95% CI = x̄ ± t(df, 0.025) × SE
Correct interpretation: "We are 95% confident that the true population mean lies within this interval." NOT "There is a 95% probability that the true mean lies in this interval" (the true mean is fixed; it either is or is not in the interval - the probability refers to the method, not the interval).
Width of CI:
- Wider CI = less precision (small sample, large variance)
- Narrower CI = more precision (large sample, small variance)
Relationship to p-value: If the 95% CI of an OR/RR excludes 1.0, the result is significant at p < 0.05. If the 95% CI of a mean difference excludes 0, p < 0.05.
Q4. What is the difference between one-tailed and two-tailed tests? When do you use each?
| One-tailed (directional) test | Two-tailed (non-directional) test |
|---|
| Hypothesis | H₁: μ₁ > μ₂ (or < ) | H₁: μ₁ ≠ μ₂ |
| Critical region | All in one tail of the distribution | Split equally between both tails |
| Critical Z value (α = 0.05) | 1.645 | 1.960 |
| Power | Greater for detecting effects in the predicted direction | Less powerful for one direction |
| When to use | Only when the direction of effect is firmly predicted and specified a priori (very rare in pharmacology) | Almost always - standard in pharmacology research |
| Risk | Cannot detect unexpected effects in the other direction | Balanced; standard |
Examiner tip: Using a one-tailed test to achieve significance should be pre-specified, scientifically justified, and not done post-hoc to cross p = 0.05. Most regulatory agencies and journals require two-tailed tests.
SECTION B: Choosing the Right Statistical Test
Q5. What is the algorithm for selecting the appropriate statistical test?
What is the OUTCOME variable?
│
├── CONTINUOUS (normally distributed)
│ ├── Compare 2 groups
│ │ ├── Independent → Independent t-test
│ │ └── Paired/matched → Paired t-test
│ └── Compare ≥3 groups
│ ├── One factor → One-way ANOVA
│ ├── Two factors → Two-way ANOVA
│ └── Repeated measures → Repeated-measures ANOVA
│
├── CONTINUOUS (non-normal or ordinal)
│ ├── Compare 2 independent groups → Mann-Whitney U
│ ├── Compare 2 paired groups → Wilcoxon signed-rank
│ ├── Compare ≥3 independent groups → Kruskal-Wallis
│ └── Compare ≥3 repeated measures → Friedman
│
├── CATEGORICAL (binary/nominal)
│ ├── Two independent groups → Chi-square (or Fisher's exact if expected cell < 5)
│ ├── Two paired groups → McNemar's test
│ └── ≥3 independent groups → Chi-square with multiple categories
│
├── CORRELATION between 2 variables
│ ├── Both continuous + normal → Pearson's r
│ └── One/both ordinal or non-normal → Spearman's ρ
│
├── PREDICTION / REGRESSION
│ ├── Continuous outcome → Linear regression (multiple)
│ ├── Binary outcome → Logistic regression
│ └── Time-to-event → Cox proportional hazards
│
└── TIME-TO-EVENT (survival)
├── Describe survival curve → Kaplan-Meier
└── Compare two survival curves → Log-rank test
SECTION C: t-Tests in Detail
Q6. Explain the independent samples t-test. What are its assumptions?
The independent samples (unpaired) t-test compares the means of two unrelated groups.
Formula: t = (x̄₁ - x̄₂) / √(Sp² × (1/n₁ + 1/n₂))
where Sp² = pooled variance
Degrees of freedom: df = n₁ + n₂ - 2
Assumptions:
- Continuous data (interval or ratio)
- Both groups approximately normally distributed (or n > 30 by CLT)
- Independence of observations (no pairing)
- Homogeneity of variance (Levene's test; if violated, use Welch's t-test which uses separate variances and adjusted df)
When NOT to use: Non-normal data with small samples (use Mann-Whitney U); paired data (use paired t-test); more than 2 groups (use ANOVA).
Q7. Explain the paired t-test. When is it appropriate?
The paired t-test compares means in two related (matched or repeated) measurements from the same subjects.
Formula: t = d̄ / (SD_d / √n)
where d̄ = mean of differences (post - pre), SD_d = SD of differences, n = number of pairs
df: n - 1 (number of pairs minus 1)
When to use:
- Before-after measurements on the same subjects (pre-treatment vs. post-treatment BP)
- Matched case-control studies
- Crossover RCTs
Advantage over independent t-test: Removes between-subject variability - more powerful for detecting within-subject changes.
Non-parametric equivalent: Wilcoxon signed-rank test.
Q8. What is the one-sample t-test?
Tests whether the sample mean is significantly different from a known or hypothesized population value (μ₀).
Formula: t = (x̄ - μ₀) / (s/√n); df = n - 1
Example: Testing whether the mean Cmax of a new formulation (sample mean) is significantly different from the reference product (known μ₀ = 500 ng/mL).
SECTION D: ANOVA
Q9. What is ANOVA? When is it used instead of multiple t-tests?
ANOVA (Analysis of Variance) tests whether there are statistically significant differences among the means of three or more groups by partitioning total variance into between-group variance and within-group variance.
F ratio = Mean Square Between / Mean Square Within
If F is large (between-group variance >> within-group variance), the null hypothesis (all means equal) is rejected.
Why not multiple t-tests? With k groups, you would need k(k-1)/2 pairwise t-tests. Each test has α = 0.05, so with 3 groups (3 tests), the familywise error rate = 1 - (1-0.05)³ = 14.3%. ANOVA controls the overall Type I error at α = 0.05 for the omnibus test.
ANOVA tells you that at least one mean differs - it does NOT tell you which pairs differ. Post-hoc tests are required.
Q10. What are post-hoc tests? Name and compare them.
Post-hoc tests are pairwise comparison tests performed AFTER a significant ANOVA to identify which specific groups differ. They control for multiple comparisons.
| Test | When Used | Character |
|---|
| Tukey's HSD (Honest Significant Difference) | Equal group sizes; all pairwise comparisons | Balanced; most commonly used |
| Bonferroni correction | Small number of pre-specified comparisons | Simple: divide α by number of comparisons; conservative |
| Scheffé's test | Complex comparisons (not just pairwise); unequal n | Most conservative; for exploratory comparisons |
| LSD (Least Significant Difference) | Only valid after significant F; liberal | Least conservative; increased Type I error |
| Dunnett's test | Compare each group only to a control group | Targeted; more powerful than Tukey for this purpose |
| Games-Howell | Unequal variances between groups | Welch-based; recommended when Levene's test significant |
Q11. What are the types of ANOVA?
| Type | Use |
|---|
| One-way ANOVA | One independent variable with ≥3 levels; one continuous outcome |
| Two-way ANOVA | Two independent variables; tests main effects and interaction |
| Repeated-measures ANOVA | Same subjects measured ≥3 times (within-subjects design) |
| Mixed ANOVA | Both within-subjects and between-subjects factors |
| ANCOVA (Analysis of Covariance) | One-way ANOVA with a continuous covariate (confounder) controlled |
| MANOVA (Multivariate ANOVA) | Multiple dependent variables simultaneously |
Assumptions of ANOVA:
- Normal distribution within each group (or n sufficiently large)
- Homogeneity of variance (Levene's test; if violated, use Welch's ANOVA)
- Independence of observations
- If repeated-measures: Sphericity (equal variances of differences between all pairs of time points; tested by Mauchly's test; if violated, apply Greenhouse-Geisser or Huynh-Feldt correction)
SECTION E: Chi-Square and Fisher's Tests
Q12. Explain the chi-square (χ²) test. What are its assumptions?
The chi-square test of independence tests whether there is a statistically significant association between two categorical variables.
Formula: χ² = Σ [(Observed - Expected)² / Expected]
where Expected = (Row total × Column total) / Grand total for each cell
Degrees of freedom: (r-1)(c-1) where r = rows, c = columns. For a 2×2 table: df = 1.
Interpretation: If χ² is large (p < 0.05), reject H₀ of independence - the variables are associated.
Assumptions:
- Categorical data
- Observations are independent
- Expected frequency in each cell ≥ 5 (if any expected cell < 5, use Fisher's exact test)
- No more than 20% of cells have expected frequency < 5
Chi-square does NOT measure the strength of association - it only tests statistical significance. Use Cramér's V or Phi coefficient for strength.
Q13. What is Fisher's Exact Test? When is it preferred over chi-square?
Fisher's Exact Test calculates the exact probability of observing the given 2×2 table (and all more extreme tables) under the null hypothesis of no association, without relying on chi-square approximation.
Preferred when:
- Any expected cell frequency < 5
- Small total sample size (n < 20-40)
- 2×2 tables specifically (for larger tables, use Monte Carlo chi-square)
Fisher's exact test is always valid (no minimum cell size assumption); chi-square is an approximation that works well only when expected frequencies are adequate.
Q14. What is McNemar's test?
McNemar's test is the paired/matched equivalent of chi-square. It is used for paired categorical (binary) data - i.e., when the same subjects are measured twice (before-after, matched pairs).
Formula: χ² = (b - c)² / (b + c), df = 1
where b = number of pairs where first measurement positive, second negative; c = number where first negative, second positive.
Only the discordant pairs (b and c) contribute to the test - concordant pairs (both positive or both negative) are irrelevant.
Example: Testing whether the proportion of patients responding to treatment changed after a dose increase in the same patients.
SECTION F: Correlation
Q15. What is Pearson's correlation coefficient (r)? How is it interpreted?
Pearson's r measures the strength and direction of the linear association between two continuous, normally distributed variables.
Range: -1 to +1
| r value | Interpretation |
|---|
| +1.0 | Perfect positive linear relationship |
| 0.7 to 0.9 | Strong positive |
| 0.5 to 0.7 | Moderate positive |
| 0.3 to 0.5 | Weak positive |
| 0 | No linear relationship |
| Negative values | Inverse (negative) direction |
Coefficient of determination (r²): The proportion of variance in Y explained by X. e.g., r = 0.8 → r² = 0.64 → 64% of variance in Y is explained by X.
Critical distinction:
- r measures the linear relationship only; it will be 0 for a perfect non-linear (e.g., U-shaped) relationship
- Statistical significance of r depends on both the magnitude AND sample size - a small r can be highly significant in a very large study but clinically meaningless
- Correlation ≠ causation
Q16. What is Spearman's rank correlation? When is it used instead of Pearson's?
Spearman's ρ (rho) is the non-parametric equivalent of Pearson's r. It calculates Pearson's r on the ranks of the data rather than the raw values.
Use instead of Pearson's when:
- One or both variables are ordinal (pain score, Likert scale)
- Data are non-normally distributed
- There are outliers that disproportionately influence Pearson's r
- The relationship may be monotonic but not strictly linear
Interpretation: Same range (-1 to +1) and direction interpretation as Pearson's. ρ = 1 means perfect monotonic (rank-order) relationship.
SECTION G: Regression Analysis
Q17. What is simple linear regression? What does the regression equation mean?
Simple linear regression models the relationship between one continuous predictor variable (X) and one continuous outcome variable (Y):
Y = a + bX + ε
where:
- a (intercept): The predicted value of Y when X = 0
- b (regression coefficient / slope): The change in Y for each one-unit increase in X
- ε (error term): Residual unexplained variation
Example: Y = serum creatinine (mg/dL); X = age (years); b = 0.01 → for every 1 year increase in age, creatinine increases by 0.01 mg/dL on average.
Assumptions (LINE):
- Linearity: Relationship is linear (check scatter plot)
- Independence: Observations independent
- Normality: Residuals (errors) normally distributed
- Equal variance (Homoscedasticity): Constant variance of residuals across values of X
Q18. What is multiple linear regression? What is multicollinearity?
Multiple linear regression models the relationship between multiple predictor variables (X₁, X₂, ... Xₖ) and one continuous outcome:
Y = a + b₁X₁ + b₂X₂ + ... + bₖXₖ + ε
Each bᵢ = change in Y per unit increase in Xᵢ, holding all other predictors constant (adjusted coefficient).
Uses in pharmacology:
- Predicting drug response from multiple patient characteristics
- Adjusting for confounders
- Dose-response modeling
Multicollinearity: When two or more predictor variables are highly correlated with each other, making it impossible to distinguish their independent effects. Detected by Variance Inflation Factor (VIF) - VIF > 10 indicates serious multicollinearity. Addressed by removing one of the correlated predictors or combining them.
Q19. What is logistic regression? How is it different from linear regression?
Logistic regression models the relationship between one or more predictors and a binary (dichotomous) outcome (e.g., responder vs. non-responder; ADR present vs. absent).
Key differences from linear regression:
| Feature | Linear Regression | Logistic Regression |
|---|
| Outcome | Continuous | Binary (0 or 1) |
| Model output | Predicted value of Y | Log-odds (logit) of P(Y=1) |
| Coefficient interpretation | Change in Y per unit X | Change in log-odds per unit X; exponentiated = Odds Ratio (OR) |
| Assumptions | Normal residuals; homoscedasticity | No normality required; uses maximum likelihood estimation |
| Predicted range | -∞ to +∞ | 0 to 1 (probability) |
Logit function: logit(p) = ln[p/(1-p)] = a + b₁X₁ + b₂X₂ + ...
Output: Each regression coefficient, when exponentiated (eᵇ), gives the adjusted OR for that predictor, controlling for all other variables. 95% CI for OR that excludes 1.0 = significant.
SECTION H: Survival Analysis
Q20. What is survival analysis? When is it used?
Survival analysis (time-to-event analysis) is a branch of statistics for analyzing the time until an event of interest occurs. Despite the name "survival," the event can be:
- Death
- Disease relapse
- First hospitalization
- Drug failure
- Adverse drug reaction
Used when:
- The outcome is the time to an event, not just whether it occurred
- Follow-up periods differ between participants (administrative censoring)
- Some participants have not experienced the event by study end (censored)
Key concepts:
- Event: Occurrence of the outcome of interest
- Censoring: Participant has not experienced the event by the time of analysis (either lost to follow-up or study ended; their exact event time is unknown but known to be > last observation time)
- Survival function S(t): Probability that the event has NOT occurred by time t
- Hazard function h(t): Instantaneous rate of event occurrence at time t given survival up to t
Q21. What is the Kaplan-Meier (KM) method? How do you read a KM curve?
The Kaplan-Meier estimator is a non-parametric method to estimate the survival function S(t) from censored time-to-event data. It recalculates the survival probability each time an event occurs.
Formula: S(tᵢ) = S(tᵢ₋₁) × [(nᵢ - dᵢ) / nᵢ]
where nᵢ = number at risk just before time tᵢ; dᵢ = number of events at time tᵢ
How to read a KM curve:
- Y-axis: Survival probability (0 to 1); starts at 1.0
- X-axis: Time (days/months/years)
- Steps (drops): Each step down = one or more events occurring
- Vertical tick marks (|): Censored observations (participants who left the study without experiencing the event)
- Median survival: Time at which survival probability = 0.5 (where the curve crosses the horizontal dashed line at 0.5)
- Two groups: When comparing Drug A vs. Drug B, two KM curves are plotted; wider separation = greater survival difference
Key examiner question: "What do the tick marks on a KM curve represent?" They indicate censored observations - patients who were lost to follow-up or reached study end without the event.
Q22. What is the log-rank test?
The log-rank test (Mantel-Cox test) is the standard non-parametric test for comparing the survival distributions (KM curves) of two or more groups.
Null hypothesis: The survival curves of the groups are identical (the groups have the same event rate over time).
Calculates: A weighted sum of observed vs. expected events at each event time point across all groups.
Output: Chi-square statistic with df = k-1 (k = number of groups); associated p-value.
Limitations:
- Only tests whether curves differ overall; does not quantify the magnitude of difference
- Most powerful when the proportional hazards assumption holds (i.e., hazard ratio is constant over time; curves don't cross)
- If curves cross (hazard ratio reverses), log-rank test loses power (consider Wilcoxon-Breslow or stratified analyses)
Q23. What is the Cox Proportional Hazards Regression Model?
The Cox model is a semi-parametric regression model for time-to-event data that estimates the effect of predictor variables (covariates) on the hazard (event rate), while adjusting for other variables.
Model: h(t) = h₀(t) × exp(b₁X₁ + b₂X₂ + ... + bₖXₖ)
where h₀(t) = baseline hazard (unspecified; this is the "semi-parametric" part)
Output:
- Hazard Ratio (HR): eᵇᵢ = ratio of hazard for a one-unit increase in Xᵢ, adjusting for all other variables
- HR > 1: Higher hazard (worse survival) with increasing X
- HR < 1: Lower hazard (better survival; protective) with increasing X
- HR = 1: No effect
- 95% CI for HR: If it excludes 1.0, statistically significant at p < 0.05
Key assumption - Proportional Hazards (PH): The HR between groups is constant over time (i.e., the two groups' hazards are proportional at every time point). If a drug halves the hazard initially but has no effect later, the PH assumption is violated.
Testing PH assumption:
- Log-log (ln[-ln(S(t))]) plot: Should be parallel lines if PH holds
- Schoenfeld residuals test (formal statistical test)
Q24. What is the difference between the log-rank test and Cox regression?
| Feature | Log-rank test | Cox regression |
|---|
| Purpose | Compares survival curves of 2+ groups | Quantifies effect of predictor(s) on hazard; adjusts for confounders |
| Covariates | Cannot adjust for covariates | Adjusts for multiple covariates simultaneously |
| Output | p-value only | Hazard Ratio + 95% CI + p-value |
| Type | Non-parametric | Semi-parametric |
| When to use | Simple group comparison (e.g., treatment A vs B) | Multivariable analysis; confounding adjustment; continuous predictors |
| Analogous to | t-test / ANOVA | Linear / logistic regression |
SECTION I: Diagnostic Test Statistics
Q25. Describe the 2×2 contingency table for a diagnostic test.
The gold standard defines true disease status; the test result defines positive or negative.
DISEASE (Gold Standard)
Present (+) Absent (-) Total
TEST Positive (+) TP (a) FP (c) a+c
Negative (-) FN (b) TN (d) b+d
Total a+b c+d N
- TP (True Positive): Test positive, disease present
- TN (True Negative): Test negative, disease absent
- FP (False Positive): Test positive, disease absent (Type I error in testing)
- FN (False Negative): Test negative, disease present (Type II error in testing)
Q26. Define and calculate sensitivity, specificity, PPV, NPV, and likelihood ratios.
| Measure | Formula | Meaning | Memory aid |
|---|
| Sensitivity (Sn) | TP / (TP + FN) = a/(a+b) | Probability of testing positive given disease IS present | "Sensitivity rules OUT disease when NEGATIVE" (SnNout) |
| Specificity (Sp) | TN / (TN + FP) = d/(c+d) | Probability of testing negative given disease is ABSENT | "Specificity rules IN disease when POSITIVE" (SpPin) |
| Positive Predictive Value (PPV) | TP / (TP + FP) = a/(a+c) | Probability of disease given a POSITIVE test result | Depends on prevalence |
| Negative Predictive Value (NPV) | TN / (TN + FN) = d/(b+d) | Probability of NO disease given a NEGATIVE test result | Depends on prevalence |
| Positive Likelihood Ratio (+LR) | Sensitivity / (1 - Specificity) | How much the post-test odds increase after a POSITIVE result | +LR > 10: strong evidence to rule in |
| Negative Likelihood Ratio (-LR) | (1 - Sensitivity) / Specificity | How much the post-test odds decrease after a NEGATIVE result | -LR < 0.1: strong evidence to rule out |
| Accuracy | (TP + TN) / N = (a+d)/N | Overall proportion of correct classifications | Misleading if disease prevalence is extreme |
Critical examiner point: PPV and NPV depend on disease prevalence (pre-test probability). The same test has higher PPV in a high-prevalence population (e.g., specialist clinic) than a low-prevalence population (general screening). Sensitivity and specificity are intrinsic properties of the test (do NOT depend on prevalence).
Q27. What is the ROC (Receiver Operating Characteristic) curve? How do you interpret AUC?
An ROC curve is a graphical plot of sensitivity (y-axis) against 1 - specificity (x-axis = false positive rate) across all possible cut-off values of a continuous diagnostic test.
How it is generated: For each possible threshold/cut-off, calculate sensitivity and (1 - specificity). Plot each pair as a point; connect them.
AUC (Area Under the ROC Curve):
| AUC value | Discrimination |
|---|
| 1.0 | Perfect test |
| 0.90 - 1.00 | Excellent |
| 0.80 - 0.90 | Good |
| 0.70 - 0.80 | Fair |
| 0.60 - 0.70 | Poor |
| 0.50 | No better than chance (diagonal line) |
| < 0.50 | Worse than chance (inverted test) |
Uses:
- Compare discriminative ability of two different tests (compare AUCs)
- Select the optimal cut-off (point closest to the top-left corner = maximizes sensitivity + specificity)
- Evaluate biomarkers for disease diagnosis or drug response prediction
Youden's Index: Sensitivity + Specificity - 1; maximized at the optimal cut-off.
Q28. What is the difference between pre-test and post-test probability? How do likelihood ratios change them?
- Pre-test probability (prevalence): The probability of disease in the patient BEFORE the test result is known
- Post-test probability: The probability of disease AFTER accounting for the test result
Conversion using Bayes' theorem and likelihood ratios:
- Convert pre-test probability to pre-test odds: Odds = P / (1 - P)
- Multiply by Likelihood Ratio: Post-test odds = Pre-test odds × LR
- Convert back: Post-test probability = Post-test odds / (Post-test odds + 1)
Practical shortcut (Fagan's nomogram): Draw a line from pre-test probability through the LR to read off post-test probability directly.
Example: Pre-test probability 30%. +LR = 10. Pre-test odds = 0.3/0.7 = 0.43. Post-test odds = 0.43 × 10 = 4.3. Post-test probability = 4.3/5.3 = 81%.
SECTION J: Agreement and Reliability Statistics
Q29. What is Cohen's Kappa? How is it interpreted?
Cohen's Kappa (κ) measures inter-rater agreement for categorical data, correcting for the level of agreement expected by chance alone.
Formula: κ = (Po - Pe) / (1 - Pe)
where Po = observed proportion of agreement; Pe = expected proportion of agreement by chance
| κ value | Strength of Agreement |
|---|
| < 0 | Less than chance (poor) |
| 0 - 0.20 | Slight |
| 0.21 - 0.40 | Fair |
| 0.41 - 0.60 | Moderate |
| 0.61 - 0.80 | Substantial |
| 0.81 - 1.00 | Almost perfect |
Examiner note: Simple percentage agreement is misleading - two raters who independently respond "yes" 90% of the time to any question will agree 81% of the time by chance alone. Kappa corrects for this.
Q30. What is the Bland-Altman plot? When is it used?
The Bland-Altman (limits of agreement) plot assesses agreement between two quantitative measurement methods (or two raters measuring a continuous variable).
Construction:
- X-axis: Mean of the two measurements (for each subject)
- Y-axis: Difference between the two measurements (Method 1 - Method 2)
- Draw horizontal lines at: Mean difference (bias), Mean difference ± 1.96 × SD of differences (= 95% Limits of Agreement)
Interpretation:
- If the mean difference is near zero: Little systematic bias between methods
- If most differences lie within the limits of agreement (±1.96 SD): Methods agree clinically
- Limits of agreement should be clinically acceptable for the methods to be interchangeable
- Fan-shaped pattern: Proportional bias (differences increase as the mean increases)
Why not just use correlation? A high correlation does NOT imply good agreement. Two methods can be highly correlated (r = 0.99) but consistently differ by 20% - which would be unacceptable clinically but invisible to a correlation coefficient.
Q31. What is the Intraclass Correlation Coefficient (ICC)?
ICC measures the reliability of continuous measurements from two or more raters or repeated measures. It simultaneously measures both consistency and agreement.
Range: 0 to 1 (higher = better agreement)
| ICC | Reliability |
|---|
| < 0.50 | Poor |
| 0.50 - 0.75 | Moderate |
| 0.75 - 0.90 | Good |
| > 0.90 | Excellent |
When to use: Preferred over Pearson's r for assessing reliability because it accounts for both correlation and systematic differences (bias) between measurements.
SECTION K: Data Transformation & Distribution Concepts
Q32. What is a skewed distribution? When do you transform data?
A skewed distribution is asymmetrical. The mean is pulled toward the tail.
| Distribution | Mean vs. Median | Example |
|---|
| Positively skewed (right) | Mean > Median > Mode | Income, drug serum concentrations, hospital length of stay |
| Negatively skewed (left) | Mean < Median < Mode | Age at death in a developed country |
| Normal | Mean = Median = Mode | Height, blood pressure in large populations |
Log transformation: Applied to right-skewed data (e.g., serum drug concentrations, pharmacokinetic parameters like AUC, Cmax). After log transformation, data approximate normality, and parametric tests become valid. Results expressed as geometric means and geometric mean ratios (relevant for bioequivalence studies).
Other transformations: Square root (count data), reciprocal, arcsine (proportions).
Q33. What is the geometric mean? When is it used in pharmacology?
The geometric mean is the nth root of the product of n values, or equivalently, the antilogarithm of the mean of log-transformed values.
Geometric mean = exp(mean of log-values) = antilog(mean of log-values)
Used in pharmacology:
- Pharmacokinetic parameters (AUC, Cmax, t½) which are log-normally distributed
- Bioequivalence studies: the 90% CI of the geometric mean ratio (Test/Reference) must be 80%-125% for equivalence
- Antibody titers, dilutions, microbiological counts
Why not arithmetic mean? For log-normally distributed data, the arithmetic mean is heavily influenced by high outliers. The geometric mean is more representative of the central tendency.
SECTION L: Multiple Testing and Corrections
Q34. What is the multiple testing problem? How is it addressed?
When k statistical tests are performed on the same dataset, the familywise Type I error rate increases:
Familywise error rate = 1 - (1-α)ᵏ
For k = 3 tests at α = 0.05: error rate = 1 - (0.95)³ = 14.3% (not 5%)
For k = 10 tests: error rate = 40%
For k = 20 tests: error rate = 64%
Correction methods:
| Method | Formula | Character |
|---|
| Bonferroni correction | αᵢ = α / k (use threshold of 0.05/k for each test) | Simple; very conservative; reduces power |
| Holm-Bonferroni (sequential Bonferroni) | Tests ranked; threshold adjusted sequentially | Less conservative than Bonferroni; more powerful |
| Benjamini-Hochberg (FDR) | Controls False Discovery Rate rather than familywise error | Less conservative; appropriate for exploratory studies |
| Pre-specification | Declare primary outcome in protocol before data collection | Methodological (not statistical) solution; most important |
Best solution: Pre-specify a single primary outcome in the protocol before data collection - this is why the statistical analysis plan (SAP) must be finalized before unblinding.
Q35. What is the Bonferroni correction? What is its limitation?
Bonferroni correction: For k simultaneous tests, use α/k as the significance threshold for each test.
Example: 3 outcomes tested → significance threshold = 0.05/3 = 0.0167 for each.
Limitation: Overly conservative (increases Type II error / reduces power), especially when:
- Tests are not independent (correlated outcomes)
- Number of comparisons is large
- It may cause clinically important effects to be dismissed as non-significant
For correlated or many comparisons, the Holm-Bonferroni or FDR methods are preferred.
SECTION M: Effect Size Measures
Q36. What is effect size? Why is it important beyond p-value?
Effect size quantifies the magnitude of a difference or association, independent of sample size. Unlike p-values, which depend on both effect size and sample size, effect size measures the clinical or practical importance of a finding.
Common effect size measures:
| Measure | Used For | Interpretation |
|---|
| Cohen's d | Two means (t-test) | d = (x̄₁ - x̄₂) / Sp; d < 0.2 trivial, 0.2-0.5 small, 0.5-0.8 medium, > 0.8 large |
| Eta-squared (η²) | ANOVA | Proportion of variance in Y explained by group membership; η² = SS_between / SS_total |
| r (Pearson/Spearman) | Correlation | r < 0.1 trivial, 0.1-0.3 small, 0.3-0.5 medium, > 0.5 large |
| Odds Ratio (OR) | Binary outcome, case-control | OR = 1 no effect; OR = 2 moderate; OR > 3 large |
| Risk Ratio (RR) | Binary outcome, cohort/RCT | Similar interpretation to OR |
| NNT / NNH | Clinical importance | See Section N |
| Hazard Ratio (HR) | Time-to-event | HR = 1 no effect; HR < 1 protective |
SECTION N: Clinical Significance vs. Statistical Significance
Q37. What is the difference between statistical significance and clinical significance?
| Statistical Significance | Clinical Significance |
|---|
| Meaning | The observed effect is unlikely to be due to chance (p < 0.05) | The magnitude of the effect is large enough to matter to patients and clinicians |
| Determined by | Sample size, effect size, variability | Clinical judgment, effect size, NNT, patient values, costs |
| Can have large n with tiny effect | Yes - a 0.5 mmHg drop in SBP can be statistically significant with n = 100,000 | No - 0.5 mmHg is not clinically meaningful |
| Can have small n with large effect | May miss real clinical effects (underpowered) | Large effects in small trials may be clinically impressive but not statistically significant |
The solution: Always report both - p-value AND effect size AND 95% CI AND NNT/NNH where applicable.
Q38. What is the MCID (Minimum Clinically Important Difference)?
The MCID is the smallest difference in an outcome that patients and/or clinicians would consider meaningful and worth the cost, risk, and inconvenience of a treatment.
Examples:
- Pain VAS: 13 mm (out of 100mm) = MCID
- NRS pain: 1.5 points (out of 10)
- HRQOL (SF-36): 5-10 points depending on domain
- Forced Expiratory Volume (FEV₁): 200 mL or 12% change
- HbA1c: 0.5% absolute change
Importance: A study powered to detect the MCID ensures that a statistically significant result is also clinically significant. Conversely, a statistically significant result that does not reach the MCID may not justify prescribing the drug.
SECTION O: Rapid-Fire Questions
Q39. What is the Z-test vs. the t-test?
- Z-test: Used when population SD is known OR sample is large (n > 30); uses Z distribution (standard normal)
- t-test: Used when population SD is unknown (estimated from sample) and/or n ≤ 30; uses t-distribution (heavier tails for small df; approaches Z as n → ∞)
Q40. What is degrees of freedom (df)? The number of independent values free to vary in a statistical calculation after constraints have been applied. Conceptually: df = n - number of parameters estimated from the data. For a one-sample t-test: df = n-1 (one mean estimated); for independent t-test: df = n₁ + n₂ - 2.
Q41. What is homoscedasticity? Constant variance of the residuals (errors) across all levels of the predictor variable. A key assumption of linear regression and ANOVA. Tested visually with a residuals-vs-fitted plot, or by Levene's test (for ANOVA). Violation = heteroscedasticity.
Q42. What is the difference between one-way and two-way ANOVA?
- One-way: Tests effect of ONE categorical independent variable (factor) with ≥3 levels on a continuous outcome
- Two-way: Tests effects of TWO categorical factors simultaneously, including their interaction (whether the effect of Factor A depends on the level of Factor B)
Q43. What are residuals in regression? Residuals are the differences between the observed values of Y and the values predicted by the regression model (Y - Ŷ). Analysis of residuals (residual plots, QQ plots) is used to check regression assumptions.
Q44. What is R² in multiple regression? The coefficient of determination - the proportion of total variance in Y that is explained by the model (all predictor variables combined). Adjusted R² penalizes for adding unnecessary predictors and is preferred for comparing models.
Q45. What is censoring in survival analysis? An observation is censored when the event of interest has not occurred by the time of analysis. Right-censoring is most common: the participant was event-free at last observation (they may or may not eventually experience the event). The key assumption: censoring is non-informative (independent of the event probability).
Q46. What is the median survival time? The time at which the estimated survival probability S(t) = 0.5 - i.e., the time by which 50% of the study population has experienced the event. Read off the KM curve where the curve crosses the 0.5 line on the y-axis. If the curve never drops below 0.5, the median survival time is undefined.
Q47. What does "number needed to treat" (NNT) mean?
NNT = 1/ARR = 1/(Control Event Rate - Experimental Event Rate). The number of patients who need to be treated for one additional patient to benefit. Lower NNT = more effective treatment. NNT should always be reported with its 95% CI.
Q48. What statistical software packages are used in biomedical research?
- SPSS (IBM): Most used in Indian medical research; menu-driven; good for basic to moderate analyses
- R (free, open-source): Most flexible; can perform virtually any analysis; used in academic/research settings
- SAS: Standard in pharmaceutical industry and regulatory submissions
- STATA: Epidemiology-focused; excellent for survival analysis
- GraphPad Prism: Easy for basic statistics and graph generation; popular in pharmacology labs
- Epi Info (CDC): Free; good for epidemiological surveys; used in India
SECTION P: Examiner's Favourite Trick Questions
1. "p = 0.04, n = 500,000. Is this finding clinically important?"
Almost certainly not. With n = 500,000, even a trivially small effect (e.g., 0.1 mmHg BP reduction) will generate p < 0.05. Statistical significance reflects only the probability that the result is due to chance - not whether it matters clinically. Always examine the absolute effect size, CI, and MCID.
2. "The t-test showed p = 0.07. Can you conclude the drugs are equivalent?"
No. p = 0.07 means the evidence is insufficient to reject H₀ (no difference), but this does NOT prove the drugs are equivalent. The study may be underpowered. To demonstrate equivalence or non-inferiority, you need an equivalence/non-inferiority trial with pre-specified margins and appropriate analysis (TOST - two one-sided tests).
3. "You have 4 groups to compare. Can you do 6 pairwise t-tests?"
No. Running 6 pairwise t-tests at α = 0.05 gives familywise error rate = 1-(0.95)⁶ = 26.5%. The correct approach is one-way ANOVA (omnibus test) followed by post-hoc tests (Tukey, Bonferroni) if the ANOVA is significant.
4. "What is the non-parametric equivalent of ANOVA?"
The Kruskal-Wallis test (for 3+ independent groups). Its post-hoc equivalent is Dunn's test with Bonferroni correction. For repeated measures, use the Friedman test (non-parametric equivalent of repeated-measures ANOVA).
5. "Pearson r = 0.92 between two measurement methods. Can they be used interchangeably?"
Not without further analysis. A high correlation means the methods move together proportionally but does NOT mean they give the same values. One could consistently read 10 units higher than the other (fixed bias) and still have r = 0.92. The correct tool is the Bland-Altman plot and limits of agreement.
6. "Sensitivity = 95%, Specificity = 60%. Is this a good test?"
It depends on the clinical context. Very high sensitivity with moderate specificity makes it a good screening test (rule OUT disease - SnNout): few true cases are missed (low FN rate). However, the low specificity means many non-diseased patients test positive (high FP rate), leading to unnecessary follow-up. This profile is acceptable for initial screening but not for confirmatory diagnosis.
7. "AUC = 0.70 for Drug A vs. 0.85 for Drug B as biomarkers. What does this mean?"
Drug B is a better discriminator between disease states than Drug A. AUC = 0.85 means that in 85% of randomly chosen patient-control pairs, Drug B correctly identifies the patient (higher level) as more likely to have the disease. The difference in AUCs can be formally tested using the DeLong method.
MASTER REFERENCE TABLE: Statistical Tests
| Comparison | Parametric | Non-parametric | Notes |
|---|
| 1 group vs. known value | One-sample t-test | Wilcoxon signed-rank | |
| 2 independent groups (continuous) | Independent t-test | Mann-Whitney U | |
| 2 paired groups (continuous) | Paired t-test | Wilcoxon signed-rank | |
| ≥3 independent groups (continuous) | One-way ANOVA | Kruskal-Wallis | + post-hoc |
| ≥3 repeated measures (continuous) | Repeated-measures ANOVA | Friedman | Sphericity check |
| 2 categorical proportions (independent) | Chi-square | Fisher's exact | Fisher if expected < 5 |
| 2 categorical proportions (paired) | McNemar | - | Discordant pairs only |
| Correlation (2 continuous, normal) | Pearson r | Spearman ρ | |
| Predict continuous outcome | Linear regression | - | Multiple covariates |
| Predict binary outcome | Logistic regression | - | Output = OR |
| Compare survival curves | Log-rank test | - | Non-parametric |
| Adjust survival for covariates | Cox proportional hazards | - | Output = HR |
| Agreement between 2 raters (categorical) | Cohen's Kappa | - | |
| Agreement between 2 methods (continuous) | Bland-Altman | ICC | |
| Test for normality | Shapiro-Wilk (n<50) | K-S test (n>50) | |
| Test for equal variances | Levene's test | - | For ANOVA |
This set covers every statistical domain an MD Pharmacology examiner will probe in a viva - from t-tests and ANOVA through logistic regression, survival analysis, diagnostic test statistics (sensitivity/specificity/ROC/LR), agreement statistics, multiple testing correction, and the critical distinction between statistical and clinical significance.