Calculations BTR

Epidemiology

• Cohort Studies
• Relative Risk (RR)
• Formula: Incidence in Exposed / Incidence in Non-exposed
• Do not make a 2x2 table for RR in cohort studies.
• Example: (50/400) / (5/100) = 2.5
• Interpretation:
• RR > 1: Indicates a risk factor (incidence increasing). Causality needs Hills criteria.
• RR < 1: Indicates it's protective.
• RR = 1: Indicates no association.
• Population Attributable Risk (PAR)
• Concept: Proportion of cases that would decrease if the risk factor was removed.
• Formula: (Incidence in Total - Incidence in Non-exposed) / Incidence in Total * 100
• Example: (55/500 - 5/100) / (55/500) * 100 ≈ 55%

• Case-Control Studies
• Odds Ratio (OR)
• Study Type: Case-control studies.
• Requires a 2x2 table.
• Table Layout: Disease (Positive/Negative) on top, Risk Factor (Positive/Negative) on side.
• Formula: (A * D) / (B * C) (Cross product)

• Attributable Risk (AR)
• Concept: Proportion of cases in the exposed group due to the exposure.
• Formula: (Incidence in Exposed - Incidence in Non-exposed) / Incidence in Exposed * 100

• Screening Tests
• Requires a 2x2 table.
• Table Layout: Disease (Positive/Negative) on top, Test (Positive/Negative) on side.
• Do not use Bayes theorem if a 2x2 table can be made.
• Positive Predictive Value (PPV)
• Formula: A / (A + B) * 100 (True positives / Total positives)
• Example: 50 / (50 + 10) * 100 ≈ 83%
• Negative Predictive Value (NPV)
• Formula: D / (D + C) (True negatives / Total negatives)
• Sensitivity
• Formula: A / (A + C) (True positives / Total diseased)
• Specificity
• Formula: D / (B + D) (True negatives / Total healthy)
• Prevalence
• Formula: (A + C) / (A + B + C + D) * 100 (Total diseased / Total population)
• Uden's Index
• Formula: Sensitivity + Specificity - 1
• Concept: Summary of ROC curve; optimal cut-off.
• Bayes Theorem
• Use: Correlates PPV/NPV with sensitivity/specificity and prevalence.
• PPV Formula: (Sensitivity * Prevalence) / (Sensitivity * Prevalence + (1 - Specificity) * (1 - Prevalence)) * 100
• NPV Formula: (Specificity * (1 - Prevalence)) / (Specificity * (1 - Prevalence) + (1 - Sensitivity) * Prevalence)
• Tip: Sensitivity goes with Prevalence; (1-Specificity) with (1-Prevalence).

Biostatistics

• Type I Error (Alpha Error)
• Concept: Probability of a false positive (result came by chance, not actually significant).
• P-value: Probability of committing an alpha error.
• Statistical Significance: P-value should be < 0.05 (< 5%).
• Confidence Level (CL): If P-value < 0.05, then CL > 95%. Most studies aim for 95% CL.
• Confidence Level is different from Confidence Interval.

• Type II Error (Beta Error)
• Concept: False negative error (study was significant but rejected).
• Power of Study: 1 - Beta.
• Increasing Power: Increase sample size (n).

• Standard Deviation (SD)
• Concept: Measures deviation/dispersion within a single data set.
• Formula: Root mean square of deviations from the mean (often identified by its symbol).

• Coefficient of Variation (CV)
• Concept: Measures relative dispersion between two different data sets or studies.
• Formula: Standard Deviation / Mean * 100

• Variance
• Formula: Standard Deviation²

• Standard Error of Mean (SEM)
• Concept: Tells about the population based on a sample; standard deviation of the population.
• Formula: Standard Deviation / √n
• Increasing sample size (n) reduces SEM.

• Confidence Interval (CI)
• Concept: Range of values likely to contain the true population parameter.
• Formula (for mean, 95% CI): Mean ± 2 * Standard Error
• Formula (for proportion): Uses √(PQ/n) as SEM (P=prevalence, Q=1-P).
• Example (mean): Mean=25, SD=10, n=400 → SEM = 0.5 → CI = 25 ± 2*0.5 = 24-26.
• Example (proportion): P=0.1, n=100 → SEM = 0.03 → CI = 0.10 ± 2*0.03 = 0.04-0.16 (4%-16%).

• Sample Size Calculation
• Formula (for proportions): 4PQ / D²
• P=prevalence, Q=1-P.
• D is the absolute error (allowable error).
• If relative precision/error is given (e.g., 20%), convert to absolute error: Relative precision * Prevalence (e.g., 0.20 * 0.10 = 0.02).
• Alpha error & power in question are distractors for this formula.
• Example: P=0.1, Relative Precision=20% → D=0.02 → Sample size = 4*0.1*0.9 / (0.02)² = 900.

• Interpreting P-value and Confidence Level
• P < 0.05: < 5% chance result is by chance (statistically significant) → > 95% confidence.
• P < 0.1: < 10% chance result is by chance → > 90% confidence.

Extra Edge Territory (Miscellaneous Biostats)

• Mode, Median, Mean Relationship (for skewed data)
• Formula: Mode = 3 * Median - 2 * Mean

• Probability
• Mutually Exclusive Events: Use Addition.
• Independent Factors: Use Multiplication.

• Odds
• Formula: P / (1 - P) (P=probability)

• Degree of Freedom (for Chi-square test)
• Formula: (Rows - 1) * (Columns - 1)

• Evaluating Intervention Studies
• CER = Event Rate in Control Group
• EER = Event Rate in Experimental Group
• Absolute Risk Reduction (ARR)
• Concept: How much incidence was prevented by the experimental drug.
• Formula: CER - EER
• Relative Risk Reduction (RRR)
• Formula: (CER - EER) / CER
• Number Needed to Treat (NNT)
• Concept: How many people need treatment to avert one event.
• Formula: 1 / ARR
• Example: CER=0.3, EER=0.2 → ARR=0.1 → NNT = 1/0.1 = 10.
• Number Needed to Harm (NNH): Used for adverse effects if experimental group incidence is higher.

• Box and Whisker Plot
• Divides data into 4 parts.
• Whiskers: First & fourth quartiles (25% each).
• Box: Middle 50% of data (interquartile range).
• Line in box center: Represents the Median.
• Skewed Data: Identified by unequal whisker length.
• Positively Skewed (Right-skewed): Longer whisker on the right side.
• Interquartile Range (IQR): Range covered by the box (between first and third quartiles).

PSM - Concepts & Definitions

• Prevalence
• Study Type: Cross-sectional studies.
• Concept: Snapshot of total cases (old + new) at a point in time.
• Formula: (Number of Cases / Total population at that point) * 100
• Measure Type: Proportion.

• Incidence
• Study Type: Cohort studies.
• Concept: Measures new cases.
• Formula: (Number of New Cases / Population at risk) * 1000
• Measure Type: Rate.

• Attack Rate
• Same as incidence, for infectious diseases.
• Formula: (New cases of infection / Population at risk) * 1000
• Expresses extent of an epidemic.

• Secondary Attack Rate (SAR)
• Concept: Secondary cases within one incubation period of a primary case.
• Formula: (Number of secondary cases in 1 incubation period / Number of susceptible contacts in close contact) * 100
• Primary case and vaccinated individuals are subtracted from denominator.
• Example: 2 secondary cases in family of 4 children with 1 primary case → SAR = (2 / (4-1)) * 100 ≈ 66%.

• Proportional Mortality Rate (PMR)
• Concept: Deaths from one particular cause as a proportion of total deaths.
• Formula: (Deaths due to a specific cause / Total deaths) * 100
• Simplest measure of burden of disease.

• Case Fatality Rate (CFR)
• Concept: Deaths among total cases of a specific disease.
• Formula: (Total number of deaths from a disease / Total cases of that disease) * 100
• Comments on the virulence of a disease.

Demography

• Denominator for many indices: mid-year population (calculated July 1st).

• Crude Birth Rate (CBR)
• Formula: (Total number of births / Mid-year population) * 1000
• Current Indian CBR: 16.9 per 1000.

• Crude Death Rate (CDR)
• Formula: (Total deaths / Mid-year population) * 1000
• Current Indian CDR: 9.1 per 1000.

• Annual Growth Rate
• Formula: (CBR - CDR) / 10
• Census 2011: 1.64%.
• Rule of 70 (Malthusian's rule): If growth rate is 1%, population doubles in 70 years.

• Fertility Indices
• General Fertility Rate (GFR): Total births (not age-specific).
• Total Fertility Rate (TFR): Age-specific births. Best for measuring completed family size. Current Indian TFR: 2.1.
• Gross Reproduction Rate (GRR): Only daughters' births.
• Net Reproduction Rate (NRR): Only daughters' births, takes mortality into account. Best measure of overall fertility of a country/community. Current Indian NRR: 1.
• India has achieved these ideal indices.

• Literacy Rate
• Formula: (Number of literates / Total population aged >= 7 years) * 100
• Literate: Can read, write, and understand any one language.
• Census 2011: 74%.

• Sex Ratio
• Formula: (Number of females / Number of males) * 1000
• Census 2011: 943.

• Child Sex Ratio
• Formula: (Number of females aged 0-6 years / Number of males aged 0-6 years) * 1000
• Census 2011: 919.

• Dependency Ratio
• Formula: (Population < 15 years + Population > 65 years) / Population aged 15-65 years (Ratio).

Mortality Indices

• Denominator:
• Live births: For MMR, Under-five mortality, IMR, NMR.
• Total births (live births + still births): For Still birth ratio/rate.

• Maternal Mortality Ratio (MMR)
• Formula: (Maternal deaths / Live births) * 100,000 (Multiplier is 1 lakh).
• Maternal Death: Deaths due to pregnancy, labor, or puerperium, till 42 days after delivery, due to birth-related causes.
• Measure Type: Ratio.
• Current Indian MMR: 97.

• Maternal Mortality Rate
• Formula: (Maternal deaths / Females in reproductive age group (15-49 years)) * 100,000
• Measure Type: Rate.

• Under-five Mortality Rate
• Formula: (Deaths in children < 5 years / Live births) * 1000
• Current Indian U5MR: 32.

• Infant Mortality Rate (IMR)
• Formula: (Infant deaths (< 1 year) / Live births) * 1000
• Example: 4 deaths, 100 live births → IMR = 40.
• Current Indian IMR: 28.

• Neonatal Mortality Rate (NMR)
• Formula: (Deaths in neonates (0-28 days) / Live births) * 1000
• Current Indian NMR: 20.

• Perinatal Mortality Rate (PMR)
• Formula: (Early neonatal deaths + Still births) / Live births * 1000
• Still births: Born after 28 weeks gestation OR birth weight > 1000g.
• Best measure of combined obstetric and pediatric care.
• Current Indian PMR: 18.

• Still Birth Ratio / Rate
• Formula: (Number of stillborns / Total births (Live births + Still births)) * 1000
• Current Indian Still Birth Rate: 21.

• Child Survival Index Number
• Formula: (1000 - Under five mortality rate) / 10

PSM - Communicable & Non-Communicable Diseases

• Dengue & Yellow Fever (Aedes mosquito)
• House Index
• Formula: (Number of positive houses / Total houses examined) * 100
• Positive House: Has Aedes breeding.
• Index > 5% is bad.
• Breteau Index
• Formula: (Number of positive containers / Total houses examined) * 100
• Index >= 20 is bad.

• Malaria Indices
• Annual Parasite Incidence (API)
• Formula: (Number of new cases of malaria / Total population at risk) * 1000 (Incidence for malaria).
• API > 2 is bad.
• Best indicator of malaria being a community problem.
• Annual Blood Examination Rate (ABER)
• Formula: (Number of blood slides made / Total population) * 100
• Best indicator for good operational efficiency of malaria program.
• Slide Positivity Rate (SPR)
• Formula: (Slides positive for malaria / Total slides made) * 100

• Non-Communicable Disease (NCD) Indices
• Quetelet Index: Same as BMI
• Formula: Weight (kg) / Height (meters²)
• Ponderal Index: Used in pediatrics.
• Formula: Weight (g) / Height (cm³)
• Broca's Index (Ideal Weight)
• Formula: Height (cm) - 100
• Corpulence Index
• Formula: Actual weight / Desirable weight (Ideally < 1.2).

PSM - Miscellaneous

• Chlorine Demand
• Apparatus: Horrock's apparatus.
• Calculation: If Nth jar changes color → N * 2g bleaching powder for 455 liters of water.

• Pearl Index
• Concept: Accidental pregnancies per 100 women-years of contraceptive exposure.
• Formula: (Number of accidental pregnancies / Total women-years of exposure) * 100
• If given in months: (Number of accidental pregnancies / Total months of exposure) * 1200

• Pregnancy Wastage Factor: Approximately 10%.

• Vaccine Wastage Factor: Varies (e.g., 50% for BCG, 2% for others). 50% wastage needs a multiplication factor of 2 for planning.

• Calculating Number of Pregnant Females
• Expected births (from CBR) → Account for wastage: Expected births / (1 - wastage factor).
• Example: 150 births, 10% wastage → 150 / 0.90 ≈ 166 pregnancies.

• Calculating ANC Registration Target: Usually 50% of expected pregnancies.
• Example: 165 pregnancies → Target ≈ 80.

• Calculating Number of Vaccines to Hold
• Expected births → Apply wastage factor.
• Example: 150 births, BCG (50% wastage) → 150 * 2 = 300 vaccines.

• Estimating Infants to be Registered at a Subcenter
• Use subcenter population & current CBR to find expected births.

Pharmacology Formulae

• Volume of Distribution (Vd)
• Concept: Amount of drug in body relative to plasma concentration.
• Formula: Amount of drug in body / Plasma concentration
• Unit: Liters (L) or L/kg.
• Example: 4g dose, 50mg/L conc. → Vd = 4000mg / 50mg/L = 80 L.

• Half-life (t½)
• Formula: 0.7 * Vd / Clearance (using 0.7 for 0.693).
• Unit: Time (e.g., hours).

• Clearance
• Formula: (Urine flow rate * Urine concentration) / Plasma concentration (UV/P).
• Unit: Volume/time (e.g., mL/min).

• Loading Dose (LD)
• Formula: (Desired Concentration * Volume of Distribution) / Bioavailability (F)
• Account for patient weight if Vd is L/kg.
• Example: Desired C=3mg/L, Vd=2L/kg, W=60kg, F=0.9 → LD = (3 * (2*60)) / 0.9 = 400 mg.

• Maintenance Dose (MD) / Rate of IV Infusion
• Formula: (Desired Concentration * Clearance) / Bioavailability (F)
• Multiply by dosing interval if applicable.
• Example (Rate of Infusion): Desired C=2mg/L, Clearance=20L/hr, F=1 → Rate = (2 * 20) / 1 = 40 mg/hr.
• Example (MD with interval): Steady state C=2mg/L, Clearance=20L/hr, Dosing interval=6hr, F=1 → MD = (2 * 20 * 6) / 1 = 240 mg.

• Therapeutic Index (TI)
• Formula: TD50 / ED50 or LD50 / ED50
• TD50/LD50: Toxic/lethal dose in 50% population.
• ED50: Efficacious dose in 50% population.
• Example: LD50=500, ED50=50 → TI = 10.

• Area Under the Curve (AUC)
• Plot of Concentration vs. Time.
• Represents Bioavailability (F).
• Decreasing first-pass metabolism ↑ bioavailability and AUC.

• Time to Reach Steady State Concentration: Takes 4-5 half-lives. Choose 5 if both options.

• Drug Kinetics
• Zero Order: A constant amount of drug eliminated per unit time.
• Example: 40mg cleared every 1.5 hrs. If 200mg initial → 120mg remain after 3 hrs (200 - 2*40).
• First Order: A constant fraction/percentage of drug eliminated per unit time.
• Example: 20% cleared every 1.5 hrs. If 200mg initial → 160mg after 1.5 hrs. Then 20% of 160mg (32mg) cleared next 1.5 hrs → 128mg remain.