Membership of the Faculty of Public Health (MFPH) Research Methods, Epidemiology and Statistics Syllabus

Define bias in epidemiology and name its two broad categories.

Bias is a systematic error in the design, conduct or analysis of a study that produces an estimate deviating from the true value. Two broad categories: selection bias (how participants enter/remain) and information (measurement) bias (how data are collected).

Give three examples of selection bias.

Healthy worker effect; non-response/volunteer bias; loss to follow-up (attrition); Berkson's (admission) bias in hospital-based studies; incidence-prevalence (Neyman) bias. Each distorts the association by non-random selection or retention of participants.

Give three examples of information (measurement) bias.

Recall bias (differential remembering of exposure by cases vs controls); observer/interviewer bias; misclassification of exposure/outcome; reporting/social desirability bias; surveillance (detection) bias. These arise from how data are measured or recorded.

Distinguish non-differential from differential misclassification and their typical effects.

Non-differential: misclassification unrelated to the other variable; for a binary exposure it usually biases the estimate towards the null. Differential: misclassification depends on outcome/exposure status; can bias in either direction (towards or away from the null), making it more dangerous.

Define a confounder and state the three criteria it must satisfy.

A confounder is a variable that distorts the exposure–outcome association. It must: (1) be associated with the exposure, (2) be an independent risk factor for (associated with) the outcome, and (3) NOT lie on the causal pathway between exposure and outcome (not an intermediate).

List methods to control for confounding at the design and analysis stages.

Design: randomisation, restriction, matching. Analysis: stratification (e.g. Mantel–Haenszel), multivariable regression adjustment, standardisation, and propensity scores. Randomisation also controls unknown/unmeasured confounders.

Define effect modification (interaction) and explain how it differs from confounding.

Effect modification occurs when the magnitude of the exposure–outcome effect differs across strata of a third variable (a real, reportable biological/social phenomenon). Confounding is a nuisance to be removed; effect modification is a finding to be described (report stratum-specific estimates), not adjusted away.

State the Bradford Hill criteria for causation (name at least seven).

Strength of association, Consistency, Specificity, Temporality (essential), Biological gradient (dose–response), Plausibility, Coherence, Experiment, Analogy. Temporality (cause precedes effect) is the only essential criterion; they are guidelines, not a checklist.

What is a counterfactual in causal frameworks, and how do potential outcomes define a causal effect?

The counterfactual is the outcome that would have occurred under the alternative (unobserved) exposure for the same individual. An individual causal effect is the difference between potential outcomes $Y_{a=1} - Y_{a=0}$; since only one is observed, we estimate average causal effects in comparable groups.

In a directed acyclic graph (DAG), what is a confounder, a mediator, and a collider?

Confounder: common cause of exposure and outcome (a 'fork' E ← C → O) — adjust for it. Mediator: on the causal pathway (E → M → O) — do not adjust if estimating total effect. Collider: common effect of two variables (X → K ← Y) — adjusting/conditioning on it induces bias.

State the key properties of the normal distribution and the empirical (68–95–99.7) rule.

Symmetric, bell-shaped, defined by mean $\mu$ and SD $\sigma$; mean = median = mode. Approximately $68\%$ of values lie within $\mu \pm 1\sigma$, $95\%$ within $\mu \pm 1.96\sigma$, and $99.7\%$ within $\mu \pm 3\sigma$.

State the Central Limit Theorem and its importance for inference.

For sufficiently large $n$, the sampling distribution of the sample mean is approximately normal with mean $\mu$ and standard error $\frac{\sigma}{\sqrt{n}}$, regardless of the population distribution's shape. This justifies using normal-based confidence intervals and tests for means.

Distinguish the standard deviation from the standard error of the mean.

SD measures the spread of individual observations around the mean. The standard error measures the precision of the sample mean as an estimate of the population mean: $$SE = \frac{s}{\sqrt{n}}$$ SE decreases as sample size increases; SD does not.

When are the binomial and Poisson distributions used in epidemiology?

Binomial: number of successes in $n$ independent trials with fixed probability $p$ (e.g. counts of cases out of a total). Poisson: count of rare events in a fixed time/space with mean = variance $= \lambda$ (e.g. incident cases over person-time, used for rate data).

Define a p-value precisely.

The probability of obtaining a result as extreme as, or more extreme than, the one observed, assuming the null hypothesis is true. It is NOT the probability that the null hypothesis is true, nor the probability the result occurred by chance alone.

Define Type I and Type II errors and relate them to $\alpha$, $\beta$ and power.

Type I error ($\alpha$): rejecting a true null hypothesis (false positive). Type II error ($\beta$): failing to reject a false null (false negative). Power $= 1 - \beta$: probability of correctly detecting a true effect.

How do you interpret a 95% confidence interval, and what does it indicate about statistical significance?

On repeated sampling, 95% of such intervals would contain the true population parameter. For a ratio measure, if the 95% CI includes 1 (or for a difference includes 0), the result is not statistically significant at the 5% level. CIs convey precision and effect size, unlike a bare p-value.

Which statistical test compares means between two independent groups, and what are its assumptions?

The independent (unpaired) two-sample t-test. Assumptions: outcome approximately normally distributed in each group, independent observations, and (for the standard version) equal variances. For paired data use the paired t-test.

Match these tests to their data: chi-squared, ANOVA, Mann–Whitney U, Wilcoxon signed-rank.

Chi-squared: association between two categorical variables (counts). ANOVA: comparing means across $\geq 3$ groups (parametric). Mann–Whitney U: two independent groups, ordinal/non-normal data (non-parametric). Wilcoxon signed-rank: paired non-parametric comparison.

When should a non-parametric test be used instead of a parametric test?

When parametric assumptions are violated: non-normal (skewed) continuous data, ordinal data, small samples where normality cannot be assumed, or presence of outliers. Non-parametric tests rank data rather than using means and SDs.

Distinguish linear from logistic regression by outcome type and output.

Linear regression: continuous outcome; coefficient $\beta$ = mean change in outcome per unit change in predictor. Logistic regression: binary outcome; models log-odds, and $e^{\beta}$ gives an adjusted odds ratio.

What outcome type does Poisson regression model, and what does its exponentiated coefficient give?

Poisson regression models count or rate data (events over person-time, often with an offset for log person-time). The exponentiated coefficient $e^{\beta}$ gives an adjusted incidence rate ratio. (Negative binomial is used when overdispersion is present.)

What is the purpose of multivariable regression in observational epidemiology?

To estimate the association between an exposure and outcome while simultaneously adjusting for multiple potential confounders, yielding an adjusted effect estimate (e.g. adjusted OR, RR, or coefficient) less distorted by confounding.

What does a Kaplan–Meier curve display, and what is censoring in survival analysis?

A Kaplan–Meier curve plots the estimated probability of surviving (event-free) over time as a step function. Censoring occurs when a participant's outcome is unknown beyond a point (lost to follow-up, withdrew, or study ended event-free); they contribute person-time until censored.

What is the hazard ratio, which model produces it, and a key assumption of that model?

The hazard ratio compares the instantaneous event rate (hazard) between groups; HR $=1$ means no difference. It is produced by the Cox proportional hazards regression model. Key assumption: proportional hazards — the HR is constant over time.

What is the log-rank test used for in survival analysis?

To compare the survival distributions (entire Kaplan–Meier curves) of two or more groups, testing the null hypothesis of no difference in survival over the whole follow-up period. It is non-parametric and weights all time points.

What four quantities determine the required sample size in a power calculation?

(1) Significance level $\alpha$ (Type I error, usually 0.05); (2) Power $1-\beta$ (usually 80–90%); (3) the minimum clinically important effect size; and (4) variability of the outcome (SD for continuous; event rates for binary). Larger effect/lower variance → smaller sample needed.

How does each of the following change the required sample size: larger effect size, smaller $\alpha$, higher power, greater outcome variance?

Larger effect size → smaller sample. Smaller $\alpha$ (more stringent) → larger sample. Higher power → larger sample. Greater outcome variance (SD) → larger sample.

Define sensitivity and specificity, including their formulas from a 2×2 diagnostic table.

Sensitivity = proportion of true cases correctly identified $= \frac{TP}{TP+FN}$ (detects disease). Specificity = proportion of true non-cases correctly identified $= \frac{TN}{TN+FP}$ (excludes disease). Both are properties of the test, independent of prevalence.

Define positive and negative predictive values with formulas.

Positive predictive value: probability disease is present given a positive test $= \frac{TP}{TP+FP}$. Negative predictive value: probability disease is absent given a negative test $= \frac{TN}{TN+FN}$. Both depend on disease prevalence.

Define the positive and negative likelihood ratios and give their formulas.

$$LR+ = \frac{\text{sensitivity}}{1-\text{specificity}}, \qquad LR- = \frac{1-\text{sensitivity}}{\text{specificity}}$$ LR+ >10 and LR- <0.1 provide strong evidence to rule in/out disease. Likelihood ratios are prevalence-independent and combine with pre-test odds: post-test odds = pre-test odds × LR.

What does an ROC curve plot, and how is the area under the curve (AUC) interpreted?

An ROC curve plots sensitivity (true positive rate) against $1 - \text{specificity}$ (false positive rate) across all thresholds. AUC = overall discriminatory ability: $0.5$ = no better than chance, $1.0$ = perfect; higher AUC means better discrimination. The optimal cut-off is often nearest the top-left corner.

Explain the effect of disease prevalence on predictive values.

As prevalence rises, PPV increases and NPV decreases (and vice versa). For a fixed-accuracy test, in low-prevalence settings even a positive result yields a low PPV (many false positives), which is why screening rare conditions produces many false positives.

Distinguish reliability from validity of a measurement.

Reliability (precision): consistency/reproducibility of repeated measurements (free of random error). Validity (accuracy): the extent to which a measure reflects the true value/construct (free of systematic error). A measure can be reliable but invalid (consistently wrong), but cannot be valid without being reasonably reliable.

Name the main types of reliability and validity assessed in measurement studies.

Reliability: test–retest, inter-rater, intra-rater, internal consistency (Cronbach's $\alpha$). Validity: face, content, criterion (concurrent and predictive), and construct (convergent and discriminant) validity.

What statistic measures inter-rater agreement for categorical data, and how is it interpreted?

Cohen's kappa ($\kappa$), which corrects observed agreement for agreement expected by chance. Guide: $<0.20$ poor, $0.21$–$0.40$ fair, $0.41$–$0.60$ moderate, $0.61$–$0.80$ good/substantial, $0.81$–$1.00$ very good/almost perfect.

List the key steps of a systematic review methodology.

Define focused question (PICO); write/register a protocol (e.g. PROSPERO); systematic literature search; screen against pre-defined inclusion/exclusion criteria; assess study quality/risk of bias; extract data; synthesise (narrative or meta-analysis); interpret and report (PRISMA).

What do PICO and PRISMA stand for in evidence synthesis?

PICO = Population, Intervention, Comparator, Outcome (framework for structuring a review question). PRISMA = Preferred Reporting Items for Systematic Reviews and Meta-Analyses (reporting guideline, including the flow diagram of study selection).

What is meta-analysis, and how do fixed-effect and random-effects models differ?

Meta-analysis statistically pools quantitative results from multiple studies into a weighted summary estimate. Fixed-effect assumes one true underlying effect (weights by inverse variance). Random-effects assumes effects vary across studies (incorporates between-study variance $\tau^2$), giving wider CIs and used when heterogeneity is present.

How is statistical heterogeneity assessed in a meta-analysis ($I^2$ and the forest plot)?

Cochran's Q (chi-squared) test and the $I^2$ statistic, which estimates the percentage of total variation across studies due to heterogeneity rather than chance: $I^2$ roughly $25\%$ low, $50\%$ moderate, $75\%$ high. A forest plot displays each study's estimate, CI, and the pooled diamond; the $\tau^2$ quantifies between-study variance.

What is publication bias, and how is it detected in a meta-analysis?

Publication bias occurs when studies with positive/significant results are more likely to be published, inflating the pooled estimate. Detected by a funnel plot (asymmetry suggests bias — small negative studies missing) and tests such as Egger's regression test.

What are the CASP checklists used for in critical appraisal?

Critical Appraisal Skills Programme (CASP) checklists are design-specific tools (for RCTs, cohort, case-control, systematic reviews, qualitative studies, etc.) structured around three questions: Are the results valid? What are the results? Will they help locally (applicability)?

What is the GRADE framework, and what are its four certainty levels?

GRADE (Grading of Recommendations, Assessment, Development and Evaluations) rates the certainty of evidence for each outcome and the strength of recommendations. Four levels: High, Moderate, Low, Very low. RCTs start High and observational studies start Low.

In GRADE, which factors downgrade and which upgrade the certainty of evidence?

Downgrade: risk of bias, inconsistency, indirectness, imprecision, and publication bias. Upgrade (for observational evidence): large magnitude of effect, dose–response gradient, and plausible residual confounding that would reduce the observed effect.

Outline the traditional hierarchy of evidence from strongest to weakest.

Systematic reviews/meta-analyses of RCTs > individual RCTs > cohort studies > case-control studies > cross-sectional/ecological studies > case series/case reports > expert opinion. (Higher levels generally have lower risk of bias and confounding.)

Define evidence-based public health and the three components informing decisions.

The conscientious, explicit use of the best available evidence, alongside professional judgement and the local context, to make decisions about populations' health. Three components: best research evidence, practitioner expertise, and population values/preferences and resource/context considerations.

Name three common qualitative research methods and the type of question they best address.

In-depth interviews, focus groups, and (participant) observation/ethnography; documentary analysis is also used. They best address 'why' and 'how' questions — exploring meanings, experiences, beliefs, and processes — rather than measuring frequency or magnitude.

What is data saturation in qualitative research, and how is it commonly analysed?

Data saturation is the point at which collecting further data yields no new themes or insights, guiding sample size. Analysis is commonly via thematic analysis or framework analysis — coding transcripts, grouping codes into themes, and interpreting them (often supported by software such as NVivo).

What four criteria (Lincoln and Guba) are used to appraise the trustworthiness/rigour of qualitative research?

Credibility (internal validity; e.g. triangulation, member checking), Transferability (external validity; thick description), Dependability (reliability; audit trail), and Confirmability (objectivity; reflexivity to acknowledge researcher influence).