Biostatistics & Epidemiology

01 Overview & Role of Biostatistics

Biostatistics and epidemiology are the quantitative foundations of evidence-based medicine. Biostatistics applies statistical methods to biological, medical, and public health data, while epidemiology is the study of the distribution and determinants of health-related states in populations. Together they provide the framework for designing studies, analyzing data, interpreting medical literature, evaluating diagnostic tests, measuring disease burden, and making clinical and public health decisions grounded in data rather than anecdote.

Core Domains

Evidence-Based Medicine Hierarchy

Not all evidence is created equal. The traditional hierarchy of evidence, from strongest to weakest: systematic reviews and meta-analyses of RCTs → individual randomized controlled trials → cohort studies → case-control studies → cross-sectional studies → case series and case reports → expert opinion and bench research. Higher-level evidence generally has better control of bias and confounding, but the best study design depends on the clinical question.

Historical Context

Modern biostatistics traces its origins to the 17^th century with John Graunt's analysis of London bills of mortality, but the discipline was transformed by the work of Pierre-Charles-Alexandre Louis in 19^th century Paris, who used the "numerical method" to disprove the benefit of bloodletting in pneumonia. The 20^th century brought Ronald Fisher's foundational work on statistical inference, the first modern randomized controlled trial (streptomycin for tuberculosis in 1948 by Bradford Hill), and the landmark Framingham Heart Study (1948), which introduced the idea of "risk factors" for cardiovascular disease and established cohort methodology as a mainstay of chronic disease epidemiology.

The discipline was further shaped by major epidemiologic achievements: John Snow tracing the 1854 London cholera outbreak to the Broad Street pump, Doll and Hill establishing the smoking-lung cancer link in the 1950s, the publication of the first Cochrane systematic reviews in the 1990s, and the emergence of large genome-wide association studies (GWAS) in the 2000s. Each of these milestones required new biostatistical methods that now form part of standard practice.

02 Core Terminology & Definitions

A shared vocabulary is essential for reading the medical literature. Misinterpretation of statistical terms is one of the most common sources of error in clinical reasoning.

Foundational Terms

Descriptive vs Analytic Epidemiology

Descriptive epidemiology answers "who, what, when, where" — characterizing disease distribution by person, place, and time. It generates hypotheses. Analytic epidemiology answers "why and how" by formally testing associations between exposures and outcomes. Most clinical research involves analytic epidemiology, but descriptive work remains essential for surveillance, outbreak detection, and public health planning.

Statistical Symbols

03 Types of Data & Variables

The type of variable dictates which descriptive statistics and which statistical tests are appropriate. Misclassification of variable type is a common error that leads to choosing the wrong statistical test.

Variable Classification

Continuous variables are further subdivided into interval data (meaningful intervals, no true zero; e.g., Celsius temperature) and ratio data (meaningful intervals with a true zero; e.g., weight, Kelvin temperature). Ratio data permits statements about multiplication ("twice as heavy"), whereas interval data does not.

Independent vs Dependent Variables

The independent variable (predictor, exposure) is the factor manipulated or observed as the presumed cause. The dependent variable (outcome, response) is the variable measured as the presumed effect. In a study of smoking and lung cancer, smoking status is the independent variable and lung cancer incidence is the dependent variable.

Data Transformation

Skewed continuous data can sometimes be transformed to approximate normality, allowing the use of parametric tests. Common transformations include the logarithmic transformation (for right-skewed data like serum triglycerides, cytokine concentrations, or hospital length of stay), the square root transformation (for count data or mildly skewed data), and the reciprocal transformation (for highly skewed data). Transformation should be pre-specified in the analysis plan whenever possible to avoid data dredging.

Dichotomization Pitfalls

Converting continuous variables to binary categories (e.g., defining hypertension as BP ≥ 140/90) is common but statistically inefficient. Dichotomization reduces statistical power, assumes a sharp biological threshold that rarely exists, and discards clinically relevant information. Where possible, continuous variables should be analyzed as continuous. Clinical cutoffs are useful for decision-making but should not drive statistical analysis.

04 Measures of Central Tendency

Measures of central tendency describe the "typical" or "center" value of a dataset. The three classical measures are the mean, median, and mode, each with different strengths depending on data distribution.

Mean, Median, Mode

Relationship in Skewed Distributions

The relative position of mean, median, and mode reveals distribution shape:

• Symmetric (normal): Mean = Median = Mode
• Positive (right) skew: Mean > Median > Mode (tail on right; e.g., income, length of hospital stay)
• Negative (left) skew: Mean < Median < Mode (tail on left; e.g., age at death, test scores with ceiling effects)

Weighted Mean & Geometric Mean

When observations carry different weights (e.g., pooled studies in meta-analysis or laboratories contributing different sample sizes), the weighted mean gives disproportionate influence to larger or more reliable data points. The geometric mean — the n^th root of the product of n values — is appropriate for log-normally distributed data like antibody titers, viral loads, or drug concentrations, where ratios matter more than differences. The harmonic mean is used for averaging rates (e.g., F₁ score combining precision and recall).

Choosing a Measure

For symmetric continuous data, the mean is most efficient and commonly reported. For skewed data (income, LOS, cost), report the median with IQR. For categorical or nominal data, report the mode or percentages. When in doubt, report multiple measures and the distribution shape, and let readers judge.

05 Measures of Dispersion

Measures of dispersion quantify how spread out data are around the center. Two datasets can share the same mean but differ dramatically in variability, which matters enormously for clinical interpretation.

Common Measures of Spread

Percentiles & Quartiles

The n^th percentile is the value below which n% of observations fall. The median is the 50^th percentile. Q1 (25^th), Q2 (50^th), and Q3 (75^th) are the quartiles, and the IQR (Q3 − Q1) contains the middle 50% of data. Box plots graphically display the median, IQR, and outliers.

06 Distributions & Normality

The shape of a data distribution determines which statistical methods are valid. Most inferential statistical tests assume specific distributional properties, and violating these assumptions can produce misleading results.

The Normal (Gaussian) Distribution

The normal distribution is a symmetric, bell-shaped curve characterized by its mean and standard deviation. Its critical properties underpin most parametric statistics:

• Symmetric about the mean; mean = median = mode
• 68% of data falls within ±1 SD of the mean
• 95% of data falls within ±1.96 SD (≈ 2 SD) of the mean
• 99.7% of data falls within ±3 SD of the mean
• Total area under the curve = 1

Other Distribution Shapes

Z-Scores & Standardization

A z-score expresses how many standard deviations a value lies from the mean: z = (x − μ) / σ. Z-scores allow comparison across variables measured on different scales. A z of +2 means the value is 2 SD above the mean (> 97.5^th percentile in a normal distribution).

Assessing Normality

Before applying parametric tests, researchers should assess whether data are approximately normal. Methods include:

• Visual inspection: Histograms, Q-Q plots, and box plots reveal skewness, bimodality, and outliers
• Formal tests: Shapiro-Wilk test (preferred for small samples), Kolmogorov-Smirnov test, Anderson-Darling test. With large samples (n > 100), these tests become overly sensitive and may reject normality for minor deviations that do not affect inference.
• Skewness & kurtosis values: Skewness near 0 and kurtosis near 3 suggest normality

07 Probability & Sampling

Probability is the mathematical language of uncertainty and the foundation of inferential statistics. Sampling methods determine whether study results can be generalized to the target population.

Rules of Probability

Sampling Methods

08 Central Limit Theorem & Standard Error

The central limit theorem (CLT) is the single most important result in statistics. It provides the theoretical foundation that allows statisticians to make inferences about population parameters from sample data even when the underlying population is not normally distributed.

Implications

The CLT means that even if individual patient blood pressures are skewed, the distribution of sample means from repeated studies will be approximately normal. This allows use of normal-based inference (z-tests, t-tests, confidence intervals) for most research questions involving means, as long as the sample is reasonably large.

Standard Error of the Mean

The standard error of the mean (SEM) quantifies the precision of the sample mean as an estimate of the population mean: SEM = s / √n. Doubling the sample size reduces SE by a factor of √2, not 2 — precision improves but with diminishing returns. Quadrupling n is required to halve the SE.

09 Confidence Intervals

A confidence interval (CI) provides a range of plausible values for a population parameter based on sample data. CIs convey both the point estimate and its precision, and are generally preferred over p-values alone for reporting results.

Interpretation

A 95% confidence interval means that if the study were repeated many times, 95% of the constructed intervals would contain the true population parameter. It does not mean there is a 95% probability the true value lies in this particular interval — a common but incorrect interpretation. The parameter is fixed; the interval varies across samples.

Formula for 95% CI of a Mean

95% CI = x̄ ± 1.96 × (SE)
For 99% CI, multiply SE by 2.58. For 90% CI, multiply by 1.645. Wider intervals correspond to higher confidence at the cost of precision.

Width Determinants

CIs for Other Parameters

CIs & Statistical Significance

• For means: if the 95% CI for the difference does not cross zero, the result is statistically significant at α = 0.05
• For ratios (RR, OR, HR): if the 95% CI does not cross 1.0, the result is statistically significant

10 Hypothesis Testing & p-Values

Hypothesis testing is the formal framework for deciding whether observed data provide enough evidence to reject a null hypothesis in favor of an alternative. It produces the ubiquitous but frequently misinterpreted p-value.

Steps in Hypothesis Testing

1. State the null (H₀) and alternative (H₁) hypotheses
2. Choose the significance level (α), typically 0.05
3. Select the appropriate statistical test based on data type and study design
4. Calculate the test statistic and corresponding p-value
5. Compare p to α: if p < α, reject H₀; if p ≥ α, fail to reject H₀
6. Interpret clinically

p-Value Definition

The p-value is the probability of observing data as extreme (or more extreme) than those actually observed, assuming the null hypothesis is true. A small p-value means the observed data would be unlikely under H₀, providing evidence against H₀.

One-Tailed vs Two-Tailed Tests

A two-tailed test examines whether an effect exists in either direction (H₁: μ ≠ μ₀) and is the default in medical research. A one-tailed test looks only for an effect in a pre-specified direction (H₁: μ > μ₀) and is justified only when an effect in the opposite direction is either impossible or clinically irrelevant. One-tailed testing doubles the power (halves the p-value) but is considered suspect when chosen post-hoc.

11 Type I, Type II Errors & Power

Statistical inference can go wrong in two ways: rejecting a true null hypothesis (Type I error) or failing to reject a false null hypothesis (Type II error). Understanding these errors is essential for designing studies and interpreting results.

Error Matrix

Key Definitions

• Type I error (α): Rejecting H₀ when it is true. Conventionally set at 0.05, meaning 5% false positive rate.
• Type II error (β): Failing to reject H₀ when it is false. Conventionally 0.10–0.20.
• Power (1 − β): Probability of correctly detecting a true effect. Studies are typically designed for 80–90% power.

Determinants of Statistical Power

Multiple Comparisons Problem

When many hypothesis tests are performed in a single study, the probability of at least one false positive rises sharply. Testing 20 independent hypotheses at α = 0.05 yields a 64% probability of at least one false positive under the null. Corrections include:

• Bonferroni correction: Divide α by the number of tests (conservative)
• Holm-Bonferroni: Sequential version, less conservative than Bonferroni
• Benjamini-Hochberg: Controls the false discovery rate (FDR) rather than the family-wise error rate
• Pre-specification of primary and secondary endpoints to limit exploratory analyses

12 Parametric Tests (t-test, ANOVA, Regression)

Parametric tests assume that data follow a known distribution (usually normal) and compare means or other parameters. They are more powerful than non-parametric alternatives when assumptions are met.

t-Tests

Assumptions: continuous outcome, approximately normal distribution, independent observations (except paired), and roughly equal variances (for independent t-test).

ANOVA (Analysis of Variance)

ANOVA extends the t-test to compare means across three or more groups. A one-way ANOVA tests one grouping variable; two-way ANOVA tests two factors simultaneously and can detect interaction effects. The overall F-test indicates whether any groups differ; post-hoc tests (Tukey, Bonferroni) identify which specific groups differ.

Linear Regression

Linear regression models the relationship between a continuous outcome and one or more predictors: Y = β₀ + β₁X₁ + ... + ε. Simple linear regression uses one predictor; multiple linear regression uses several. The coefficient β₁ represents the average change in Y for a one-unit change in X₁, adjusting for other variables. R² quantifies the proportion of variance in Y explained by the model.

Assumptions of Linear Regression

• Linearity: The relationship between predictor and outcome is linear
• Independence: Residuals are independent of each other
• Homoscedasticity: Constant variance of residuals across predictor values
• Normality of residuals: Residuals are approximately normally distributed
• No multicollinearity: Predictor variables are not highly correlated with each other

Violations can be detected with residual plots, Q-Q plots, and variance inflation factors (VIF). VIF > 5–10 suggests problematic multicollinearity that may require dropping or combining predictors.

ANCOVA

Analysis of covariance (ANCOVA) combines ANOVA with regression by comparing group means while adjusting for one or more continuous covariates. It is commonly used in RCTs to adjust outcomes for baseline values, increasing precision compared to unadjusted analysis.

13 Non-Parametric Tests (Chi-Square, Mann-Whitney)

Non-parametric tests make fewer assumptions about the underlying distribution. They are appropriate for ordinal data, small samples, or continuous data that is clearly non-normal and cannot be transformed.

Tests for Categorical Data

Tests for Continuous/Ordinal Data

14 Survival Analysis & Cox Regression

Survival analysis handles time-to-event data, including the challenge of censoring — subjects whose event has not occurred by study end or who are lost to follow-up. It is essential in oncology, cardiology, and transplant medicine.

Kaplan-Meier Analysis

The Kaplan-Meier method estimates the survival function — the probability of surviving past time t — and produces the familiar stepwise survival curve. At each event time, the survival probability drops by the fraction of subjects experiencing the event. Censored subjects appear as tick marks and contribute data until censoring.

Log-Rank Test

The log-rank test compares two or more Kaplan-Meier survival curves under the null hypothesis that they are identical. It is the most common test for comparing survival between treatment arms in RCTs.

Cox Proportional Hazards Regression

Cox regression models the hazard ratio (HR) — the instantaneous risk of the event in one group relative to another — while adjusting for covariates. HR = 1 means no difference; HR > 1 means higher hazard; HR < 1 means lower hazard. The key assumption is that hazards are proportional over time (constant HR).

Censoring

Censoring occurs when a subject's event time is not observed — because the study ended, the subject was lost to follow-up, or died from an unrelated cause. Right censoring (the most common type) means the event, if it occurs, will occur after the last observed time. Survival analysis methods assume that censoring is non-informative — that censored subjects have the same underlying risk as those who remain in the study. Violations of this assumption (e.g., sicker patients dropping out) bias the estimates.

Competing Risks

When subjects can experience multiple mutually exclusive outcomes (e.g., death from cancer vs death from heart disease), standard Kaplan-Meier methods overestimate the probability of the outcome of interest. Competing risk methods such as the cumulative incidence function (CIF) and Fine-Gray regression properly account for these alternative events.

15 Correlation & Logistic Regression

Correlation Coefficients

Correlation measures the strength and direction of association between two variables. It does not imply causation.

• Pearson's r: Linear correlation between two continuous, normally distributed variables. Range: −1 to +1.
• Spearman's ρ: Rank-based correlation for ordinal or non-normal continuous data.
• r = 0: no linear relationship; r = ±1: perfect linear relationship
• |r| < 0.3: weak; 0.3–0.7: moderate; > 0.7: strong

Intraclass Correlation & Kappa

When evaluating agreement between observers or methods, different measures apply depending on data type. For categorical data, Cohen's kappa (κ) adjusts observed agreement for chance agreement: κ < 0.2 is slight, 0.2–0.4 fair, 0.4–0.6 moderate, 0.6–0.8 substantial, 0.8–1.0 almost perfect. For continuous data, the intraclass correlation coefficient (ICC) measures reliability between raters. Bland-Altman plots visualize agreement between two measurement methods.

Logistic Regression

Logistic regression is used when the outcome is binary (yes/no, dead/alive, disease/no disease). It models the log-odds of the outcome as a linear function of predictors: ln(p/(1−p)) = β₀ + β₁X₁ + .... Coefficients exponentiated (e^β) give adjusted odds ratios, allowing simultaneous adjustment for multiple confounders.

16 Sensitivity, Specificity, PPV & NPV

Evaluating diagnostic tests requires understanding their intrinsic properties (sensitivity, specificity) and how those properties translate into clinical predictive values given disease prevalence.

The 2×2 Diagnostic Table

Core Definitions

Prevalence Dependence of PPV and NPV

Sensitivity and specificity are intrinsic test properties (do not vary with prevalence). PPV and NPV depend heavily on disease prevalence. As prevalence increases, PPV rises and NPV falls. This explains why a highly specific screening test produces many false positives when used in low-prevalence populations (e.g., mammography in 30-year-olds).

Spectrum Bias

The sensitivity and specificity of a test can appear different in different populations due to spectrum bias — the phenomenon that test performance depends on the distribution of disease severity in the study population. A cardiac biomarker tested in patients with obvious STEMI will show higher sensitivity than when tested in patients with ambiguous chest pain. Clinicians should interpret published test characteristics in light of the spectrum of patients studied, not their own clinic.

Trade-Off Between Sensitivity and Specificity

For any continuous diagnostic test, lowering the cutoff increases sensitivity at the expense of specificity and vice versa. The ROC curve visualizes this trade-off. Choosing the cutoff requires weighing the relative costs of false positives and false negatives, which depend on disease severity, treatment risks, and downstream workups.

17 Likelihood Ratios & ROC Curves

Likelihood Ratios

Likelihood ratios combine sensitivity and specificity into a single number that quantifies how much a test result changes the probability of disease. Unlike PPV/NPV, LRs are independent of prevalence.

• Positive LR (LR+) = SN / (1 − SP) — how much more likely a positive result occurs in diseased vs healthy
• Negative LR (LR−) = (1 − SN) / SP — how much more likely a negative result occurs in diseased vs healthy

Probability-to-Odds Conversion

Conversion: odds = p / (1 − p) and p = odds / (1 + odds). Knowing the relationship is essential for applying Bayes theorem in the odds form.

ROC Curves & AUC

A Receiver Operating Characteristic (ROC) curve plots sensitivity (true positive rate) against 1 − specificity (false positive rate) across all possible cutoff values. The area under the curve (AUC) measures overall test discrimination:

18 Bayes Theorem & Pre/Post-Test Probability

Bayes theorem formalizes how prior knowledge (pre-test probability) combines with new evidence (test results) to update the probability of disease (post-test probability). It is the mathematical foundation of clinical diagnostic reasoning.

The Theorem

P(Disease | Test+) = P(Test+ | Disease) × P(Disease) / P(Test+)

Clinical Form Using Odds and LRs

Post-test odds = Pre-test odds × LR

1. Estimate pre-test probability of disease (from prevalence, history, exam)
2. Convert probability to odds: odds = p / (1 − p)
3. Multiply by LR for the observed test result
4. Convert back to probability: p = odds / (1 + odds)

Example

A patient with chest pain has a 30% pre-test probability of acute coronary syndrome. Troponin is positive with an LR+ of 25. Pre-test odds = 0.30/0.70 = 0.43. Post-test odds = 0.43 × 25 = 10.7. Post-test probability = 10.7/11.7 = 91%. Diagnosis essentially confirmed.

Fagan Nomogram

The Fagan nomogram is a graphical tool that allows bedside application of Bayes theorem without calculation. A line drawn from the pre-test probability through the LR intersects a post-test probability axis. Clinicians with a stored mental estimate of pre-test probability and a memorized LR for common tests can execute diagnostic reasoning rapidly.

Sequential Testing

When multiple tests are applied in sequence, the post-test probability of the first test becomes the pre-test probability for the second, provided the tests are conditionally independent (each test adds unique information). Applying dependent tests sequentially can give a falsely inflated sense of certainty because the second test's information overlaps with the first.

19 Measures of Disease Frequency

Epidemiology quantifies how common diseases are in populations. The core measures are incidence (new cases) and prevalence (existing cases), each with distinct uses and interpretations.

Core Frequency Measures

Prevalence-Incidence Relationship

Prevalence ≈ Incidence × Duration (for stable, low-prevalence conditions). Chronic diseases with long durations (HIV, diabetes) have high prevalence relative to incidence. Acute diseases with short duration (common cold, fulminant sepsis) have prevalence much lower than annual incidence.

Mortality Measures

Person-Time & Dynamic Populations

When subjects are observed for different lengths of time, incidence is calculated per person-time at risk rather than per person. A study following 100 people for an average of 2 years each contributes 200 person-years. If 10 develop disease, the incidence rate is 10/200 = 5 per 100 person-years. This approach accommodates losses to follow-up, deaths, and late entries to the study.

20 Measures of Association (RR, OR, NNT)

Measures of association quantify the strength of the relationship between exposure and outcome. Different measures are appropriate for different study designs.

2×2 Table for Exposure/Outcome

Relative Measures

RR = 1 means no association; RR > 1 means exposure increases risk; RR < 1 means exposure is protective. The OR approximates the RR when disease is rare (< 10% prevalence) but overestimates RR when disease is common.

Why OR Overestimates RR in Common Diseases

Mathematically, OR = RR × [(1 − p_control) / (1 − p_exposed)]. When disease is rare (both p's are small), the correction factor approaches 1 and OR ≈ RR. When disease is common (e.g., 30% in each group), the correction factor deviates substantially from 1 and OR substantially overestimates the true relative risk. This is why journalists reporting "twice the risk" from an OR of 2.0 can be misleading when the condition is common.

Absolute Measures

Interpreting Effect Measures

Confidence Intervals Around Effect Measures

When a 95% CI for a relative measure (RR, OR, HR) crosses 1.0, the result is not statistically significant. The closer the lower bound is to 1.0, the less robust the finding. Wide confidence intervals for effect measures usually indicate small sample size and should prompt caution in clinical interpretation.

21 Standardization & Adjusted Rates

Comparing crude rates between populations can be misleading because of differences in underlying structure (e.g., age distribution). Standardization adjusts for these differences.

Direct vs Indirect Standardization

The standardized mortality ratio (SMR) is observed deaths divided by expected deaths (indirect method). SMR > 1 indicates higher mortality than the standard; SMR < 1 indicates lower. SMRs are widely used in occupational epidemiology to detect excess mortality in worker cohorts.

22 Observational Study Designs

Observational studies observe exposures and outcomes without intervention. They are essential when randomization is unethical or impractical but are more vulnerable to bias and confounding than experiments.

Descriptive Designs

Analytic Observational Designs

Nested and Hybrid Designs

Advantages & Disadvantages Summary

23 Randomized Controlled Trials & Phases

The randomized controlled trial is the gold standard for establishing causation and evaluating interventions. Random allocation controls for both known and unknown confounders, allowing causal inference.

Key Features of RCTs

• Randomization: Allocation by chance eliminates selection bias and distributes confounders equally
• Allocation concealment: Those enrolling patients cannot know or predict the next assignment
• Blinding: Single-blind (patient only), double-blind (patient + investigator), triple-blind (+ analyst)
• Control group: Placebo or active comparator
• Intention-to-treat (ITT) analysis: Patients analyzed in their assigned group regardless of adherence — preserves randomization
• Per-protocol analysis: Only patients who completed assigned treatment — can introduce bias

RCT Variants

Clinical Trial Phases

Randomization Methods

Bias Prevention in RCTs

The CONSORT (Consolidated Standards of Reporting Trials) guidelines mandate transparent reporting of randomization, allocation concealment, blinding, primary and secondary outcomes, and loss to follow-up. Risk of bias tools (e.g., Cochrane Risk of Bias 2) systematically assess each domain. Trials with unconcealed allocation or inadequate blinding consistently overestimate treatment effects compared to rigorously conducted trials.

24 Meta-Analysis, Systematic Review & GRADE

Systematic reviews and meta-analyses synthesize evidence across multiple studies to produce more precise estimates and resolve conflicting findings. They sit at the top of the evidence hierarchy when well-conducted.

Systematic Review vs Meta-Analysis

• Systematic review: Structured, comprehensive, reproducible synthesis of all relevant literature on a question using predefined criteria.
• Meta-analysis: Statistical combination of results from multiple studies to produce a pooled effect estimate.
• Every meta-analysis should be based on a systematic review; not every systematic review yields a meta-analysis.

Key Concepts in Meta-Analysis

GRADE Framework

The Grading of Recommendations Assessment, Development and Evaluation (GRADE) framework rates the quality of evidence (high, moderate, low, very low) and strength of recommendations (strong or weak/conditional). RCTs start at high quality and can be downgraded for risk of bias, inconsistency, indirectness, imprecision, and publication bias. Observational studies start at low quality and can be upgraded for large effects, dose-response, or plausible confounding that would bias toward null.

PRISMA & Reporting Standards

The PRISMA (Preferred Reporting Items for Systematic reviews and Meta-Analyses) statement provides a checklist for transparent reporting. Other reporting standards include CONSORT for RCTs, STROBE for observational studies, STARD for diagnostic accuracy studies, and TRIPOD for prediction model studies. Familiarity with these standards is valuable both for authors writing papers and for readers critiquing them.

Network Meta-Analysis

When several treatments have been compared to various controls in different trials, a network meta-analysis combines direct (head-to-head) and indirect (via common comparator) evidence to rank treatments and estimate comparative effects that were never directly tested. This methodology is increasingly important for guideline development when multiple competing therapies exist.

25 Bias & Error Types

Bias is systematic error that distorts study results in a particular direction. Unlike random error, bias cannot be fixed by increasing sample size — it must be prevented through careful study design.

Selection Bias

Information (Measurement) Bias

Time-Related Biases

Random vs Systematic Error

Detection & Control of Bias

Bias cannot be eliminated entirely, but its influence can be minimized through careful study design, strict protocols, and thoughtful analysis. Sensitivity analyses can test how robust conclusions are to plausible biases. External validation of findings in independent populations remains one of the most powerful tools for confirming that a result is not an artifact of bias in the original study.

26 Confounding, Effect Modification & Causation

Confounding

A confounder is a variable that is (1) associated with the exposure, (2) independently associated with the outcome, and (3) not on the causal pathway between exposure and outcome. Confounding distorts the apparent relationship between exposure and outcome.

Methods to Control Confounding

Effect Modification (Interaction)

Effect modification occurs when the effect of exposure on outcome differs across strata of a third variable. Unlike confounding, which is a nuisance to be controlled, effect modification is a biological or clinical finding to be reported. For example, aspirin reduces cardiovascular events more in men than in women — sex is an effect modifier, not a confounder.

Internal vs External Validity

• Internal validity: Extent to which study findings accurately reflect the true relationship in the study population. Threatened by bias, confounding, chance.
• External validity (generalizability): Extent to which findings apply to other populations, settings, or conditions. Threatened by restrictive inclusion criteria, artificial settings.

Hill Criteria for Causation

Sir Austin Bradford Hill's 1965 criteria remain the standard framework for inferring causation from observational data:

1. Strength of association (larger RR more likely causal)
2. Consistency across studies and populations
3. Specificity of association (one cause, one effect)
4. Temporality (cause precedes effect) — only absolute requirement
5. Biological gradient (dose-response)
6. Plausibility (biological mechanism)
7. Coherence with existing knowledge
8. Experiment (intervention supports effect)
9. Analogy (similar causes produce similar effects)

Example: Confounding by Indication

A particularly challenging form of confounding in pharmacoepidemiology is confounding by indication, where the reason a drug was prescribed (disease severity, comorbidities) is itself associated with the outcome. Observational studies of antibiotic use and mortality are often confounded this way: sicker patients are more likely to receive antibiotics and more likely to die, making antibiotics appear harmful when they are not. This is one reason RCTs are essential for evaluating therapies.

Detecting Effect Modification

Effect modification is assessed by testing for statistical interaction — adding an interaction term (exposure × modifier) to a regression model. A significant interaction suggests the exposure effect differs across levels of the modifier. Effect modification should be reported, not eliminated. Stratum-specific estimates are the primary output, not pooled summary measures.

27 Screening & USPSTF Principles

Screening is the testing of asymptomatic individuals to detect disease at an earlier, more treatable stage. Effective screening requires meeting specific criteria to justify its cost, harms, and population impact.

WHO / Wilson-Jungner Criteria for Screening

1. Disease is an important health problem
2. Natural history of disease is understood
3. Recognizable early or latent stage exists
4. Suitable screening test available (sensitive, acceptable, affordable)
5. Effective treatment available for early-stage disease
6. Treatment at early stage improves outcomes vs later treatment
7. Facilities for diagnosis and treatment are available
8. Cost-effective relative to health benefit
9. Continuous process, not one-time effort

USPSTF Recommendation Grades

Major USPSTF Grade A & B Recommendations

Overdiagnosis

Overdiagnosis is the detection of disease that would never have caused symptoms or death during the patient's lifetime. It differs from misdiagnosis (wrong diagnosis) in that the pathology is real but indolent. Overdiagnosis is particularly common in cancers with highly variable biology (prostate, thyroid, early breast, indolent lung lesions). Every overdiagnosed patient is exposed to treatment harms without possibility of benefit.

28 High-Yield Review

The following is a distilled review of the most commonly tested and clinically essential concepts in biostatistics and epidemiology.

Statistical Test Selection Cheat Sheet

Top 20 Concepts to Master

1. Sensitivity, specificity, PPV, NPV and the effect of prevalence
2. Likelihood ratios and Bayesian updating of pre-test probability
3. Relative risk, odds ratio, absolute risk reduction, NNT
4. Confidence intervals: interpretation and construction
5. p-values: definition and common misinterpretations
6. Type I/II errors and statistical power
7. Central limit theorem and sampling distributions
8. Normal distribution properties (68-95-99.7 rule)
9. Mean, median, mode in symmetric vs skewed data
10. Standard deviation vs standard error
11. Choosing parametric vs non-parametric tests
12. Chi-square and Fisher exact for categorical data
13. Kaplan-Meier survival curves and log-rank test
14. Cohort vs case-control vs cross-sectional designs
15. RCT features: randomization, blinding, ITT analysis
16. Systematic review and meta-analysis (forest plot, I²)
17. Bias types: selection, information, lead-time, length-time
18. Confounding vs effect modification
19. Hill criteria for causation
20. USPSTF grades and screening principles

Must-Know Formulas

Study Design Quick Reference

Common Pitfalls & Misinterpretations

• p < 0.05 does not mean clinically important. Always evaluate effect size and CI.
• Non-significant does not mean no effect. Check power and CI width.
• Correlation does not equal causation. Consider confounding and reverse causation.
• RR and OR are not identical. OR overestimates RR when disease is common.
• PPV depends on prevalence. High specificity is not enough in low-prevalence screening.
• Lead-time bias makes screened patients appear to live longer even without benefit.
• ITT preserves randomization. Per-protocol analysis introduces bias.
• Confidence intervals beat p-values because they convey both direction and precision.
• Funnel plot asymmetry suggests publication bias in meta-analyses.
• Ecologic fallacy — group-level data cannot be used to infer individual-level relationships.

Key Rules of Thumb

• n ≥ 30 is usually large enough for the central limit theorem to apply
• Expected cell counts ≥ 5 are needed for chi-square; otherwise use Fisher exact
• Power ≥ 80% is the conventional minimum for trial design
• I² > 50% suggests substantial heterogeneity in meta-analysis
• LR+ > 10 and LR− < 0.1 are clinically useful thresholds
• κ > 0.6 indicates substantial inter-rater agreement
• AUC > 0.8 indicates good discrimination for a diagnostic test
• VIF > 5 suggests problematic multicollinearity

Landmark Trials & Studies

High-Yield Epidemiology Pearls

• Incidence measures new cases; prevalence measures existing cases.
• Prevalence = Incidence × Duration (approximately, for stable conditions).
• A highly SeNsitive test rules disease OUT; a highly SPecific test rules disease IN.
• Likelihood ratios are prevalence-independent and combine with pre-test odds via Bayes.
• LR+ > 10 or LR− < 0.1 are clinically powerful.
• Randomization controls for both known and unknown confounders.
• Blinding prevents ascertainment and measurement bias, not selection bias.
• Hill criteria: temporality is the only absolute requirement for causation.
• Overdiagnosis is the most underappreciated harm of modern cancer screening.
• NNT is the most clinically intuitive measure of treatment benefit.
• Case-control studies yield odds ratios; cohort studies yield relative risks.
• Confidence intervals crossing 1.0 (for ratios) or 0 (for differences) are not significant.
• p-values do not measure effect size or clinical importance.
• Loss to follow-up > 20% threatens internal validity of cohort studies.
• Confounding is a property of the data; effect modification is a biological finding.

Critical Appraisal Framework

When reading a clinical research paper, apply a structured checklist:

1. Research question: What was the PICO (population, intervention, comparison, outcome)?
2. Study design: Is the design appropriate for the question?
3. Internal validity: Was randomization adequate? Were patients blinded? Was ITT used? What was loss to follow-up?
4. Results: What is the effect size? Is it statistically and clinically significant? What is the precision (CI width)?
5. External validity: Do the patients resemble mine? Was the intervention feasible?
6. Harms: What adverse effects were reported? How do benefits compare to harms (NNT vs NNH)?
7. Conflicts of interest: Funding source? Author disclosures?

Common Board Exam Questions

Clinical Epidemiology Tools

These clinical prediction rules apply biostatistical models at the bedside, transforming risk factor data into actionable probability estimates. Their development and validation illustrate the integration of epidemiology with clinical decision-making.