Medical Statistics & Study Design Review

I. Study Designs

Case Series: Describes a small group with a shared condition; useful for rare diseases or complications.
Cross-Sectional Study: Evaluates associations at a single point in time; measures prevalence.
Case-Control Study: Compares cases (with disease) to controls (without); good for rare diseases.
Cohort Study: Follows exposed vs unexposed groups over time.
- Retrospective: Both exposure and outcome have occurred.
- Prospective: Cohort assembled before outcome; good for rare exposures.

Randomized Controlled Trial (RCT): Random assignment to treatment vs control; minimizes confounding.
Blinding:
- Single-blind: patient unaware
- Double-blind: patient and researcher unaware
Analysis Types:
- Intention-to-Treat (ITT): analyzed by original assignment
- Per Protocol: analyzed by actual treatment received
Crossover Study: Subjects switch groups; each serves as own control.
Open-Label Study: No blinding.
Post-Hoc Analysis: Exploratory analysis after study ends.
Subgroup Analysis: Examines specific patient subsets; risk of false positives.

Systematic Review: Synthesizes evidence using a predefined protocol.
Meta-Analysis: Combines data to produce a summary effect size; uses forest plots.

Study Design	Type	Sampling Method	Purpose	Strengths	Limitations
Case Series	Observational	Patients with shared condition	Describe rare diseases or complications	Quick, inexpensive, hypothesis-generating	No control group, cannot infer causality
Cross-Sectional	Observational	Population at one time point	Measure prevalence and associations	Fast, useful for public health	Cannot determine causality
Case-Control	Observational	Based on outcome status	Identify risk factors for rare diseases	Efficient, good for rare outcomes	Recall and selection bias
Cohort (Prospective)	Observational	Based on exposure status	Assess incidence and risk over time	Can establish temporality	Time-consuming, expensive
Cohort (Retrospective)	Observational	Historical data	Assess associations using records	Less costly, faster	Limited by data quality
Randomized Controlled Trial	Experimental	Random assignment	Test efficacy of interventions	Minimizes bias and confounding	Expensive, ethical constraints
Crossover Study	Experimental	Same subjects switch treatments	Compare interventions within individuals	Reduces variability	Requires washout, not for permanent effects
Systematic Review	Evidence synthesis	Predefined search strategy	Summarize existing research	Comprehensive, transparent	Quality depends on included studies
Meta-Analysis	Evidence synthesis	Quantitative pooling	Estimate overall effect size	Increases statistical power	Heterogeneity may limit conclusions

Continuous: Infinite values (e.g., BP)
Categorical:
- Nominal: unordered (e.g., blood type)
- Ordinal: ordered (e.g., income level)

Standard Deviation & Confidence Intervals

How to calculate range using standard deviation:

Range = μ \pm (Z \cdot σ)

Use the formula:

Range = Mean ± (Z-score × Standard
        Deviation)

Example: For 99% confidence, use Z = 2.576 (see table below)

Where:

Common Confidence Levels

Incidence: New cases over time
Prevalence: Total cases at a point in time
Sensitivity: TP / (TP + FN)
Specificity: TN / (TN + FP)
PPV: TP / (TP + FP)
NPV: TN / (TN + FN)
Likelihood Ratios:
- +LR = Sensitivity / (1 – Specificity)
- –LR = (1 – Sensitivity) / Specificity
ROC Curve: Sensitivity vs 1 – Specificity

Relative Risk (RR):
- RR = Incidence in exposed / Incidence in unexposed
- RR = 1 → no association
- RR > 1 → increased risk
- RR < 1 → decreased risk (protective)
- Used in cohort studies and clinical trials
Attributable Risk: Incidence in exposed − Incidence in unexposed
Odds Ratio (OR):
- OR = Odds of exposure in cases / Odds of exposure in controls
- OR = 1 → no association
- OR > 1 → exposure more likely in cases
- OR < 1 → exposure less likely in cases (protective)
- Used in case-control studies
Hazard Ratio (HR):
- Compares instantaneous risk of events between groups
- HR = 3 → one group has 3× the event rate of the other
- Used in survival analysis
Number Needed to Treat (NNT):
- NNT = 100 / Absolute Risk Reduction
- Represents number of patients needed to treat to prevent one adverse outcome
- Lower NNT = more effective treatment
- Example: NNT = 100 → treat 100 patients to benefit 1