Topic Map (what these 8 pages cover)

1. Observational study designs - case series, cross-sectional, case-control, cohort, twin concordance, adoption, ecological studies
2. Clinical trials - phases 0-4, crossover trials, intention-to-treat vs per-protocol vs as-treated analysis, off-label drug use, Bradford Hill criteria for causation
3. Measures of risk from 2x2 tables - odds ratio, relative risk, relative risk reduction, attributable risk, absolute risk reduction, NNT, NNH, case fatality rate
4. Population health measures - mortality rate, attack rate, demographic transition, population pyramids, birth rate, life expectancy
5. Likelihood ratios & Kaplan-Meier survival curves
6. Diagnostic test evaluation - sensitivity, specificity, PPV, NPV, ROC curves
7. Precision vs accuracy, and Incidence vs prevalence
8. Bias and study errors - selection bias (Berkson, attrition), recall bias, measurement bias (Hawthorne effect), procedure bias, observer-expectancy bias, lead-time bias, length-time bias
9. Confounding vs effect modification

Quick Overview

Topic Map (what these 8 pages cover)

1. Observational study designs - case series, cross-sectional, case-control, cohort, twin concordance, adoption, ecological studies
2. Clinical trials - phases 0-4, crossover trials, intention-to-treat vs per-protocol vs as-treated analysis, off-label drug use, Bradford Hill criteria for causation
3. Measures of risk from 2x2 tables - odds ratio, relative risk, relative risk reduction, attributable risk, absolute risk reduction, NNT, NNH, case fatality rate
4. Population health measures - mortality rate, attack rate, demographic transition, population pyramids, birth rate, life expectancy
5. Likelihood ratios & Kaplan-Meier survival curves
6. Diagnostic test evaluation - sensitivity, specificity, PPV, NPV, ROC curves
7. Precision vs accuracy, and Incidence vs prevalence
8. Bias and study errors - selection bias (Berkson, attrition), recall bias, measurement bias (Hawthorne effect), procedure bias, observer-expectancy bias, lead-time bias, length-time bias
9. Confounding vs effect modification

Quick Overview

PAGE 256 — Observational Studies

Case series

• Design: "Describes several individual patients with the same diagnosis, treatment, or outcome."
  • Think of this as a doctor writing up "I saw 5 patients with this rare disease, here's what happened to each of them." There's no comparison group.
• Measure: "Description of clinical findings and symptoms. Has no comparison group, thus cannot show risk factor association with disease."
  • Why: Without a control group (people without the disease to compare against), you cannot say a certain exposure caused anything — you're just describing what you saw. It's the weakest form of evidence but useful for spotting new/rare diseases (e.g., first AIDS case reports).

Cross-sectional study

• Design: "Frequency of disease and frequency of risk-related factors are assessed in the present. Asks, 'What is happening?'"
  • This is a snapshot in time. Imagine taking a photograph of a population right now — who currently has the disease, and who currently has the risk factor.
• Measure: "Disease prevalence. Can show risk factor association with disease, but does not establish causality."
  • Prevalence = the proportion of a population that has a disease at one moment (defined properly later on page 261).
  • Why no causality: Because you're looking at one moment in time, you can't tell whether the risk factor came before the disease or after it. Example: if you survey people today and find diabetics are more likely to be overweight, you don't know if obesity caused diabetes, or if having diabetes changed their diet/weight. Timing is unclear, so no cause-effect claim can be made.

Case-control study

• Design: "Retrospectively compares a group of people with disease to a group without disease. Looks to see if odds of prior exposure or risk factor differ by disease state. Asks 'What happened?'"
  • Retrospective means looking backward in time. You start with people who already have the disease ("cases") and people who don't ("controls"), then you look back into their history to see who had the exposure.
  • This is the design shown in the diagram: Past → Present. You start in the present with diseased cases and healthy controls, and look backward to compare risk factor frequency.
• Measure: "Odds ratio (OR). Control the case in the OR." with the example: "Patients with COPD had higher odds of a smoking history than those without COPD."
  • COPD = Chronic Obstructive Pulmonary Disease, a long-term lung disease (like severe bronchitis/emphysema) usually caused by smoking.
  • Odds ratio is the statistic used specifically for case-control studies (explained fully on page 258).
  • Why case-control studies are useful: they're fast and cheap, and great for rare diseases — instead of following thousands of healthy people for years waiting for a rare disease to appear (impractical), you find people who already have the rare disease and work backward.

Cohort study

• Design: "Compares a group with a given exposure or risk factor to a group without such exposure. Looks to see if exposure or risk factor is associated with later development of disease. Can be prospective or retrospective, but risk factor has to be present prior to disease development. Asks, 'What will happen?'"
  • Cohort = a defined group of people followed over time.
  • Prospective = forward-looking (start now, follow people into the future to see who develops disease). Retrospective cohort = you use old records to reconstruct exposure and then see who already developed disease afterward, but the key defining feature is that exposure is confirmed to have occurred before the disease — that's what separates a cohort study from a cross-sectional one.
  • Diagrams show two types:
    • Retrospective cohort study: "Review previous records" → compare risk factor+ vs risk factor− groups → "compare disease incidence." You're looking backward through records that already exist.
    • Prospective cohort study: risk factor+ vs risk factor− groups are followed forward → "compare disease incidence" as it happens in real time.
• Measure: "Disease incidence. Relative risk (RR)." Example: "People who smoke had a higher risk of developing COPD than people who do not. Cohort = relative risk."
  • Incidence = rate of new cases arising over a time period (as opposed to prevalence, which counts all existing cases — full explanation on page 261).
  • Relative risk is the natural statistic for cohort studies because you directly measured the risk (probability) of disease in the exposed group vs. the unexposed group.

Twin concordance study

• Design: "Compares the frequency with which both monozygotic twins vs both dizygotic twins develop the same disease."
  • Monozygotic twins = identical twins (one fertilized egg split into two — same DNA).
  • Dizygotic twins = fraternal twins (two separate eggs — genetically like regular siblings, just born at the same time).
  • Concordance = both twins in a pair having the same trait/disease.
• Measure: "Measures heritability and influence of environmental factors ('nature vs nurture')."
  • Logic: If identical twins (100% shared genes) develop a disease together far more often than fraternal twins (50% shared genes, like regular siblings), that difference points to a genetic cause. If concordance is similar in both types of twins, it points more to shared environment than genetics.

Adoption study

• Design: "Compares behavioral traits/genetics in siblings raised by biological vs adoptive parents."
• Measure: "Measures heritability and influence of environmental factors."
  • Logic: Because adopted children share genes with biological parents but environment with adoptive parents, this study design can separate nature from nurture even more cleanly than twin studies — you're comparing "genetic parents' traits" against "the environment the child actually grew up in."

Ecological study

• Design: "Compares frequency of disease and frequency of risk-related factors across populations. Measures population data not necessarily applicable to individuals (ecological fallacy)."
• Measure: "Used to monitor population health. COPD prevalence was higher in more polluted cities."
  • This is the broadest, crudest design — you compare entire populations (e.g., cities, countries) rather than individuals.
  • Ecological fallacy is a critical concept: just because a city with more pollution has more COPD does not mean the specific individuals with COPD in that city are the ones who were most exposed to pollution. You're drawing conclusions about individuals from group-level data, which can be misleading.

PAGE 257 — Clinical Trials, Off-Label Use, Bradford Hill Criteria

Clinical therapeutic trial

• "Experimental study involving humans. Compares therapeutic benefits of ≥2 interventions (eg, treatment vs placebo, treatment vs treatment). Study quality improves when clinical trial is randomized, controlled, and double-blinded (ie, neither subject nor researcher knows whether the subject is in the treatment or control group). Triple-blind refers to additional blinding of the researchers analyzing the data."
  • This is an experimental (not observational) study — the researcher actively decides who gets what treatment.
  • Randomized = assignment to treatment or placebo is done by chance (like a coin flip), so the two groups end up similar in every other way (age, health, habits) — this cancels out confounding variables (explained on page 263).
  • Controlled = there's a comparison group (placebo or standard treatment) to compare against.
  • Double-blinded: "blind" means "unaware." Neither the patient nor the doctor/researcher administering treatment knows who's getting the real drug vs. the placebo. This prevents bias — if a doctor knows a patient got the real drug, they might unconsciously report better outcomes (see observer-expectancy bias, page 262).
  • Triple-blind: even the statisticians analyzing the results don't know which group is which, preventing them from unconsciously skewing analysis.
• Crossover clinical trial: "Compares the effect of a series of ≥2 treatments on a subject. Order in which subjects receive treatments is randomized. Washout period occurs between treatments. Allows subjects to serve as their own controls."
  • Instead of comparing Group A (drug) to Group B (placebo), the same person gets the drug for a while, then (after a washout period — enough time for the first drug to completely clear from the body) gets the placebo, or vice versa.
  • Why powerful: it removes person-to-person variability entirely, since each subject is compared to themselves.

Three ways trial data can be analyzed:

• Intention-to-treat analysis: "All subjects are analyzed according to their original, randomly assigned treatment. No one is excluded, ie, once randomized, always analyzed from attrition, crossover, and nonrandom noncompliance. Attempts to avoid bias from dilute the true effects of intervention, but may dilute the true effects of intervention, but may be analyzed according to the treatment they actually received." ↓ risk of bias.
  • Attrition = subjects dropping out of the study partway through.
  • Crossover = a subject switches from one study arm to the other during the trial (not to be confused with the crossover trial design above).
  • Noncompliance = a subject doesn't follow the assigned regimen properly (e.g., forgets to take pills).
  • Logic: intention-to-treat mimics real-world effectiveness — in real life, some patients won't stick perfectly to a drug regimen, so counting everyone as originally assigned gives a more realistic (if slightly diluted) picture of how well a treatment "works" in practice. This is considered the gold-standard, least biased approach because it preserves the benefit of randomization.
• As-treated analysis: "Subjects are analyzed according to the treatment they actually received," regardless of original assignment. ↑ risk of bias.
  • Why more biased: people who switch treatments or don't comply often do so for a reason connected to their health status (e.g., too sick to continue), so grouping by what they actually took can distort the picture.
• Per-protocol analysis: "Subjects who fail to complete treatment as originally, randomly assigned are excluded." ↑ risk of bias.
  • This only counts people who followed the rules perfectly. It can overestimate how well a drug works, because sicker patients who dropped out (maybe due to side effects) are removed from the picture, leaving only patients who tolerated it well.
• Clinical trials occur after preclinical studies and consist of five phases ("Can I SWIM"). This is a mnemonic where each letter/word maps onto a phase:
  • Preclinical: "Test drug in lab animals and in vitro experiments" — before any humans are involved at all, testing happens in cells (in vitro = literally "in glass," i.e., in a test tube/lab dish) and animals.
  • Phase 0: "Initial pharmacokinetic and pharmacodynamic assessment via microdosing. Often skipped." Very small number of healthy volunteers or patients with disease of interest. Open label.
    • Pharmacokinetics = what the body does to the drug (absorption, distribution, metabolism, excretion).
    • Pharmacodynamics = what the drug does to the body (its effects).
    • Microdosing = giving a tiny, sub-therapeutic dose just to study these properties safely.
    • Open label = everyone knows who's getting the drug (no blinding) — this phase is about basic safety data, not effectiveness comparison.
  • Phase 1: "Safety assessment via dose escalation. Determine maximum tolerable dose." Small number of healthy volunteers or patients with disease of interest. Open label.
    • Dose escalation = gradually increasing the dose to find the point where side effects become too severe (the maximum tolerable dose) — this is where the mnemonic's "S" for Safety comes from.
  • Phase 2: "Efficacy assessment (does it work?). Provides additional data on short-term adverse effects." Moderate number of patients with disease of interest. Randomized, controlled, and (sometimes) blinded.
    • This is the "W" ("Will it work?") stage in the mnemonic — testing whether the treatment actually has a beneficial effect, in a limited group.
  • Phase 3: "Effectiveness assessment via comparison with current standard of care (placebo/active control)." Large number of patients with disease of interest. Randomized, controlled, and blinded.
    • The "I" (comparison with current standard) — this is the big trial that compares the new drug against the best existing treatment (or placebo), and is usually what's submitted for FDA approval.
  • Phase 4: "Provides data on long-term or rare adverse effects (can it stay on the market?). Postmarketing surveillance of patients with disease of interest. Open label."
    • The "M" (post-Market) — happens after the drug is already approved and being sold, to catch rare side effects that wouldn't show up in smaller trials (e.g., a side effect that occurs in 1 in 100,000 people would never be caught in a Phase 3 trial with only a few thousand participants, but might show up once millions of people are using the drug).

Off-label drug use

• "Use of a drug to treat a disease in a form, population group, or dosage that is not specifically approved by the FDA. Reasons for off-label use include treatment of an illness with no approved options, exploring alternative treatments after failure of approved options. Example: use of tricyclic antidepressants for treating neuropathic/chronic pain."
  • Off-label means a doctor is legally allowed to prescribe an FDA-approved drug for a different purpose than what it was originally approved for, based on clinical judgment and evidence, even without a formal new approval for that specific use.
  • Tricyclic antidepressants: a class of antidepressant drugs, which (interestingly) also happen to reduce nerve-related pain (neuropathic pain), so doctors use them for chronic pain even though they weren't originally approved for that.

Bradford Hill criteria

• This is a checklist used to argue that an observed association is likely a true cause-effect relationship, not just coincidence. Each row is one criterion:
  • Strength: "Repeated observations of the findings in multiple distinct samples." — the bigger/stronger the association, the more believable it's causal.
  • Consistency: "The more specific the presumed cause is to the effect, the stronger the association." (i.e., Specificity in the list — the presumed cause reliably produces this specific effect and not many unrelated effects.)
  • Temporality: "The presumed cause precedes the effect by an expected amount of time." — cause has to come before effect; this is one of the few criteria considered essential.
  • Biological gradient (dose-response relationship): "Greater effect observed with greater exposure to the presumed cause (eg, dose-response relationship)." — more exposure → more disease (e.g., more cigarettes smoked → higher lung cancer risk).
  • Plausibility: "A conceivable mechanism exists by which the cause may lead to the effect." — there's a believable biological explanation for how A causes B.
  • Coherence: "The presumed cause and effect do not conflict with existing scientific consensus."
  • Experiment: "Empirical evidence supporting the presumed cause and effect (eg, animal studies, in vitro studies)."
  • Analogy: "The presumed cause and effect are comparable to a similar, established cause and effect."
  • Why "necessary but not sufficient": meeting these criteria strengthens the case for causation, but none of them (individually or even together) can prove causation with mathematical certainty — that's why the only definitive way to demonstrate causation is a well-run randomized controlled experiment.

PAGE 258 — Quantifying Risk (the 2×2 table)

Odds ratio (OR)

• "Typically used in case-control studies. Represents the odds of exposure among cases (a/c) vs odds of exposure among controls (b/d). OR = 1 → odds of exposure are equal in cases and controls. OR > 1 → odds of exposure are greater in cases. OR < 1 → odds of exposure are greater in controls."
• Formula: OR = (a/c) / (b/d) = ad/bc
• Example: "If in a case-control study, 20/30 patients with lung cancer and 5/25 healthy individuals report smoking, the OR is 8; so the patients with lung cancer are 8 times more likely to have a history of smoking. You take a case to the OR." (mnemonic: case-control → Odds Ratio)
  • Worked out: a=20 (cases who smoked), c=10 (cases who didn't, since 30 total cases), b=5 (controls who smoked), d=20 (controls who didn't, since 25 total controls). OR = (20×20)/(10×5) = 400/50 = 8.
  • Why odds ratio and not relative risk here: in a case-control study, you chose how many cases and how many controls to enroll — the proportions don't reflect true disease incidence in the population, so you can't calculate a true "risk." Odds ratio is a valid approximation instead.

Relative risk (RR)

• "Typically used in cohort studies. Risk of developing disease in the exposed group divided by risk in the unexposed group. RR = 1 → no association between exposure and disease. RR > 1 → exposure associated with ↑ disease occurrence. RR < 1 → exposure associated with ↓ disease occurrence."
• Formula: RR = [a/(a+b)] / [c/(c+d)]
• Example: "If 5/10 people exposed to radiation are diagnosed with cancer, and 1/10 people not exposed to radiation are diagnosed with cancer, the RR is 5; so people exposed to radiation have a 5 times greater risk of developing cancer. For rare diseases (low prevalence), OR approximates RR."
  • This makes sense mathematically: when a disease is rare, "b" (exposed without disease) is nearly the same as "a+b" and "d" is nearly the same as "c+d," so the odds ratio formula becomes numerically almost identical to the relative risk formula.

Relative risk reduction (RRR)

• "The proportion of risk reduction attributable to the intervention/treatment (ART) as compared to control (ARC)."
• Formulas: RRR = 1 − RR, or RRR = (ARC − ART)/ARC
• Example: "If 2% of patients who receive a flu shot develop the flu, while 8% of unvaccinated patients develop the flu, then RR = 2/8 = 0.25, and RRR = 0.75."
  • In plain language: the vaccine reduced the relative chance of getting the flu by 75% compared to not getting the vaccine.

Attributable risk (AR)

• "The difference in risk between exposed and unexposed groups."
• Formula: AR = a/(a+b) − c/(c+d)
• Example: "If risk of lung cancer in people who smoke is 21% and risk in people who don't smoke is 1%, then the attributable risk is 20%."
  • This tells you how much of the disease risk in smokers is actually due to smoking (20 percentage points worth), as opposed to background risk everyone has anyway.

Absolute risk reduction (ARR)

• "The difference (proportion) attributable to the intervention as compared to a control."
• Formula: ARR = c/(c+d) − a/(a+b)
• Example: "If 8% of people who receive a placebo vaccine develop the flu vs 2% of people who receive a flu vaccine, then ARR = 8% − 2% = 6% = 0.06."
  • Note the distinction from RRR: ARR is the actual percentage-point drop (6 points), while RRR is the relative drop (75% of the original risk). Both numbers describe the same data but tell very different stories — RRR sounds more impressive, ARR is often more clinically meaningful.

Number needed to treat (NNT)

• "Number of patients who need to be treated to benefit 1 patient. Lower number = better treatment."
• Formula: NNT = 1/ARR
  • Logic: if a treatment gives an absolute risk reduction of 6% (0.06), you'd need to treat 1/0.06 ≈ 17 people with the treatment for one extra person to actually benefit (i.e., avoid the flu) who wouldn't have benefited otherwise.

Number needed to harm (NNH)

• "Number of patients who need to be exposed to a risk factor for 1 patient to be harmed. Higher number = safer exposure."
• Formula: NNH = 1/AR

Case fatality rate (CFR)

• "Percentage of deaths occurring among those with disease."
• Formula: CFR% = (deaths/cases) × 100
• Example: "If 4 patients die among 10 cases of meningitis, the case fatality rate is 40%."
  • Note: this is not the same as a population mortality rate — CFR is calculated only among people who already have the disease (out of those diagnosed, what fraction die), not out of the whole population.

PAGE 259 — Population Measures, Likelihood Ratios, Kaplan-Meier

Mortality rate

• "Number of deaths (in general or due to specific cause) within a population over a defined period." Formula: Deaths/1000 people per year.
• Example: "If 80 people in a town of 10,000 die over 2 years, mortality rate is 4 per 1000 per year." (80 deaths ÷ 10,000 people ÷ 2 years × 1000 = 4 per 1000/year)

Attack rate

• "Proportion of exposed people who become ill." Formula: People who become ill / Total people exposed.
• Example: "If 80 people in a town are exposed and 60 people become ill, attack rate is 75%." (Used especially in outbreak investigations — e.g., "75% of people who ate the potato salad got food poisoning.")

Demographic transition

• "As a country proceeds to higher levels of development, birth and mortality rates decline to varying degrees, changing the age composition of the population."
  • This is a sociological/public-health concept: poorer/developing countries tend to have high birth rates and high death rates (young, fast-growing population); as countries develop (better healthcare, sanitation, education), both birth and death rates fall, and the population ages.

Population pyramid

• A bar chart showing age groups on the y-axis and population percentage on the x-axis, split by sex (male/female), showing:
  • Birth rate ↑↑, Mortality rate ↑, Life expectancy Short, Population Growing = a wide-based pyramid (many young people, few old people) — typical of a developing nation with high births but also high deaths.
  • Birth rate →, Mortality rate →, Life expectancy Long, Population Stable = a more rectangular/columnar shape — typical of a developed nation with balanced births and deaths and long lifespans.
  • The shape of the pyramid visually tells you about a population's growth trajectory and age structure at a glance.

Likelihood ratio (LR)

• This measures how much a test result shifts the probability that someone has a disease.
• LR+ (positive likelihood ratio) = probability of a positive result in a patient with the disorder ÷ probability of a positive result in a patient without the disorder = sensitivity / (1 − specificity) = TP rate / FP rate.
• LR− (negative likelihood ratio) = probability of a negative result in a patient with the disorder ÷ probability of a negative result in a patient without the disorder = (1 − sensitivity) / specificity = FN rate / TN rate.
• "LR+ > 10 indicates a highly specific test, while LR− < 0.1 indicates a highly sensitive test."
• "Pretest odds × LR = posttest odds. Posttest probability = posttest odds / (posttest odds + 1)."
  • In plain terms: before you even run a test, a patient has some baseline probability of having a disease (based on symptoms, risk factors, etc — "pretest probability/odds"). The likelihood ratio tells you how much a specific test result (positive or negative) should shift your belief. A big LR+ means a positive result strongly rules the disease in; a very small LR− means a negative result strongly rules the disease out.

Kaplan-Meier curve

• "Used to estimate probability of survival over time. Graphic representation shows the survival probabilities (y-axis) vs length of time (x-axis) data. Outcomes examined may include any event, but frequently include mortality. Survival probability = 1 − (event probability). P value for the survival difference can be calculated using log rank test or Cox regression."
  • This is the classic "staircase" survival graph you see in cancer research papers. Each downward step happens exactly when an event (e.g., death) occurs in the study. The two lines (e.g., "Drug" vs "Control" in the figure) let you visually compare how a treatment affects survival over time — if the "Drug" line stays higher for longer, that treatment group is surviving better.
  • Log rank test / Cox regression: statistical methods used to calculate whether the difference between the two survival curves is statistically significant (i.e., not just due to random chance).

PAGE 260 — Evaluation of Diagnostic Tests

• "Sensitivity and specificity are fixed properties of a test. PPV and NPV vary depending on disease prevalence in population being tested. Test efficiency = (TP+TN)/(TP+TN+FP+FN)."

Sensitivity (true-positive rate)

• "Proportion of all people with disease who test positive, or the ability of a test to correctly identify those with the disease. Value approaching 100% is desirable for ruling out disease and indicates a low false-negative rate."
• Formula: Sensitivity = TP/(TP+FN) = 1 − FN rate.
• Mnemonic given: SN-N-OUT = highly SeNsitive test, when Negative, rules OUT disease. High sensitivity tests are used for screening (you want to catch every possible case, even if some healthy people falsely test positive too — you'll sort that out later with more specific tests).

Specificity (true-negative rate)

• "Proportion of all people without disease who test negative, or the ability of a test to correctly identify those without the disease. Value approaching 100% is desirable for ruling in disease and indicates a low false-positive rate."
• Formula: Specificity = TN/(TN+FP) = 1 − FP rate.
• Mnemonic: SP-P-IN = highly SPecific test, when Positive, rules IN disease. High specificity tests are used for confirmation — once someone screens positive, you use a highly specific test to be sure before diagnosing, because a positive result on this test is trustworthy.

Positive predictive value (PPV)

• "Probability that a person who has a positive test result actually has the disease."
• Formula: PPV = TP/(TP+FP).
• "PPV varies directly with pretest probability (baseline risk, such as prevalence of disease). High pretest probability → high PPV."
  • Why: if a disease is common in the population you're testing (high prevalence), a positive test is more likely to be a true positive rather than a false alarm.

Negative predictive value (NPV)

• "Probability that a person with a negative test result actually does not have the disease."
• Formula: NPV = TN/(TN+FN).
• "NPV varies inversely with prevalence, ie, ↑ prevalence → ↑ PPV and ↓ NPV."
  • Why: if disease is very common, even a negative test result carries more risk of being wrong (a false negative), because there are simply more sick people around overall.

Choosing a test cutoff

• The bell-curve diagram shows two overlapping distributions: "Disease present" (red curve) and "Disease absent" (blue curve), plotted against "Test results." Wherever you draw the vertical cutoff line determines your TP, FP, FN, TN zones.
• "Possible cutoff values for ⊕ vs ⊖ test result: A = 100% sensitivity cutoff value; B = practical compromise between specificity and sensitivity; C = 100% specificity cutoff value."
• "Lowering the cutoff value (B→A): ↑ sensitivity, ↓ specificity. Raising the cutoff value (B→C): ↑ specificity, ↓ sensitivity."
  • This is a fundamental tradeoff: sensitivity and specificity move in opposite directions as you shift where you draw the "positive vs negative" line on a continuous test measurement (like a blood sugar level cutoff for diagnosing diabetes). You can't maximize both simultaneously with a single cutoff.

Receiver operating characteristic (ROC) curve

• "Demonstrates how well a diagnostic test can distinguish between 2 groups (disease vs healthy). Plots the true-positive rate (sensitivity) against the false-positive rate (1 − specificity). The better performing test will have a higher area under the curve (AUC), with the curve closer to the upper left corner."
  • Each point on the ROC curve represents a different cutoff choice, plotting sensitivity vs. (1−specificity) at that cutoff.
  • AUC (area under the curve) summarizes overall test performance in one number: AUC = 1.0 is a perfect test (curve hugs the upper-left corner); AUC = 0.5 (a straight diagonal line) means the test is no better than random guessing/flipping a coin.

PAGE 261 — Precision vs Accuracy; Incidence vs Prevalence

Precision vs accuracy

• Precision (reliability): "The consistency and reproducibility of a test. The absence of random variation in a test." Illustrated by 4 dartboard diagrams (accuracy on one axis, precision on the other):
  • Random error ↓ precision → ↓ reproducibility (statistical noise, points scattered).
  • ↑ precision → ↑ statistical power (1 − β) (tighter grouping means you need a smaller sample to detect a true effect).
• Accuracy (validity): "The closeness of test results to the true values. The absence of systematic error or bias in a test."
  • Systematic error ↓ accuracy → ↑ bias (consistently off-target in one direction, even if tightly grouped).
  • Key distinction using the dartboard analogy: Precision = how tightly clustered your shots are (repeatability), regardless of whether they're near the bullseye. Accuracy = how close to the bullseye (true value) your shots are, regardless of how scattered. You can be precise but inaccurate (tight cluster, but off to one side — this is bias), or accurate but imprecise (scattered around the bullseye but average location is correct).

Incidence vs prevalence

• Incidence: "looks at new cases (incidents) (per unit of time)." Formula: Incidence = (# of new cases) / (# of people at risk).
• Prevalence: "looks at all current cases (at a point in time)." Formula: Prevalence = (# of existing cases) / (Total # of people in a population).
• Relationship: Prevalence/(1 − Prevalence) = Incidence rate × average duration of disease.
• "Prevalence = incidence × duration of the disease. Prevalence > incidence for chronic diseases, due to large # of existing cases (eg, diabetes). Prevalence = incidence for short duration disease (eg, common cold)."
  • Intuition: if a disease lasts a long time (chronic, like diabetes), cases pile up in the population over the years, so at any given moment, prevalence (total existing cases) is much bigger than incidence (new cases this year). If a disease is short-lived (like a common cold, resolved in days), people recover or die quickly, so the pool of "current cases" stays close to the number of "new cases" — incidence ≈ prevalence.

Table: Effect of various situations on incidence vs prevalence

• ↑ survival time: incidence unchanged (—), prevalence ↑ (people live longer with the disease, so more accumulate as existing cases).
• ↑ mortality rate: incidence unchanged (—), prevalence ↓ (people die faster, so fewer remain as "current" cases).
• Faster recovery time: incidence unchanged (→), prevalence ↓ (people leave the "currently sick" pool faster).
• Extensive vaccine administration: incidence ↓ (fewer new cases), prevalence ↓ (fewer people become sick at all).
• ↓ risk factors: incidence ↓, prevalence ↓.
• ↑ diagnostic sensitivity: incidence ↑ (a better test catches more true cases that would've been missed before), prevalence ↑.
• New effective treatment started: incidence unchanged (—), prevalence ↓ (people are cured/removed from the sick pool faster).
• ↓ contact between infected and noninfected patients with airborne infectious disease: incidence ↓, prevalence ↓ (less transmission, so fewer new and fewer existing cases).

PAGE 262 — Bias and Study Errors

Recruiting participants (Selection bias)

• Nonrandom sampling of subjects — "the allocation of study population is not representative of target population."
  • Berkson bias: "cases and/or controls selected from hospitals are less healthy and have different exposures" than the general population — hospital patients aren't a random slice of everyone, they're already sicker/different in some way.
  • Convenience sampling: "patients are enrolled on basis of ease of contact." — e.g., surveying only people who happen to walk by your table, which skews who's included.
  • Attrition bias: "participants lost to follow-up have a different prognosis than those who complete the study." — if the sicker (or healthier) people are the ones who drop out, the remaining group no longer represents the original population fairly.
  • Strategy to reduce: "Randomization (creates 2 groups with similar distributions of known and unknown variables). Ensure the choice of the right comparison/reference group."

Performing the study

• Recall bias: "Awareness of disorder alters recall by subjects; common in retrospective studies." Example: "Patients with disease recall exposure after learning of similar cases." — someone who got sick is more likely to rack their brain and remember/report past exposures ("Was it something I ate? Oh yes, I remember eating that undercooked chicken!") than a healthy person who was never prompted to think hard about it.
  • Strategy: "Decrease time from exposure to follow-up; use medical records as data source." Objective records don't rely on people's fallible memory.
• Measurement bias: "Information is gathered in a manner that systematically distorts it." Example: "Using a faulty automatic sphygmomanometer" (a blood pressure cuff/machine) consistently gives wrong readings for everyone measured with it.
  • Hawthorne effect (also called measurement bias in this context): "participants change behavior upon awareness of being observed" — Example: "Patients with disease recall... " actually the example given is "awareness of being observed (Hawthorne watches you)." People behave differently simply because they know they're being watched (e.g., patients might report feeling better, or take medication more diligently, just because researchers are checking on them).
  • Strategy: "Use objective, standardized, and previously tested methods of data collection that are planned ahead of time."
• Procedure bias: "Subjects in different groups are not treated the same." Example: "Patients in treatment group spend more time in highly specialized hospital units."
  • Strategy: "Blinding (masking) and use of placebo reduce influence of participants on treatment outcome." If patients (or staff) don't know who's in which group, they can't unconsciously treat groups differently.

Interpreting results

• Observer-expectancy bias: "Researcher's belief in the efficacy of a treatment changes the outcome of that treatment (also called Pygmalion effect)." Example: "An observer expecting treatment group to show signs of recovery is more likely to document positive outcomes."
  • Pygmalion effect: named after the myth of a sculptor who fell in love with his own statue — it refers generally to how expectations shape reality/perception. Here, a doctor who expects a treatment to work may subconsciously interpret ambiguous results more favorably.
  • Strategy: "Use blinded, objective outcome measures on procedures and interpretation of outcomes so neither are aware of group assignments."
• Lead-time bias: "Early detection interpreted as ↑ survival, but the disease's course has not changed." Example: "Breast cancer diagnosed early by mammography may appear to ↑ survival time (compared to when it's diagnosed later) because time of diagnosis, but patients are known to have the cancer for longer." —
  • This is a subtle but very important trap: if a screening test finds cancer earlier, patients technically "survive longer after diagnosis" simply because the clock started ticking sooner — even if they die at the exact same age as they would have without screening. It looks like the screening improved survival, but it didn't change the actual disease course at all.
  • Strategy: "Measure 'back-end' survival (adjust survival according to the severity of disease at the time of diagnosis); a caveat of adjusting for severity is it's the potential masking of causality."
• Length-time bias: "Screening test detects diseases with long latency period, while those with shorter latency period become symptomatic earlier." Example: "A slowly progressive cancer is more likely to be detected by a screening test than a rapidly progressive cancer."
  • Latency period = the time between when a disease begins and when it would cause symptoms.
  • Logic: Slow-growing (less deadly) cancers sit around long enough to be caught by a periodic screening test, while fast-growing (more deadly) cancers might cause symptoms and get diagnosed in between screenings, or even kill the patient before the next scheduled screening. So screening programs end up preferentially "catching" the less dangerous cancers, which makes screening look artificially more successful than it truly is.
  • Strategy: "A randomized controlled trial or the assigning subjects to the screening program or not to no screening."

PAGE 263 — Confounding vs Effect Modification

Confounding

• "Factor related to both exposure and outcome (not on a causal pathway) distorts the effect on the outcome. No association after stratification."
• Example: "Coffee appears to be linked to lung cancer, but smoking is the true cause, as coffee drinkers tend to smoke more." — Here, smoking is the confounder: it's related to both the exposure (coffee) and the outcome (lung cancer), and it's not part of any causal chain connecting coffee to lung cancer. It's just an innocent bystander habit that happens to travel together with coffee drinking.
• How you detect/fix it — Stratified analysis: You split ("stratify") your data into subgroups by the confounder (smokers vs. nonsmokers) and check the exposure-outcome relationship within each subgroup separately.
  • Crude analysis (before stratifying): Drinking coffee → strong association → Lung cancer.
  • Stratified analysis: Among smokers: Drinking coffee → weak/no association → Lung cancer. Among nonsmokers: Drinking coffee → weak/no association → Lung cancer.
  • "Note: Association disappeared after stratification, ie, there was a very strong association between OCP use and DVT, but when these data were stratified by smoking, there was no such association in people who do not smoke." (This description actually matches the effect-modification/confounding example given about OCPs, described below.)
• Strategies to reduce confounding: "Crossover studies (subject serves as self-control); Matching (patients with similar characteristics in both treatment and control groups); Analytic techniques (eg, regression analysis when confounding variables are known and were measured)."

Effect modification

• "Exposure leads to different outcomes in subgroups stratified by factor. True association exists."
• Example: "A study among women using OCPs showed significant risk of DVT, but when these data were stratified by smoking, there was a very strong association between OCP use and DVT among smokers, but there was no such association in people who do not smoke."
  • OCP = Oral Contraceptive Pill (birth control pill). DVT = Deep Vein Thrombosis (a blood clot forming in a deep vein, usually the leg — dangerous because it can travel to the lungs).
  • Key difference from confounding: here, smoking doesn't create a fake association that disappears on stratification — instead, it genuinely changes the strength of a real association (OCP truly does increase DVT risk more in smokers than nonsmokers). The association is real in both groups, but the magnitude differs sharply between subgroups — that's the hallmark of effect modification, not confounding.
• Diagram logic: In confounding, stratifying makes a crude (strong) association vanish into "no association" in every subgroup — implying the crude result was an illusion caused by the third factor. In effect modification, stratifying reveals that the association is strong in one subgroup and weak/absent in another — both are real findings, just different in degree depending on the subgroup.

Big-Picture Takeaway

1. Pick a study design (observational for cheap/rapid hypothesis generation, experimental/RCT for the strongest causal proof).
2. Quantify the association you found using the correct statistic for that design (OR for case-control, RR for cohort).
3. Check whether a diagnostic test used along the way is any good (sensitivity/specificity/PPV/NPV/ROC).
4. Understand background population dynamics (incidence, prevalence, mortality) that context your numbers.
5. Interrogate your result for tricks — is it a biased study, or is a confounder/effect modifier secretly at play?
6. Only after all that can you use something like the Bradford Hill criteria to argue the association you found is truly causal.