Paper B stats

Main sampling methods

• Random
• Stratified
• Systematic
• Purposive
• Snowball

Difference between nominal, ordinal, interval, and ratio data

• Nominal: Unordered groups
• Ordinal: Ordered groups with unequal spacing
• Interval: Equal spacing, arbitrary zero
• Ratio: Equal spacing, true zero

When to use mean, median, and mode

• Mean: Normal distributions
• Median: Skewed data
• Mode: Most frequent value

Difference between Standard Deviation (SD) and Interquartile Range (IQR)

• Standard Deviation (SD): Used for normal data
• Interquartile Range (IQR): Used for skewed data

Formula for Standard Error of the Mean (SEM)

$$\text{SEM} = \frac{\text{population SD}}{\sqrt{n}}$$

Meaning of a $95\%$ Confidence Interval (CI)

There is a $95\%$ chance that the calculated confidence interval contains the true population value.

Difference between Standard Deviation (SD) and Standard Error (SE)

• Standard Deviation (SD): Measures the distribution/spread of individual data points
• Standard Error (SE): Measures the precision of the sample mean estimate

Empirical rule for normal distribution ($1$, $2$, and $3$ standard deviations)

• $1\text{ SD}$: Contains $68\%$ of data
• $2\text{ SD}$: Contains $95.4\%$ of data
• $3\text{ SD}$: Contains $99.7\%$ of data

Identification of positive vs. negative skew

• Positive skew: Long tail at the higher end (right)
• Negative skew: Long tail at the lower end (left)

Components of a box-and-whisker plot

• Thick center line: Median
• Box edges: Upper ($Q_3$) and lower ($Q_1$) quartiles
• Whiskers: Highest and lowest values

The null hypothesis ($H_0$)

The proposition that there is no real difference or effect between populations.

Definition of p-value

The probability of observing a difference by chance if the null hypothesis is true.

Difference between Type I and Type II errors

• Type I error ($\alpha$): False positive
• Type II error ($\beta$): False negative

Power in hypothesis testing

The probability ($1 - \beta$) of detecting a real effect if one truly exists.

Effect of sample size ($n$) on the p-value

As sample size ($n$) increases, the $p\text{-value}$ generally decreases (gets smaller).

Judging statistical significance from a Confidence Interval (CI)

If the $95\% \text{ CI}$ includes the 'no effect' point (e.g., $0$ for difference, $1$ for ratio), the result is not statistically significant.

Difference between statistical and clinical significance

• Statistical significance: Can occur even with trivial differences in large samples
• Clinical significance: Requires judgment on whether the magnitude of difference is clinically meaningful

Cohen's d thresholds for effect size

• Small effect: $0.2$
• Moderate effect: $0.5$
• Large effect: $0.8$

Types of scale validity

• Face & Content
• Criterion (Concurrent/Convergent & Divergent/Discriminant)
• Predictive
• Construct

Internal validity

The assurance that the observed difference is truly due to the treatment/intervention rather than bias or confounding.

Inter-rater reliability

The level of agreement between different independent raters.

Purpose of the Bland-Altman method

Assessing agreement between two quantitative measurement methods.

Internal consistency

The degree to which items expected to measure the same construct correlate with each other.

Relationship between reliability and validity

Yes, a measurement scale must be reliable in order to be valid.

Difference between bias and random error

• Bias: Systematic error
• Random error: Natural fluctuation/variation

Information bias

Inaccurate measurement or classification resulting from reporting errors or observer bias.

Definition of a confounder

A third variable associated with both the exposure and outcome, but not on the causal pathway.

Key distinction between a confounder and a mediator

• Mediator: Lies on the causal pathway
• Confounder: Lies outside the causal pathway

Methods for controlling confounding

• Design Stage:
  • Restriction
  • Matching
  • Randomization
• Analysis Stage:
  • Stratification
  • Multivariable regression

Effect modification

A situation where a third variable changes the strength or direction of an exposure-outcome relationship.

Four possible explanations for an observed group difference

1. Reverse causation
2. Bias
3. Confounding
4. Chance

Allocation concealment

A procedure performed before randomization to prevent selection bias.

Blinding in research

A procedure performed after randomization to prevent performance or information bias.

The 5 steps of a 'gold standard' Randomized Controlled Trial (RCT)

1. Recruit sample
2. Randomly allocate
3. Carry out treatment
4. Measure outcome
5. Analyze data

Biases minimized by randomization

• Selection bias
• Confounding

Quasi-randomization

Allocation by a non-random systematic method that risks selection bias.

Primary rationale for Cluster RCTs

Used when individual randomization is impractical or risks contamination.

Purpose of a placebo run-in period

To increase statistical power by identifying and excluding non-compliant subjects or early responders before randomization.

Difference between parallel and crossover trial designs

• Parallel: Different groups receive different treatments simultaneously
• Crossover: Each participant receives all treatments sequentially over time

Single blinding

Only one party (typically the outcomes assessor or participant) is blinded to group allocation.

Intention-to-Treat (ITT) analysis

Analyzing participants according to their original group allocation to prevent biased exclusion.

Common strategies for handling dropout data

• Last Observation Carried Forward (LOCF)
• Sensitivity analysis
• Statistical imputation

Primary purpose of a t-test

Comparing sample means between two groups.

Heteroscedasticity

Unequal variances (standard deviations) across comparison groups.

Primary purpose of ANOVA

Comparing sample means across more than two groups.

Difference between one-way and two-way ANOVA

• One-way ANOVA: One grouping factor
• Two-way ANOVA: Two grouping factors

ANCOVA (Analysis of Covariance)

A regression method that tests if group means differ while adjusting for baseline covariates.

Non-parametric equivalent of an independent t-test

Mann-Whitney U test

Formula for degrees of freedom ($df$) in a chi-squared test

$$df = (\text{columns} - 1) \times (\text{rows} - 1)$$

Primary application of a Kaplan-Meier curve

Visualizing and analyzing time-to-event data.

Formula for Number Needed to Treat (NNT)

$\text{NNT} = \frac{1}{\text{ARR}}$(where $\text{ARR}$ is Absolute Risk Reduction)

Definition of QALY

Quality-Adjusted Life Year

NICE cost-effectiveness threshold in England

Approximately $\pounds 20,000$ to $\pounds 30,000$ per QALY gained.

Difference between cost-minimization and cost-benefit analysis

• Cost-minimization: Compares costs only
• Cost-benefit: Evaluates all costs and benefits in a single monetary unit

Incidence risk

The proportion of an at-risk population that develops a disease condition over a given period.

Formula for Standardized Mortality Ratio (SMR)

$$\text{SMR} = \left(\frac{\text{Actual Deaths}}{\text{Expected Deaths}}\right) \times 100$$

Main limitation of cross-sectional studies

Inability to establish causality because exposure and outcome are measured at the same time.

Limitation of cross-sectional studies in etiology

Because exposure and outcome are assessed simultaneously, temporality cannot be established.

Core definition of a cohort study

Study design where groups are defined by exposure status at the start and followed forward to observe outcomes.

Core definition of a case-control study

Study design where groups are defined by outcome status and evaluated retrospectively for prior exposure.

Relative strengths of prospective cohort studies

• Confirms exposure precedes outcome
• Minimizes information/recall bias
• Excellent for rare exposures

Relative strengths of case-control studies

• Inexpensive and fast
• Avoids attrition bias
• Excellent for rare outcomes

Nested case-control study

Cases and controls drawn from within an existing cohort to combine efficiency with prospective exposure timing.

Neyman (survivor) bias

Bias resulting from excluding individuals who died from the outcome prior to recruitment.

Unit of analysis and key risk in ecological studies

• Unit of analysis: Aggregate groups (not individuals)
• Key risk: Ecological fallacy (assuming aggregate findings apply to individuals)

Causation in observational studies

No, observational studies show association, not causation, as unmeasured confounding cannot be ruled out.

Distinction between linear, logistic, and Cox regression

• Linear regression: Continuous outcomes
• Logistic regression: Binary outcomes
• Cox regression: Time-to-event outcomes

Indication of a significant interaction term in regression

Indicates effect modification, meaning one variable's effect on the outcome depends on the level of another variable.

Limitation of multiple regression vs. randomization for confounding

Multiple regression only adjusts for measured confounders, whereas randomization balances both measured and unmeasured confounders.

Difference between a systematic review and a meta-analysis

• Systematic review: Structured qualitative synthesis of literature
• Meta-analysis: Quantitative statistical pooling of results across studies

Funnel plot purpose and publication bias detection

• Purpose: Plots treatment effect against study precision/size
• Bias detection: Asymmetry indicates potential publication bias

Key visual components of a forest plot

• Study line: Box (point estimate, size $\propto$ weight) and horizontal line ($95\% \text{ CI}$)
• Pooled estimate: Diamond at bottom
• Vertical line: Line of no effect

Difference between clinical and statistical heterogeneity

• Clinical heterogeneity: Differences in populations, interventions, or outcomes
• Statistical heterogeneity: Variability in effect estimates beyond chance

Difference between fixed-effects and random-effects meta-analysis

• Fixed-effects: Assumes a single true effect size
• Random-effects: Accounts for true effect size variation across studies

Network meta-analysis

A technique combining direct and indirect evidence across trials to compare and rank multiple treatments.

Formulas for sensitivity, specificity, PPV, and NPV

• Sensitivity: $\frac{a}{a+c}$
• Specificity: $\frac{d}{d+b}$
• PPV: $\frac{a}{a+b}$
• NPV: $\frac{d}{c+d}$

Effect of disease prevalence on diagnostic test metrics

• PPV & NPV: Vary with prevalence
• Sensitivity & Specificity: Remain constant regardless of prevalence

Formulas for Positive and Negative Likelihood Ratios (LR+ and LR−)

• $\text{LR}+$: $\frac{\text{Sensitivity}}{1 - \text{Specificity}}$
• $\text{LR}-$: $\frac{1 - \text{Sensitivity}}{\text{Specificity}}$

Calculation of post-test probability using Fagan's nomogram / odds

1. $\text{Post-test Odds} = \text{Pre-test Odds} \times \text{LR}+$
2. $\text{PPV} = \frac{\text{Post-test Odds}}{\text{Post-test Odds} + 1}$

Axes of a Receiver Operating Characteristic (ROC) curve

• Y-axis: Sensitivity
• X-axis: $1 - \text{Specificity}$

Core features of qualitative research

• Non-numerical analysis
• Interpretative focus
• Small, purposively selected samples

Main limitation of qualitative research

Low generalizability.

Grounded theory

Codes and categories emerge inductively from data using constant comparison until saturation.

Three types of triangulation in research

1. Data triangulation
2. Investigator triangulation
3. Theory triangulation

Reflexivity in qualitative research

The researcher's critical reflection on how their presence and assumptions influence the research.

Bracketing in qualitative research

Setting aside personal biases and preconceptions during analysis.

Common qualitative research methodologies

• Ethnography
• IPA (Interpretative Phenomenological Analysis)
• Thematic analysis
• Member checking

Key pro and con of Randomized Controlled Trials (RCTs)

• Pro: Minimizes selection bias and confounding
• Con: Expensive and may have limited generalizability

Key pro and con of cohort studies

• Pro: Confirms exposure precedes outcome
• Con: Cannot rule out residual confounding

Key pro and con of case-control studies

• Pro: Cheap and fast
• Con: Prone to recall bias

Key pro and con of qualitative studies

• Pro: Provides deep contextual detail
• Con: Low statistical generalizability

Attrition bias

Systematic bias arising from differential participant drop-out rates between groups.

Non-response / volunteer bias

Bias occurring when individuals who agree to participate differ systematically from those who decline.

Performance bias and its prevention

• Definition: Systematic differences in care provided to groups other than the intervention
• Prevention: Blinding and standard control groups