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USMLE Step 1 High‐Yield Biostatistics Topics
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Biostatistics
High Yield USMLE Step 1 Notes
Welcome to the Biostatistics High-Yield Notes for Step 1.
These are the most commonly tested topics on the exam—ideal for quick review in your last 2 weeks before the exam, when you’re short on time, or when you’re just starting out and want to focus on what is high yield. Created and peer-reviewed by physicians who scored 260+ on Step 1 in a Q&A style to reinforce active learning.
How to use this file
- Read the question ➔ cover the answer ➔ self-quiz before revealing.
- Review the NOTES ➔ they include high-yield details you don’t want to miss.
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Table of Contents
Study Design
1. A study enrolls 100 patients with lung cancer and 100 without. Researchers ask about their smoking history. What type of study is this?
➔ Case-control study
- Note: Starts with outcome (lung ca.), then looks backward for exposure (smoking). Recall bias risk.
- Efficient for rare diseases. Cannot calculate incidence or prevalence.
2. Researchers follow 200 smokers and 200 non-smokers over 10 years to assess the development of coronary artery disease. What is the study design?
➔ Prospective cohort study
- Note: Starts with exposure, follows over time for outcome.
- Can assess incidence and establish temporal relationships. Loss of follow-up bias risk.
3. Medical records of 400 patients from 2015 were reviewed to identify those with a BMI over 30 and a control group with a BMI under 25. These patients’ records are then reviewed up to 2020 to see how many in each group developed diabetes. What type of study is this?
➔ Retrospective cohort study
- Note: Both exposure and outcome have already occurred. Based on existing data.
4. A survey of 1,000 people is done to assess current smoking status and whether they have COPD. What is the study design?
➔ Cross-sectional study
- Note: Measures exposure and outcome at the same time.
- Can estimate prevalence but not causality.
5. A study compares city-level fast food outlet density and obesity rates. What is this study type?
➔ Ecological study
- Note: Uses population-level data rather than individual-level data.
- Useful for generating hypotheses but subject to ecological fallacy.
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6. In a twin study, schizophrenia concordance is 50% in monozygotic twins and 15% in dizygotic twins. What type of study is this?
➔ Twin concordance study
- Note: Helps assess the relative contribution of genetics vs environment. Greater concordance in monozygotic twins suggests a genetic component.
Clinical Trial Phases
7. A new drug is tested on 50 healthy volunteers to assess safety and pharmacokinetics. What phase is this?
➔ Phase I clinical trial
- Note: First-in-human studies. Focus on safety and side effects.
8. A randomized controlled trial assigns 1,000 patients to receive either a new drug or a placebo to assess efficacy. What phase is this?
➔ Phase III clinical trial
- Note: Large-scale trial to confirm effectiveness, monitor side effects, and compare to standard treatments. Used for FDA approval.
9. A drug has been approved and is now being monitored for rare or long-term side effects in the general population. What phase is this?
➔ Phase IV clinical trial
- Note: Post-marketing surveillance. Detects rare side effects.
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Risk Calculations
10. Lung cancer occurs in 10% of smokers and 2% of non-smokers. What is the relative risk (RR)?
➔ RR = Incidence in exposed/ incidence in unexposed= 10% / 2% = 5.0
- Note: RR > 1 means the exposure (smoking) is associated with increased disease risk.
- RR < 1 means the exposure (smoking) is associated with decreased disease risk.
- RR=1 means there is no relation between the exposure and the disease
11. A vaccine reduces the risk of meningitis from 9% to 3%. What is the relative risk reduction (RRR)?
➔ RRR = 1- RR= 1 – (3% / 9%) = 67%
- Note: RRR quantifies how much the risk is reduced in the treatment group compared to the control group.
12. Lung cancer occurs in 10% of smokers and 2% of non-smokers. What is the absolute risk reduction(ARR) and number needed to treat (NNT)?
➔ ARR = 10% – 2% = 8%
NNT = 1 / ARR = 1 / 0.08 = 12.5
- Note: NNT tells how many people must avoid the exposure (or be treated) to prevent one case.
13. A study finds that 60% of lung cancer patients smoked, compared to 20% of controls. Calculate the odds ratio
➔ OR = AD/BC= (60X80)/ (20X40)= 6
| Group | Smokers (Exposed) | Non-Smokers (Unexposed) | Total |
|---|---|---|---|
| Cases (Cancer) | 60% (a) | 40% (b) | 100% |
| Controls | 20% (c) | 80% (d) | 100% |
Test performance
14. A new COVID-19 rapid test is compared to PCR in a population of 1,000. The results of the test are compared to the gold standard PCR test:
| PCR Positive (Standard Test) | PCR Negative (Standard Test) | Total | |
|---|---|---|---|
| Test Positive | 180 (TP) | 20 (FP) | 200 |
| Test Negative | 30 (FN) | 770 (TN) | 800 |
| Total | 210 | 790 | 1,000 |
1. What is the probability of correctly identifying diseased people?
➔ Sensitivity= TP/(TP+FN) =180/(180+30)= 85.7%
“rules out disease (snout), Best test for screening.”
2. What is the probability of correctly identifying healthy people?
➔ Specificity= TN/ (TN+FP) = 770/(770+20)= 97.5%
“Rules in disease (spin), Best test for confirmation.”
3. What is the probability of having the disease if the test result is positive?
➔ PPV= TP/ (TP+FP)= 180/180+20= 90%, increases with ↑ prevalence.
4. What is the probability of being healthy if the patient’s test result is negative?
➔ NPV= TN/ (TN+FN)= 770/(770+30) = 96%, decreases with ↑ prevalence.
5. A new troponin test for DM has sensitivity = 90% and specificity = 80%. What are LR+ and LR–?
➔ LR+=Sensitivity/(1−Specificity) = 0.9/(1-0.8) = 4.5
“A positive test makes MI 4.5× more likely- not affected by prevalence”
➔ LR−=(1−Sensitivity)/Specificity= (1-0.9)/0.8=0.125
15. Lowering test cutoff (left shift) → ↑ SeNsitivity, ↑ NPV, ↓ SPecificity, ↓ PPV.
➔ Raising test cutoff (right shift) → ↑ sPecificity, ↑ PPV – ↓ SeNsitivity, ↓ NPV.
Created with BioRender.com
16. A BP cuff gives repeated 150/90 readings, but the true BP is 120/80. What does this indicate?
➔ High precision, low accuracy
- Note: Precision = reproducibility (low random error).
- Accuracy = closeness to true value (affected by systematic error).
17. How is prevalence calculated?
➔ Prevalence = Total cases / Total population
- Note: Indicates burden of disease. Includes both old and new cases.
18. How is incidence calculated?
➔ Incidence = New cases / Population at risk
- Note: Reflects rate of new disease over time.
19. What happens to incidence and prevalence in the following?
➔ Common cold (short duration): incidence ≈ prevalence
➔ Chronic disease (e.g., diabetes): prevalence > incidence
➔ Vaccination program: ↓ incidence → ↓ prevalence
➔ Improved treatment: incidence same, ↓ prevalence
- Note: Prevalence = Incidence × Disease duration
Bias & Confounding
20. Controls selected from hospitalized patients → What is the bias?
➔ Berkson bias
- Note: Selection bias from using hospital-based controls who may have different exposures.
21. High dropout rate in a cohort study → What is the bias?
➔ Attrition bias
- Note: Loss to follow-up can distort the exposure-outcome relationship.
22. How to address attrition bias?
➔ Intention-to-treat: includes all subjects as randomized → ↑ external validity
- Note: Per protocol: includes only those who completed the study → ↓ external validity
23. A patient’s blood sugar improves when monitored. What is the bias?
➔ Hawthorne effect
- Note: Behavioral change due to awareness of being observed. Reduced by blinding.
24. A mother overreports vitamin use during pregnancy. What is the bias?
➔ Recall bias
- Note: Common in case-control studies relying on patient memory.
25. A doctor expects better outcomes in the treatment group. What is the bias?
➔ Observer bias
- Note: Prevent with double blinding.
26. Coffee drinkers show higher lung cancer rates. Further investigations showed coffe drinkers smoke more. What is the issue?
➔ Confounding
- Note: Smoking is a confounder. Addressed by matching and randomization.
27. A drug lowers stroke risk more effectively in smokers than non-smokers. What is this?
➔ Effect modification
- Note: Effect modification = when the effect of an exposure (the drug) on an outcome (stroke risk) differs depending on the level of a third variable (smoking status “modifier”).
- The effect of the drug is modified by whether or not a person smokes.
28. A new test detects SLE 6 months earlier, but survival remains unchanged. What bias?
➔ Lead-time bias
- Note: Early diagnosis falsely appears to prolong survival.
29. A screening test detects many slow-growing tumors but doesn’t reduce mortality. What bias?
➔ Length-time bias
- Note: Detects less aggressive cases, making the test seem more effective.
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Biostatistics & Distribution
30. A study measures BP in 10 adults. The BP values were: (118, 120, 120, 122, 125, 126, 130, 134, 138, 190). Calculate Mean, Mode, and Median
➔ Mean = Sum of values / Number of values = 1201/ 10 = 120.1. “most affected by outliers/ extreme BP readings”
➔ Mode = Value that appears most = 120. “least affected by outliers”
➔ Median = The middle number when data is ordered = (125+126) /2= 125.5.
31. A test score is normally distributed with a mean of 70 and SD of 5. What proportion of students scored above 80?
➔ 80 is +2 SD → top 2.27%
- Note: Normal distribution: (68% within ±1 SD – 95.4% within ±2 SD – 99.7% within ±3 SD)
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Hypothesis Testing
32. A trial compares antihypertensive drug X vs a placebo. What is the null hypothesis?
➔ There is no difference between drug X and placebo
- Note: The Null hypothesis assumes no effect. If it is an abstract question, then the Null hypothesis will be the opposite of the abstract objective.
33. A drug lowers glucose by 8 mg/dL vs placebo (p = 0.02). What does this mean?
➔ Statistically significant
- Note: p < 0.05 → reject null hypothesis. There’s a low probability that the result is due to chance.
34. A study shows BP difference of –3 mmHg between the new drug and the placebo (95% CI –8 to +2). What does this mean?
➔ Not statistically significant
- Note: CI includes 0 → no difference between groups.
- If we use RR or Odds ratio, then the CI should not contain 1.
Errors & Study Power
35. A test for heart failure has p = 0.03, but wrongly classifies many healthy people as positive. What is this?
➔ Type I error (false positive)
- Note: Rejecting a true null.
- Type II error = false negative.
36. What increases study power?
➔ ↑ sample size
➔ ↑ effect size
➔ ↓ variability (standard deviation)
➔ ↓ type II error (β) → Power = 1 – β
- Note: More power = greater ability to detect true differences.
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Statistical Tests
37. Comparing mean glucose between 2 groups?
➔ t-test
- Note: Used for numerical data, 2 independent groups.
38. Comparing cholesterol across keto, Mediterranean, and low-fat diets?
➔ ANOVA
- Note: For ≥3 groups with continuous outcomes.
39. Studying the association between physical activity and hypertension in 500 adults?
➔ Chi-square test
- Note: For categorical variables (e.g., active vs sedentary and hypertensive vs not).
40. Assessing correlation between muscle strength and exercise hours?
➔ Pearson correlation
- Note: Tests linear relationship between two continuous variables.
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🏁 Final Thoughts
You made it to the end—well done! These high-yield notes are designed to save you time and keep you focused on what actually matters for Step 1. Review these vignettes regularly—steady practice beats cramming.
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Disclaimer
Version 1.0 May 2025. No part of this document may be reproduced or distributed without written permission. For personal study only. Medical information herein is for educational purposes and does not constitute clinical advice. Always confirm with current guidelines and your institution’s policies.
Prefer a narrative review instead of Q&A style? Scroll down to the section below for high-yield concepts in paragraph format (they cover the same concepts).
Narrative Format
High-Yield Biostatistics Topics
High-yield Biostatistics review for USMLE: Study designs (case-control, cohort), bias, hypothesis testing, and interpreting results (RR, OR, p-value). Ace your exam!
Table of Contents
- Epidemiology
○ Observational Studies - Phases of Clinical Trials
- How we analyze cohort and clinical trials
○ Attributable Risk Percent (ARP)
○ How we analyze Case Control Studies
○ Evaluation of Diagnostic Tests - Test CUTTOFF CURVES
○ Precision, Accuracy, Incidence & Prevalence - Incidence vs. Prevalence
- Bias & Study Errors
- Biostats
- Statistical Hypothesis
○ Statistical Tests
○ Correlation Coefficient (r)
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Epidemiology
Observational Studies
1. Case-Control Study (Retrospective)
- People with a disease (cases) vs people without disease (controls), evaluate past exposure.
- Best for rare diseases; can’t assess incidence or prevalence.
- Measures exposure Odds Ratio (OR). Liable to recall bias.
How it is tested:
A study aims to assess the relation between smoking and lung cancer; they compared lung cancer patients vs healthy individuals and found that smoking is more common in cancer patients. What is the study design? Case-control study
2. Cohort Study (Prospective or Retrospective)
- Follow a group with a risk factor vs a group without to see who develops the disease.
- Prospective Cohort: Follows participants forward in time (e.g., tracking smokers vs. non-smokers to see if lung cancer develops).
- Retrospective Cohort: Looks back in time at already collected data (e.g., reviewing old medical records of smokers vs non-smokers to see if they got lung cancer).
- It can assess incidence and causality but not prevalence. loss to follow-up bias.
- Measures: Relative Risk (RR).
How it is tested:
Researchers followed 500 obese Vs 500 non-obese individuals for 10 years to compare DM rates. What is the study design? Prospective Cohort Study.
Researchers checked adult medical records from 2010 to determine which individuals developed type 2 diabetes by age 30-40. >>> >>> Retrospective Cohort Study.
3. Cross-Sectional Study (Snapshot Study)
- “What’s happening now?” → Measures disease prevalence and associations at one point in time. Surveys are the most common example. Cannot determine causality.
- Measured by prevalence Odds Ratio (OR).
How it is tested:
A study surveyed 1,000 adults for their smoking status and current COPD diagnosis. What study type is this?
Cross-Sectional Study (Single point in time, measures prevalence).
4. Ecological Study
- Compares population-level data, not individuals. Assess prevalence, not incidence.
- Risk of Ecological Fallacy (study conclusions do not apply to all individuals in the population).
How it is tested:
A study finds that countries with high red meat consumption have higher colon cancer rates. What type of study is this? Ecological Study
We want to compare high-altitude cities vs sea-level cities to see if there is a significant difference in their hematocrit level.
If states with more fast-food restaurants have higher obesity rates, concluding that everyone who eats fast food is obese is an Ecological Fallacy.
5. Twin Concordance Study
A twin concordance study compares the likelihood of both twins having a disease to determine the relative influence of genetics vs. environment.
How it is tested:
A study on Schizophrenia found that monozygotic twins (MZ) have 50% concordance while dizygotic twins (DZ) have 15% concordance. They concluded that genetics plays a major role in developing Schizophrenia.
Phases of Clinical Trials
Phase 1:
- A small number of healthy volunteers evaluate
Phase 2:
- Larger groups of patients test efficacy and dosing regimen.
Phase 3:
- Large-scale trials comparing the new treatment vs. standard treatment/placebo. Double-blind and randomized.
- Determines clinical effectiveness and monitors adverse effects. Used for FDA approval.
Phase 4 (Post-Marketing Surveillance):
- Observe long-term safety and rareside effects. It can lead to drug withdrawal.
How it is tested:
A new drug is tested in 50 healthy volunteers to determine the possible side effects. Which phase? Phase 1
Blinding in Clinical Trials:
Single-Blind >> Patient only >> Reduces placebo effect.
Double-Blind >> Patient and Researcher >> Reduces observer bias.
Randomization prevents selection bias.
How we analyze cohort and clinical trials
1. Relative Risk (RR) – Cohort Studies
Likelihood of disease in exposed vs unexposed groups.
RR=Incidence in exposed/ incidence in unexposed
- RR = 1 → No association, > 1 → Exposure increases risk, < 1 → Exposure is protective.
How it is tested:
In a cohort study, lung cancer occurs in 10% of the smokers group and 2% of the non-smokers group. What is the relative risk?
Answer: RR = (10% / 2%) = 5 (Smokers have 5x higher risk).
2. Relative Risk reduction:
The proportion of risk reduction attributable to an intervention. RRR= 1- RR
How it is tested:
If 3% of patients who took the meningococcal vaccine developed meningitis, while 9% of those who did not take the vaccine developed meningitis. What is the RRR?
RRR= 1- RR→ RR= 3/9=.67 → RRR= 1-0.67= 0.33
4. Attributable Risk (AR) “risk factor”– Absolute risk reduction “intervention”
Excess risk due to exposure (excess risk attributed to the risk factor).
AR= Incidence in exposed−Incidence in unexposed
How it is tested: Lung cancer occurs in 10% of smokers and 2% of non-smokers. What is the attributable risk? AR = 10% – 2% = 8%
Attributable Risk Percent (ARP)
The proportion of disease in an exposed group that can be attributed to the exposure.
ARP= (Incidence in Exposed−Incidence in Unexposed) / Incidence in Exposed×100
ARP= (Relative Risk−1)/ Relative Risk
How it is tested: A study finds that smokers have a lung cancer incidence of 20%, while non-smokers have a lung cancer incidence of 2%. What percentage of lung cancer risk can be attributed to smoking?
ARP= (Incidence in Exposed−Incidence in Unexposed) / Incidence in Exposed×100
(20% – 2%)/ 20% × 100= 90% of lung cancer cases can be attributed to smoking.
5. Number Needed to Treat (NNT) & Number Needed to Harm (NNH)
NNT → How many patients need treatment to prevent 1 bad outcome, Lower is better (fewer patients needed to treat). NNT=1/ Absolute Risk Reduction (ARR).
NNH → How many patients exposed to a risk factor cause 1 bad outcome, Higher is better (fewer patients harmed). NNH=1/ Attributable Risk (AR).
How it is tested:
A new drug lowers MI risk from 10% to 5%. What is the NNT?
ARR = 10% – 5% = 5% → NNT = 1/0.05 = 20 (we need to treat 20 patients to prevent 1 MI).
How we analyze Case-Control Studies
Odds Ratio (OR)
Compares odds of exposure in cases vs. controls (used in case-control studies).
OR=Odds of exposure in cases/ Odds of exposure in controls = AD/BC
OR > 1 → Exposure is associated with disease, OR < 1 → Exposure is protective. In rare diseases, OR= RR.
How it is tested:
A study finds that 60% of lung cancer patients smoked, compared to 20% of controls. What is the odds ratio?
Cases (Lung Cancer Patients): 60% smoked → 60% exposed, 40% non-exposed.
Controls (No Lung Cancer): 20% smoked → 20% exposed, 80% non-exposed.
| Group | Smokers (Exposed) | Non-Smokers (Unexposed) | Total |
|---|---|---|---|
| Cases | 60 (a) | 40 (b) | 100 |
| Controls | 20 (c) | 80 (d) | 100 |
OR = AD/BC= 60X80/ 20X40= 6
Evaluation of Diagnostic Tests
Pretest probabilities:
1. Sensitivity (True Positive Rate): → Probability that a test detects disease when it is present. Sensitivity=TP/(TP+FN) “Everyone in the calculation is diseased”
Higher Sensitivity = fewer false negatives → used for screening (SnOUT: Sensitive test rules OUT disease).
2. Specificity (True Negative Rate) → Probability that a test correctly identifies non-disease. Specificity=TN/ (TN+FP) “Everyone in the calculation is not diseased”
Higher Specificity = Fewer false positives → used for confirmation (SpIN: Specific test rules IN disease).
Post-test probabilities:
- Positive Predictive Value (PPV) → Probability that a positive test result means the patient truly has the disease. Increases with high prevalence. PPV=TP/ (TP+FP)
- Negative Predictive Value (NPV): → Probability that a negative test result means the patient is truly disease-free. decreases with high prevalence. NPV=TN/ (TN+FN)
How it is tested: A new rapid test for diagnosing COVID-19 is being evaluated in a population of 1,000 individuals. The results of the test are compared to the gold standard PCR test:
| PCR Positive | PCR Negative | Total | |
|---|---|---|---|
| Test Positive | 180 | 20 | 200 |
| Test Negative | 30 | 770 | 800 |
| Total | 210 | 790 | 1,000 |
- What is the probability of correctly identifying diseased people? = Sensitivity= TP/(TP+FN) =180/(180+30)= 85.7%
- What is the probability of correctly identifying healthy people? = specificity= TN/ (TN+FP) = 770/(770+20)= 97.5%
- What is the probability of having the disease if the patient’s test result is positive? = PPV= TP/ (TP+FP)= 180/180+20= 90%
- What is the probability of being healthy if the patient’s test result is negative? = NPV= TN/ (TN+FN)= 770/(770+30) = 96%
PPV and NPV change with prevalence, but Sensitivity and Specificity do NOT;
↑ prevalence of the disease → ↑ PPV, ↓ NPV, while Sensitivity and Specificity are the same
↓ prevalence of the disease → ↓ PPV, ↑ NPV, while Sensitivity and Specificity are the same
3. Accuracy
percentage of correct results in all tested individuals.
Accuracy= TP+TN/(TP+TN+FP+FN)
Positive Likelihood Ratio (LR⁺):
How much a positive test increase disease likelihood.
LR+=Sensitivity/(1−Specificity). Higher LR⁺> 10 = More likely the disease is present.
Negative Likelihood Ratio (LR⁻):
How much a negative test decreases disease likelihood.
LR−=(1−Sensitivity)/Specificity. Lower LR⁻ < 0.1 = More likely the disease is absent.
LR is not affected by disease prevalence while affected by sensitivity and specificity.
How it is tested: A new troponin test for MI has sensitivity = 90% and specificity = 80%. What is the LR⁺ and LR⁻ ?
LR+=Sensitivity/(1−Specificity)= 0.9/(1-0.8)= 4.5, A positive test makes MI 4.5× more likely.
LR−=(1−Sensitivity)/Specificity= (1-0.9)/0.8=0.125, The test strongly rules out MI
Test CUTTOFF CURVES
Created with BioRender.com
Lowering cutoff (shift left): (B → A)
- ↑ Sensitivity, ↑ NPV- ↓ Specificity, ↓ P
- Choose low cutoff if missing disease is fatal “↓ FN”. example: cancer screening, HIV screening
Raising cutoff (shift right): (B → C)
- ↑ Specificity, ↑ PPV- ↓ Sensitivity, ↓ N
- Choose high cutoff if false positives are harmful “↓ FP”. example: organ transplant candidacy
Cutoff Points
- ↑ Overlap between diseased “right” and healthy “left” → ↓ sensitivity, ↓ specificity.
- ↓ Overlap → ↑ both sensitivity and specificity.
How it is tested: A new blood-based test is being considered as a screening tool for colon cancer. researchers are considering lowering the threshold to detect more cases early. Which of the following is correct?
A) Decreased sensitivity and increased specificity
B) Increased sensitivity and decreased specificity
C) Increased both sensitivity and specificity
D) Increased positive predictive value and increased specificity
E) Decreased false positive rate and increased negative predictive value
Correct answer: B) Increased sensitivity and decreased specificity
Lowering cutoff (B → A): ↑ Sensitivity, ↑ NPV- ↓ Specificity, ↓ PPV.
Receiver Operating Characteristic (ROC) Curve
- Evaluates the performance of a diagnostic test:
○ X-axis: False Positive Rate (FPR) = 1 − Specificity.
○ Y-axis: True Positive Rate (TPR) = Sensitivity. - Helps determine the optimal cutoff value for a test. Also comparing two diagnostic tests (higher AUC = better test).
- The ROC curve is not affected by disease prevalence (unlike PPV/NPV)
Features
- Perfect test: ROC curve touches the top-left corner (TPR = 100%, FPR = 0%).
- Useless test (random chance): Diagonal line (AUC = 0.5).
- Area Under the Curve (AUC):
○ 9–1.0: Excellent test.
○ 7–0.9: Good test.
○ <0.7: Poor test.
Cutoff Selection
- High sensitivity (low cutoff): Few false negatives (e.g., screening tests).
- High specificity (high cutoff): Few false positives (e.g., confirmatory tests).
- Optimal cutoff: Closest to the top-left corner (maximizes both sensitivity & specificity).
How it is tested: a question with ROC curve comparing between a number of diagnostic tests, and asks you which test is bettter? Pick the highest AUC “in below example, test A is the best”
Kaplan-Meier Curve (Survival Analysis)
Estimates survival probability over time in a cohort (e.g., cancer patients).
Median survival time: Time at which survival probability = 50%.
KM curve does not establish causation, (observational only).
Oncology trials (e.g., 5-year survival in breast cancer) and Transplant graft survival.
Key Features:
- X-axis: Time (e.g., months/years).
- Y-axis: Cumulative survival probability (starts at 100% → declines with events).
- Steps: Drops at each event (e.g., death); plateaus between events.
Precision, Accuracy, Incidence & Prevalence
1. Precision (Reliability):
- How consistent and reproducible a test is. “similar results on repeat measurements”
- Low random error = High precision.
- High precision → ↓ SD, ↑ study Power.
2. Accuracy (Validity):
- How close a measurement is to the true value. It decreases by systematic error.
How it is tested:
A BP cuff gives repeated readings of 150/90, but true BP is 120/80. What does this indicate? High precision, low accuracy (Consistent but wrong).
2. Incidence vs. Prevalence
Incidence:
New cases in a population. Old and dead cases are not included. Incidence = New cases/Total at-risk population
How it is tested: A researcher conducts a 10-year cohort study to investigate the incidence of lung cancer among smokers and non-smokers in a population of 10,000 adults, 4,000 participants were smokers, and 6,000 were non-smokers. During the study period, 200 smokers and 50 non-smokers were diagnosed with lung cancer. What is the incidence of lung cancer among smokers? /What is the risk of developing lung cancer in smokers? 200/4000=.05
Prevalence:
Total cases (new + old) at a specific time. dead cases are not included.
Prevalence = All cases/ Total population, also = Incidence × Disease Duration
- Chronic diseases (diabetes) → High prevalence, low incidence.
- Acute temporary diseases (common cold) → Low prevalence, high incidence.
How it is tested:
1. A researcher is investigating the burden of hypertension in a community. A cross-sectional study is conducted, and 1,200 adults are screened for hypertension. Of these, 240 individuals are diagnosed with hypertension. What is the prevalence of hypertension? 240/1200=20%
2. changes in incidence and Prevalence in these situations:
- primary prevention such as vaccines or exercise: ↓incidence, ↓ Prevalence.
- secondary prevention such as effective drugs: same incidence, ↓ Prevalence.
- therapy prolongs life: same incidence, ↑ Prevalence.
Bias & Study Errors
1. Selection Bias: (The Sample doesn’t represent the population, reduced by randomization).
- Berkson Bias → when hospitalized patients are used as controls (very sick!).
How it is tested:
Researchers conducted a study to examine the association between alcohol use and pancreatitis; Cases were hospitalized patients with pancreatitis and Controls were hospitalized patients without pancreatitis. The study shows no significant association between alcohol use and pancreatitis→ Berkson bias, Hospitalized controls may have higher alcohol use but hospitalized for other conditions (like GI bleeds or liver disease), this makes alcohol use seem common in both cases and controls, which clears the real association between alcohol and pancreatitis.
- Healthy Worker Effect → Workers tend to be healthier than the general population.
- Attrition Bias → In prospective studies, patients who are lost to follow-up affect results. Possible solutions are;
- Intention-to-Treat (ITT) Analysis
Includes all participants (including dropouts) → realistic “high external validity”. - Per-Protocol Analysis
Only includes participants who fully adhered to the study protocol → More efficacy “internal validity”, but less generalizabile “lower external validity, not realistic”.
How it is tested:
A randomized controlled trial is conducted to assess the effect of a new DM drug on blood glucose control. Some patients in the treatment group stop taking the medication due to side effects. However, the final analysis includes all patients in their originally assigned groups, regardless of whether they completed the treatment → Intention-to-Treat (ITT).
2. Measurement Bias: (Systematic errors in measurement and data collection)
1. Leading Question Bias
Questions that direct the participant to respond in a particular way.
How it is tested: A researcher asks, “You don’t smoke, right?” instead of, “Do you smoke?”
This may lead to underreporting of smoking.
2. Hawthorne Effect
Subjects change their behavior because they know they are being observed. Reduced by blinding and control groups to reduce this bias.
How it is tested: Diabetic patients improve blood sugar control during a study because they know they’re being monitored, not because of the intervention.
3. Recall Bias
In retrospective studies, occur when cases remember past exposures inaccurately.Reduce by using objective records instead.
How it is tested: Mothers of children with birth defects may overreport past infections or medication use compared to mothers of healthy children.
4. Reporting Bias
Participants misreport behaviors due to embarrassment or social desirability. Usually with smoking, substance abuse, or sexual problems. Use anonymous surveys.
How it is tested:
A medical student underreports smoking on a health survey.
5. Observer Expectancy Bias (Pygmalion effect)
The researcher’s beliefs or expectations influence how they interpret or record outcomes. Prevent with double blinding.
How it is tested: A doctor knows which group takes the new drug and unconsciously records better outcomes for it.
5. Confounding Bias
A third variable affects both the exposure & outcome, creating a false association. Reduced by:
Randomization (equal distribution of unknown confounders).
Matching; cases & controls with similar characteristics as age and gender.
How it is tested: A study finds coffee drinkers have higher lung cancer rates; smoking (a confounder) is more common among coffee drinkers.
Effect modification occurs when the effect of an exposure on an outcome differs due to a third variable. It reflects a true effect, not a bias.
A study finds that oral contraceptive use is associated with an increased risk of DVT among smokers more than non-smokers (smoking is a modifier).
Aspirin reduces heart attack risk more in men (gender is a modifier)
Confounding by Indication:
The treatment is not randomly assigned; instead, it is given based on the patient’s underlying condition, which distorts the exposure-outcome relationship.
How it is tested: (Exposure: Beta-blockers, Outcome: Mortality)
Patients with severe heart disease (higher mortality risk) are more likely to receive beta-blockers, so Beta-blockers appear to increase mortality → The bias arises because sicker patients are more likely to receive them
The solution is Intention-to-treat analysis; which helps reduce bias by preserving the initial random treatment assignment, regardless of whether participants adhere to the treatment or disease severity.
Effect modification is related only to outcome, unlike confounding is related to both exposure and outcome. It can be distinguished from confounding by performing a stratified analysis on the variable of interest for example,
A study shows that OCPs increase breast cancer risk RR= 1.5. After we stratified and classified data by family history, the RR became 3.33, P-Value= 0.02 → Effect modification.
A study shows that alcohol use increases bladder cancer risk, RR= 1.9. After we stratified and classified data by smoking history, the RR became 0.98, P-Value= 0.032 → confounding.
6. Lead-Time Bias (screening test)
Early detection makes survival appear longer, but the actual disease course is unchanged. reduced by considering disease severity at the time of diagnosis.
How it is tested:
A new screening test detects pancreatic cancer 6 months earlier than the standard test.
Patients diagnosed with the new test live 18 months after diagnosis, while those diagnosed with the old method live 12 months. What is the bias? Lead-Time Bias
7. Length-Time Bias
When slow-progressing diseases are more likely to be detected by screening.
How it is tested:
A new breast cancer screening tool is implemented. Compared to unscreened women, those who undergo regular screening with the new tool are more likely to be diagnosed with slow-growing, less aggressive tumors and show improved survival rates.
However, the actual mortality from breast cancer remains the same in both groups. What is the bias? Length-Time Bias
Biostats
1. Mean (Average)
Formula: Sum of values / Number of values. Example: Mean of 2, 4, 6 = (2+4+6)/3 = 4
Most affected by outliers
2. Median (Middle value)
Middle number when data is ordered. Example: Median of 3, 7, 1, 5, 9→ 1, 3, 5, 7, 9= 5
If even number→ average of two middle values. Example: Median of 1, 3, 5, 100 = (3+5)/2 = 4
Not affected by outliers
3. Mode (Most frequent value)
Value that appears most often. Not affected by outliers. Example: Mode of 2, 3, 3, 3, 5 = 3
How it is tested: A clinical trial measures systolic blood pressure (SBP) in 500 adults. The SBP values are recorded (in mmHg): 118, 120, 120, 122, 125, 126, 130, 134, 138, 190
Which of the following values is most affected by the extremely high blood pressure reading/ outliers?
A) Median
B) Mode
C) Mean
D) Range
E) Interquartile range
Correct answer: C) Mean
Normal Distribution curve
- Bell-shaped, symmetric curve. Mean = Median = Mode (at the center).
- 68% of values fall within 1 standard deviation (SD) of the mean, 95% fall within 2 SDs, and 7% fall within 3 SDs.
Created with BioRender.com
2. Non-normal distributions (not symmetric).
- Positive (Right) Skew: (Mean pulled right).
○ The tail is longer on the right. Mean >Median > Mode.
○ Example: Income distribution (few people earn extremely high salaries). - Negative (Left) Skew: (Mean pulled left)
○ The tail is longer on the left. Mean <Median < Mode.
○ Example: Age of death (most people die at an older age; few die very young).
Created with BioRender.com
Statistical Hypothesis
1. Null vs. Alternative Hypothesis
- Null Hypothesis (H₀) → No difference exists: “Drug A is not better than placebo”.
- Alternative Hypothesis (H₁) → A real difference exists: “Drug A is effective”.
2. p-Value & Statistical Significance
- p-value → Probability that the results occurred by chance.
- If p < 0.05→ Reject H₀ → Statistically significant, p > 0.05 → Fail to reject H₀ → No significant difference.
- Clinical significance represents the real or clinical effect of the intervention.
How it is tested:
A trial evaluates the effectiveness of a new antihypertensive drug X compared to a placebo. The results show that drug X lowers blood pressure by 8 mmHg more than the placebo, with a p-value of 0.03:
The difference in blood pressure reduction is statistically and clinically significant
3. Type I & Type II Errors “errors in hypothesis testing”.
- Type I Error α (False Positive)
- Rejecting H₀ when it’s true, “Saying the drug works when it doesn’t”.
- Probability = Significance Level (α, usually 0.05).
- Type II Error β (False Negative)
- Failing to reject H₀ when H₁ is true: “the drug works, but the study says no”.
- Lower β = Higher statistical power (Power = 1 – β).
How it is tested:
A new test for diagnosing DVT is evaluated against the gold standard D-Dimer. The study finds that the test has a p-value of 0.03 when comparing it to D-Dimer results. However, after further clinical use, it is found that many patients without DVT are being diagnosed as positive. Which best describes the type of statistical error present in this scenario?
Type I error (α) – False positive conclusion
4. Significance Level (α) & Confidence Interval (CI)
- Significance Level (α = 0.05) → Risk of making a Type I Error.
- Confidence Interval (CI) → Range in which the true population value lies with 95% certainty → If 95% CI includes “0” (for mean difference) or “1” (for relative risk/odds ratio), the result is NOT statistically significant.
How it is tested: A study evaluating a BP drug finds that the drug reduces BP by -5 mmHg (95% CI: -8 to -2). What does this mean? Statistically significant (CI does not include 0).
A study finds an odds ratio (OR) of 2.0 for smoking and lung cancer, with a 95% CI of (0.8–4.5). What does this mean? NOT statistically significant (CI includes 1.0).
Study power increases by:
- ↑ sample size, ↑effect size, ↑ precision
- ↓ type 2 error (Power=1-β), ↓ SD “Lower variability”.
How it is tested: A trial is designed to evaluate a new drug for DM. Researchers plan to enroll 100 patients in each group. The primary outcome is a reduction in systolic blood glucose. Which of the following would most likely increase the power of the study?
A) Use a higher p-value threshold (e.g., p < 0.10 instead of p < 0.05)
B) Enroll fewer participants in each group
C) Increase the sample size
D) Increase the variability (standard deviation) of measurements
E) Use a two-tailed test instead of a one-tailed test
Correct answer: C) Increase the sample size
Statistical Tests
1. t-Test (Means Comparison)
Compares means of two groups (numerical data).
How it is tested:
A study compares the average systolic BP in patients on Drug A vs. patients on Placebo. What statistical test should be used? t-test (Comparing two groups, numerical).
2. ANOVA (Analysis of Variance)
Compare means of ≥ 3 groups (numerical data).
How it is tested:
A researcher compares HbA1c levels among three diet plans: keto, Mediterranean, and low-fat. What test should be used? ANOVA (Comparing three or more groups, numerical).
3. Chi-Square Test (Categorical Data)
Compare proportions or categorical variables (Yes/No, Disease/No Disease).
How it is tested:
A study examines the association between smoking (yes/no) and lung cancer (present/absent) in 500 patients. What test? Chi-square test (Comparing categorical data).
4. Pearson Correlation (r)
Measures strength & direction of linear relationship between two numerical variables.
How it is tested:
A study analyzes the relationship between BMI and systolic BP. What test should be used? Pearson correlation.
Correlation Coefficient (r)
Measures the strength & direction of a linear relationship between two numerical variables.
- Range: -1 to +1
○ +1 → Perfect positive correlation (as X ↑, Y ↑), LDL& risk of atherosclerosis.
○ -1 → Perfect negative correlation (as X ↑, Y ↓), Smoking & lung function (FEV1).
○ → No correlation (random association), Shoe size & IQ.
How it is tested: 1. A study finds that as calcium intake increases, fracture risk decreases, with an r-value of -0.8. What does this mean? a strong negative correlation (as calcium ↑, fractures ↓).
2. A study analyzing height and intelligence finds r = 0.02. interpretation? No correlation.
Created with BioRender.com
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