• a. If observations are arranged in ascending or descending order:
  • Median: 50% of observations are below and 50% are above this value.
  • 1st Quartile ($Q_1$): 25% of observations are below and 75% are above this value.
  • 3rd Quartile ($Q_3$): 75% of observations are below and 25% are above this value.
• b. Rate: Numerator is a part of the denominator and has a time dimension. Ratio: Numerator is not part of the denominator (comparison of two separate quantities).
• c. Case-control study: Retrospective (starts with disease and looks back for exposure/antecedent). Cohort study: Prospective (starts with exposure and follows forward to observe outcome/disease).
• d. Incidence: Number of new cases occurring in a defined population during a specified period of time. Prevalence: Total number of all cases (old and new) existing at a given point in time (point prevalence) or over a period (period prevalence).

In infants of mothers who received antenatal steroids, the odds of developing HMD are 45% less ($\text{OR}=0.55$) compared to those whose mothers did not receive antenatal steroids. However, because the 95% confidence interval ($0.3\text{–}2.1$) crosses $1.0$, this reduction is not statistically significant ($p>0.05$).

Bayes' Theorem / Conditional Probability:

• Let $D=\text{Early neonatal death}$, $P(D)=0.05$ (5%)
• Let $LBW=\text{Low birth weight}$, $P(LBW)=0.30$ (30%)
• Given $P(LBW\mid D)=0.60$ (60%)

$P(D\mid LBW)=\frac{P(LBW\mid D)\times P(D)}{P(LBW)}=\frac{0.60\times 0.05}{0.30}=\frac{0.03}{0.30}=0.10=10\mathrm{\%}$

Probability that a low-birth-weight baby would die in the early neonatal period is 10%.

Arranging in ascending order:
98, 98, 98, 99, 100, 101, 101, 101, 101, 102

• a. $\text{Mean}=\frac{\sum X}{N}=\frac{1000}{10}=100\text{ cm}$
• b. $\text{Mode}=\text{Most frequent observation}=101\text{ cm}$ (appears 4 times)
• c. $\text{Median}=\frac{5\text{th}+6\text{th}\text{ observation}}{2}=\frac{100+101}{2}=100.5\text{ cm}$

• a. $\text{Specificity}=\frac{d}{b+d}\times 100=\frac{\text{True Negative}}{\text{All Non-Diseased}}\times 100$
• b. $\text{Sensitivity}=\frac{a}{a+c}\times 100=\frac{\text{True Positive}}{\text{All Diseased}}\times 100$
• c. $\text{Positive Predictive Value (PPV)}=\frac{a}{a+b}\times 100=\frac{\text{True Positive}}{\text{All Test Positives}}\times 100$
• d. $\text{Negative Predictive Value (NPV)}=\frac{d}{c+d}\times 100=\frac{\text{True Negative}}{\text{All Test Negatives}}\times 100$

• a. Calculations:
  • 1. $\text{Stillbirth Rate}=\frac{\text{No. of fetal deaths }(\ge 1000\text{g})}{\text{Total live births}+\text{stillbirths }(\ge 1000\text{g})}\times 1000=\frac{5}{40+5}\times 1000=\frac{5}{45}\times 1000=111.1\text{ per 1000}$
  • 2. $\text{Neonatal Mortality Rate}=\frac{\text{No. of deaths in first 28 days}}{\text{Total live births}}\times 1000=\frac{5}{40}\times 1000=125\text{ per 1000}$
• b. Perinatal Mortality Rate (PMR): Total number of late fetal deaths ($\ge 28\text{ weeks}$ of gestation or fetus $\ge 1000\text{ g}$) plus early neonatal deaths (first 7 days of life) per 1000 total births.

• a. $\text{Prevalence Rate}=\frac{\text{Existing}+\text{New cases}}{\text{Total Population at risk}}\times 100=\frac{500+100}{5000}\times 100=\frac{600}{5000}\times 100=12\mathrm{\%}$
• b. $\text{Incidence Rate}=\frac{\text{New cases}}{\text{Population at risk}}\times 1000=\frac{100}{5000}\times 1000=20\text{ per 1000 per year}$
• c. $\text{Case Fatality Rate}=\frac{\text{Deaths due to malnutrition}}{\text{Total cases of malnutrition}}\times 100=\frac{20}{600}\times 100=3.33\mathrm{\%}$
• d. Advantages of Prevalence Rate:
  • i. Estimates the overall burden/magnitude of the disease in the community.
  • ii. Identifies high-risk target groups.
  • iii. Useful for health administrative planning, resource allocation, and hospital bed requirements.

• a. p-value: The probability of obtaining results as extreme as, or more extreme than, the observed results purely by chance, assuming the null hypothesis is true (probability of Type I error).
• b. Paired Student's 't' test (paired comparisons on same subjects before and after).
• c. Non-parametric tests are applied when data does not follow a normal (Gaussian) distribution (skewed data), sample size is small, or data is on nominal/ordinal scales.

• a. Odds Ratio (OR):
  $\text{OR}=\frac{\text{Odds of exposure in cases}}{\text{Odds of exposure in controls}}=\frac{a/c}{b/d}=\frac{a\times d}{b\times c}=\frac{ad}{bc}$
• b. Significance:
  • Odds ratio measures the strength of association between exposure and disease in retrospective case-control studies.
  • $\text{OR}=1$: Exposure does not affect odds of outcome (no association).
  • $\text{OR}>1$: Exposure associated with higher odds of outcome (risk factor).
  • $\text{OR}<1$: Exposure associated with lower odds of outcome (protective factor).

• a. Forest Plot (Blobbogram); primarily used in Meta-analyses and Systematic Reviews to display pooled effect estimates from multiple studies.
• b. Diamond (represents the pooled overall summary effect estimate with its 95% confidence interval).
• c. Study done by Kay (has the largest effect size and narrowest confidence interval).

• a. Relative Risk (RR):
  $\text{Incidence in Zinc group}=\frac{12}{39}=0.308$
  $\text{Incidence in Racecadotril group}=\frac{6}{26}=0.231$
  $\text{RR}=\frac{12/39}{6/26}=\frac{0.308}{0.231}=1.33\text{ to }1.52$
• b. Improvement with zinc therapy is $1.33\text{–}1.52$ times more likely compared to racecadotril therapy.

• a. Child Survival Index:
  $\text{Child Survival Index}=\frac{1000-\text{U5MR}}{10}=\frac{1000-5}{10}=\frac{995}{10}=99.5$
• b. Student's unpaired 't' test (for two independent continuous means).
• c. Chi-Square (${\chi }^2$) test or Fisher's exact test (for two categorical proportions).

• a. Box-and-Whisker Plot (Boxplot).
• b. Displays a 5-number summary of continuous variables: Minimum, 1st Quartile (25th percentile), Median (50th percentile), 3rd Quartile (75th percentile), Maximum, and Outliers.
• c. Components:
  • The central rectangular box spans the Interquartile Range (IQR, 25th to 75th percentile).
  • The horizontal band inside the box represents the Median.
  • Whiskers extend to the minimum and maximum values within $1.5\times \text{IQR}$.
  • Outliers / extreme points are plotted individually beyond the whiskers.

• a. v. Randomization (balances both known and unknown confounding variables).
• b. iv. It reduces systematic bias between the treatment and control groups (prevents observer and subject bias).
• c. ii. Median (In a normal distribution, Mean = Median = Mode).
• d. iii. 4/28 ($\text{Odds}=\frac{\text{Events}}{\text{Non-events}}=\frac{4}{28}$).

• Sensitivity $=\frac{\text{TP}}{\text{TP}+\text{FN}}=\frac{300}{325}=92.3\mathrm{\%}$
• Specificity $=\frac{\text{TN}}{\text{TN}+\text{FP}}=\frac{75}{175}=42.9\mathrm{\%}$
• Positive Predictive Value (PPV) $=\frac{\text{TP}}{\text{TP}+\text{FP}}=\frac{300}{400}=75.0\mathrm{\%}$
• Negative Predictive Value (NPV) $=\frac{\text{TN}}{\text{TN}+\text{FN}}=\frac{75}{100}=75.0\mathrm{\%}$

• a. Odds Ratio:
  $\text{OR}=\frac{ad}{bc}=\frac{98\times 48}{92\times 112}=\frac{4704}{10304}=0.45$
• b. Difference:
  • Relative Risk (RR): Ratio of probability of disease in exposed vs unexposed group ($\frac{a/(a+b)}{c/(c+d)}$); used exclusively in prospective/cohort studies.
  • Odds Ratio (OR): Ratio of odds of exposure in cases vs controls ($\frac{ad}{bc}$); used primarily in retrospective case-control studies (estimates RR when disease prevalence is low).

All the given statements are correct (True).
$\text{Power}=1-\beta$ (Probability of detecting a true difference).

• a. False (It tests already formulated hypotheses; descriptive studies generate hypotheses).
• b. False (It can be conducted on relatively small sample sizes compared to cohort studies).
• c. False (It is inherently retrospective).
• d. True (It analyzes the association between exposure and disease with a comparison control group).
• e. True (The investigator observes exposure status without administering an experimental intervention).

• a. Number of cigarettes smoked $\to$ ii. Ratio (or Discrete variable)
• b. Body temperature $\to$ iii. Interval
• c. Age in completed years $\to$ iv. Metric (or Ratio)
• d. Age in categories (child, adolescent, adult) $\to$ i. Ordinal
• e. Stage of a cancer $\to$ i. Ordinal / vi. Discrete variable
• f. Blood sugar levels $\to$ v. Continuous variable

• a. Positive Predictive Value (PPV): If PPV is 90%, it means there is still a 10% chance that the person with a positive test does not have the disease (False positive rate among test positives is $1-\text{PPV}$).
• b. Test with high Sensitivity (SnNOut: High Sensitivity test when Negative rules OUT disease) / High NPV.
• c. Test with high Specificity (SpPIn: High Specificity test when Positive rules IN disease) / High PPV.

• a. Attack Rate:
  $\text{Attack Rate}=\frac{\text{Total cases in a year}}{\text{Total susceptible population at risk}}\times 100$
  $\text{Susceptible children}=1300-800=500$
  $\text{Attack Rate}=\frac{10}{500}\times 100=2\mathrm{\%}$

• b. Secondary Attack Rate (SAR):
  $\text{SAR}=\frac{\text{Number of secondary cases}}{\text{Susceptible contacts exposed to primary cases}}\times 100$
  $\text{SAR}=\frac{8}{15}\times 100=53.33\mathrm{\%}$

• Assume 100 total pregnancies reaching $\ge 28$ weeks:
  • Fetal deaths (Stillbirths) $=2$
  • Live births $=100-2=98$
  • Early neonatal deaths (within 1 week) $=3\mathrm{\%}\text{ of }98=2.94$

$\text{Perinatal Mortality Rate (PMR)}=\frac{\text{Stillbirths}+\text{Early Neonatal Deaths}}{\text{Total Births}}\times 1000$
$\text{PMR}=\frac{2+2.94}{100}\times 1000=\frac{4.94}{100}\times 1000=49.4\approx 49\text{ per 1000 total births}$