Disease Control: Reduction to acceptable level by continuous intervention (e.g., Malaria control).
Disease Elimination: Zero incidence in defined region, measures continue (e.g., Leprosy elimination).
Disease Eradication: Permanent global zero, no intervention needed (e.g., Smallpox).
Index case = first reported; First case = actual earliest case.
| Exposure | Ill | Not Ill | Total |
|---|---|---|---|
| Ate fish fry | 40 | 40 | 80 |
| Did not eat | 10 | 30 | 40 |
Attack rate exposed = 40/80 = 0.5 ; Attack rate unexposed = 10/40 = 0.25.
RR = \( \frac{0.5}{0.25} = 2 \) → fish fry eaters had 2× higher risk → suspected food item.
Test A (Se=80%, Sp=70%), Test B (Se=90%, Sp=90%), Pop=3000, Prev=5% (D=150, ND=2850).
After A: TP=120, FN=30 ; TN=1995, FP=855. Test B on positives (975):
TP₂=108, FN₂=12 ; TN₂=769.5, FP₂=85.5.
Final TN = 1995+769.5 = 2764.5 ; Final FP=85.5.
Net Specificity = \( \frac{2764.5}{2764.5+85.5} = \frac{2764.5}{2850} = 0.97 \) (97%).
| TB Yes | TB No | Total | |
|---|---|---|---|
| MO₁ TB Yes | 20 | 10 | 30 |
| MO₁ TB No | 5 | 15 | 20 |
| Total | 25 | 25 | 50 |
Percentage agreement = \( \frac{20+15}{50}=70\% \).
Positive agreement = \( \frac{20}{20+10+5}= \frac{20}{35} \approx 57.14\% \).
Case-control: starts with disease, OR, rare diseases. Cohort: starts with exposure, RR, rare exposure.
Type I error (α): reject true H₀ (false positive). Type II error (β): accept false H₀ (false negative).
PAR = \( I_t - I_0 \) (excess risk in population due to exposure).
Iₑ=95/10000, Iᵤ=15/10000, Pₑ=0.4.
AR = \( \frac{95-15}{10000} = \frac{80}{10000} \) = 80 per 10,000.
PAR = \( 0.4 \times \frac{80}{10000} = \frac{32}{10000} \) = 32 per 10,000.
Confounding may explain correlation. Hill’s criteria: Strength, Consistency, Specificity, Temporality (most important), Biological gradient, Plausibility, Coherence, Experiment, Analogy.
Crude OR = \( \frac{60\times164}{140\times36}=1.95 \).
Age <40: OR=1 ; Age ≥40: OR=1 → crude OR differs → Age is a confounder.
Classes: 100–150(25),150–200(30),200–250(35),250–300(10). Midpoints:125,175,225,275.
Mean = \( \frac{19000}{100}=190 \).
Median class 150–200: Median = \( 150 + \frac{50-25}{30}\times50 = 191.67 \).
Mode = \( 200 + \frac{35-30}{70-30-10}\times50 = 208.33 \).
n=100, old mean=65, wrong 60 → correct 55. Corrected mean = \( \frac{6500-60+55}{100}=64.95 \) kg.
Corrected SD ≈ 5.07 kg (after Σx² correction).
n=60, success p=0.4 → mean = 24, SD = \( \sqrt{60\times0.4\times0.6}=3.79 \).
Birth weight: μ=2.8, σ=0.4, P(X<2.5): z=-0.75 → prob≈0.2266 → expected newborns = \( 0.2266\times500 \approx 113 \).
P(correct)=0.6, P(death|correct)=0.4, P(death|wrong)=0.7. P(death)=0.52.
P(correct|death) = \( \frac{0.24}{0.52} \approx 0.4615 \) (46.15%).
x: 60,65,70,75,80 ; y:140,145,150,155,160 → perfect linear → r = +1.
Regression y on x: slope b=1, intercept a=80 → y = x + 80.
Standard population: young=13000, old=14000. X std rate = \( \frac{0.008625\times13000 + 0.01045\times14000}{27000} = 0.00957 \) (9.57/1000).
Y std rate = \( \frac{0.0096\times13000 + 0.02\times14000}{27000}=0.01499 \) (14.99/1000).
Observed: 13804,13930,13863,14023,14345,14944,15044 ; total=99953, expected=14279.
χ² = Σ(O−E)²/E ≈ 113.30, critical (df=6, α=0.05)=12.59 → significant → cars not equally distributed.
n=10, mean=66, SD=3, H₀: μ=64. t = \( \frac{66-64}{3/\sqrt{10}} = 2.108 \).
Tabulated t₀.₀₅,₉ = 2.262 → 2.108 < 2.262 → not significant; cannot conclude mean height >64 inches.