Biostatistics and Branches of Biostatistics

1. Introduction

2. Definitions

Narrow Definition

Broad Definition (Park's Textbook of Preventive and Social Medicine)

Statistics vs. Biostatistics

3. Importance of Biostatistics

1. Planning research - helps define the hypothesis, select study design, and calculate sample size
2. Analyzing clinical trials - determines whether an intervention is effective
3. Epidemiology - measures disease frequency, risk factors, and associations
4. Health policy - mortality rates, birth rates, and disease burden inform resource allocation
5. Evidence-based medicine - systematic reviews and meta-analyses depend entirely on statistical synthesis
6. Quality control - monitoring hospital infection rates, surgical outcomes
7. Demography and vital statistics - tracking population changes, births, deaths, migration

4. Basic Terminology

• Population: The entire group of individuals about which information is desired
• Sample: A subset of the population selected for study
• Variable: Any characteristic that can take different values (e.g., blood pressure, age)
• Data: Observed values of a variable
• Parameter: A numerical summary of the population
• Statistic: A numerical summary of the sample

Types of Variables

5. Branches of Biostatistics

Branch 1: Descriptive Statistics

• Measures of Central Tendency: Mean (arithmetic average), Median (middle value), Mode (most frequent value)
• Measures of Dispersion: Range, Standard Deviation (SD), Variance, Coefficient of Variation (CV)
• Graphical methods: Bar charts, pie charts, histograms, frequency polygons, box-and-whisker plots
• Tabulation: Frequency tables, relative frequency

Branch 2: Inferential Statistics

• Hypothesis testing: Null hypothesis (H₀) vs. Alternative hypothesis (H₁)
• Parametric tests: Student's t-test, ANOVA (Analysis of Variance), Pearson correlation, linear regression
• Non-parametric tests: Mann-Whitney U test, Kruskal-Wallis test, Chi-square test
• Confidence intervals: A range of values within which the true population parameter likely falls
• p-value: Probability of obtaining results as extreme as observed, assuming H₀ is true (significance threshold usually p < 0.05)

• Frequentist statistics: Conclusions based only on observed data
• Bayesian statistics: Incorporates prior knowledge along with observed data

Branch 3: Vital Statistics

• Civil registration systems (birth and death registration)
• Census data
• Hospital records
• Notifiable disease reports
• Sample Registration System (SRS)

• Crude Birth Rate (CBR): Number of live births per 1,000 population per year
• Crude Death Rate (CDR): Number of deaths per 1,000 population per year
• Infant Mortality Rate (IMR): Deaths under 1 year per 1,000 live births
• Maternal Mortality Ratio (MMR): Maternal deaths per 100,000 live births
• Life Expectancy at Birth: Average number of years a newborn is expected to live

Branch 4: Epidemiological Statistics (Epidemiostatistics)

• Prevalence: Proportion of a population with a disease at a given time
• Incidence rate: Number of new cases per unit population per unit time
• Relative Risk (RR): Risk in exposed group / Risk in unexposed group (used in cohort studies)
• Odds Ratio (OR): Odds of exposure in cases / Odds of exposure in controls (used in case-control studies)
• Attributable Risk (AR): Excess risk due to a specific exposure
• Number Needed to Treat (NNT): Number of patients treated to prevent one outcome

• Cross-sectional studies
• Case-control (retrospective) studies
• Cohort (prospective) studies
• Ecological studies
• Randomized Controlled Trials (RCTs)

Branch 5: Demography

• Age-sex pyramid (population pyramid)
• Dependency ratio
• Fertility rate (Total Fertility Rate - TFR)
• Net Reproduction Rate (NRR)
• Population growth rate
• Standardized mortality/morbidity ratios

• Formal demography: Mathematical and statistical analysis of population data
• Social demography: Interaction between demographic variables and social factors (income, education, religion)

Branch 6: Clinical Biostatistics (Clinical Trial Statistics)

• Sample size calculation: Power of a study (usually 80-90%), Type I error (α = 0.05), Type II error (β = 0.20)
• Randomization: Ensures equal distribution of confounding variables between groups
• Blinding: Single-blind (patient unaware), Double-blind (patient + investigator unaware), Triple-blind (including data analyst)
• Intention-to-treat (ITT) analysis: Analyzes patients in the group they were randomized to, regardless of protocol deviation
• Per-protocol analysis: Analyzes only patients who completed the trial as planned

• Phase I: Safety and dosing (small healthy volunteers)
• Phase II: Efficacy and side effects (small patient groups)
• Phase III: Large-scale efficacy comparison with standard treatment
• Phase IV: Post-marketing surveillance

Branch 7: Survival Analysis

• Kaplan-Meier curves: Graphical display of survival probability over time
• Log-rank test: Compares survival between two or more groups
• Cox proportional hazards regression: Identifies risk factors affecting time-to-event
• Hazard ratio (HR): The relative risk of the event at any point in time

Branch 8: Systematic Reviews and Meta-analysis

1. Systematic literature search (PubMed, Cochrane, EMBASE)
2. Quality assessment of included studies (GRADE criteria, Cochrane risk-of-bias tool)
3. Data extraction and pooling using weighted average
4. Forest plot: Graphical display of individual and pooled effect sizes
5. Funnel plot: Assessment of publication bias

• Pooled Risk Ratio / Odds Ratio / Mean Difference
• Heterogeneity (I² statistic): I² > 50% indicates substantial heterogeneity
• Random effects model vs. Fixed effects model

Branch 9: Health Statistics (Medical Statistics)

• Bed occupancy rate
• Average length of hospital stay
• Surgical site infection rates
• Readmission rates
• Disease-specific mortality rates

• World Health Organization (WHO) - Global Health Observatory
• National Health Profile (India)
• Centers for Disease Control and Prevention (CDC) - USA
• Office of National Statistics (ONS) - UK

6. Relationship Between the Branches

             BIOSTATISTICS
                  |
    ┌─────────────┼─────────────┐
    |             |             |
Descriptive   Inferential   Vital Statistics
Statistics    Statistics         |
    |             |         Demography
  Graphs     Hypothesis         |
  Tables      Testing       Health Planning
    |             |
Epidemio-    Clinical
statistics   Biostatistics
    |             |
  Risk       Clinical Trials
Measures    Meta-analysis
                  |
           Survival Analysis

7. Applications of Biostatistics

8. Limitations of Biostatistics

1. A statistical association does not prove causation (e.g., correlation does not equal causation)
2. Results depend entirely on the quality and representativeness of the sample - garbage in, garbage out
3. p-values can be misleading; clinical significance and statistical significance can differ
4. Biological variation is high, making precise predictions difficult
5. Requires expertise - misuse of statistical tests leads to erroneous conclusions
6. Cannot account for all confounding variables in observational studies

9. Summary Table: Branches of Biostatistics

10. Conclusion

References used:

• Barash, Cullen, and Stoelting's Clinical Anesthesia, 9th Edition - Chapter on Experimental Medicine & Data Analysis
• Park's Textbook of Preventive and Social Medicine - Chapter on Health Information Systems
• The Harriet Lane Handbook (Johns Hopkins), 23rd Ed. - Section on Biostatistics and Evidence-Based Medicine

Descriptive and Inferential Statistics - Detailed Explanation with Examples

PART A: DESCRIPTIVE STATISTICS

1. Definition

"The quantification of information in meaningful summaries and comparisons is the domain of statistical analysis. Descriptive statistics provide a consistent framework for calculating or estimating the central tendency of continuous data in the familiar forms of mean, median, and mode. The variation in data is generally described by the mathematical calculations of variances and standard deviations."

2. Components of Descriptive Statistics

A. Measures of Central Tendency

"The sample mean is equal to the sum of the measurements divided by the number of observations. The median of a set of measurements is the number that falls in the middle. The mode is the most frequently occurring number in a set of measurements."

• If data is normally distributed (bell-shaped) → use Mean
• If data is skewed or has outliers → use Median
• If data is categorical → use Mode

"Another way is to examine the SD; when it is very large (e.g., larger than the mean value with which it is associated), the data often have an asymmetric distribution and should be described by the median and interquartile range. When in doubt, the median should always be used over the mean."

B. Measures of Dispersion (Spread)

"Coefficient of variation (CV) is the standard deviation of a set of data points divided by the mean result expressed as a percentage or as a decimal fraction."

C. Graphical / Visual Descriptive Tools

• Bar chart - for categorical data (e.g., blood groups in a ward)
• Histogram - for continuous data (e.g., distribution of ages)
• Pie chart - proportions of a whole
• Box-and-whisker plot - shows median, IQR, and outliers
• Frequency polygon - shape of distribution
• Scatter plot - relationship between two continuous variables

3. Normal Distribution and the 68-95-99.7 Rule

• 68% of values fall within 1 SD of the mean
• 95% fall within 2 SD
• 99.7% fall within 3 SD

4. Detailed Worked Example - Descriptive Statistics

PART B: INFERENTIAL STATISTICS

1. Definition

"In comparative research designs, the primary question is typically 'which treatment is superior?' Answering this question in an objective and quantitative manner requires statistical inference. Much like a criminal trial, which commences with a fundamental presumption of innocence - a comparative study commences with a fundamental presumption of 'no difference,' known as the null hypothesis."

2. Core Concepts in Inferential Statistics

A. Hypothesis Testing - Step by Step

B. The p-value

• p < 0.05: Statistically significant - reject H₀
• p ≥ 0.05: Not statistically significant - fail to reject H₀
• p < 0.01: Highly significant
• p < 0.001: Very highly significant

"If the probability of the null hypothesis being true falls below a certain reasonable (albeit arbitrary) threshold, we can conclude that the two treatments likely differ. In the medical literature, this threshold is typically set at a value of less than 5% (i.e., p < .05)."

"A coin tossed 10 times, landing heads all 10 times has a probability of 0.5¹⁰ ≈ p < 0.001. Therefore the null hypothesis (fair coin) is rejected - the result is 'statistically significant.'"

C. Type I and Type II Errors

D. Confidence Interval (CI)

"Confidence interval (CI) is the interval that is computed to include a parameter such as the mean with a stated probability (e.g., commonly 90%, 95%, 99%) that the true value falls into that interval."

• A 95% CI means: if we repeated the study 100 times, 95 of those intervals would contain the true population mean.
• Narrow CI = more precise estimate (larger sample)
• Wide CI = less precise (smaller sample)

3. Choosing the Right Statistical Test

For Comparing Groups (Parametric - assumes normal distribution):

For Non-parametric Data (skewed, ordinal, or small samples):

For Categorical Data:

"Comparison of data typically asks the question whether one group is different from another group. These comparisons are usually done by t-test or by analysis of variance depending on whether two or more groups of continuous data are compared. If the data are discrete, comparison is done by chi-square analysis."

4. Detailed Worked Example - Inferential Statistics

• Group 1 (Drug A): 30 hypertensive patients → Mean SBP after treatment = 128 mmHg, SD = 10 mmHg
• Group 2 (Placebo): 30 hypertensive patients → Mean SBP after treatment = 140 mmHg, SD = 12 mmHg

• H₀: There is no difference in mean SBP between Drug A and placebo (μ₁ = μ₂)
• H₁: Drug A significantly lowers mean SBP compared to placebo (μ₁ ≠ μ₂)

• α = 0.05 (5%)

• Two independent groups, continuous data, approximately normal → Independent samples t-test

Difference in means = 140 - 128 = 12 mmHg

Standard Error (SE) = √[(SD₁²/n₁) + (SD₂²/n₂)]
                    = √[(100/30) + (144/30)]
                    = √[3.33 + 4.80]
                    = √8.13 ≈ 2.85

t = Difference / SE = 12 / 2.85 ≈ 4.21

95% CI = Difference ± (1.96 × SE)
       = 12 ± (1.96 × 2.85)
       = 12 ± 5.59
       = (6.41 to 17.59 mmHg)

"The mean SBP was significantly lower in the Drug A group (128 ± 10 mmHg) compared to the placebo group (140 ± 12 mmHg). The mean difference was 12 mmHg (95% CI: 6.4 to 17.6 mmHg; p < 0.001). The null hypothesis is rejected. Drug A produces a statistically significant reduction in systolic blood pressure."

"Two competing treatments may produce statistically different outcomes, but the calculated difference may still fail to reach the threshold for clinical importance (i.e., the MCID)... Despite the statistically significant difference, the conclusion must be that there is no clinical advantage."

PART C: COMPARISON - Descriptive vs. Inferential Statistics

PART D: How They Work Together in Practice

1. Descriptive statistics first - characterize the study population (Table 1: age, gender, baseline BP, comorbidities). This helps assess whether the groups are comparable before treatment.
2. Inferential statistics second - test the primary and secondary hypotheses and quantify uncertainty (Tables 2-3: treatment outcomes, p-values, CIs).

"While descriptive studies may report descriptive statistics as an end per se, analytic studies generally use descriptive statistics to outline the baseline characteristics of participants. This summary of baseline characteristics is critical to readers' assessment of prognostic balance between groups."

Summary

• Descriptive statistics = a photograph of your data (what is)
• Inferential statistics = a telescope aimed at the population (what likely is, with measured uncertainty)
• Both are essential: you cannot make valid inferences without first accurately describing your data
• In medicine, the goal is not just statistical significance (p-value) but clinical significance (does the difference matter to the patient?)

References:

• Rockwood and Green's Fractures in Adults, 10th ed., 2025 - Statistical Inference chapter
• Henry's Clinical Diagnosis and Management by Laboratory Methods - Statistics in Laboratory Medicine
• Cummings Otolaryngology Head and Neck Surgery - Habit 2: Describe Before You Analyze

Descriptive Statistics

"The average weight of these 5 patients is 70 kg with a standard deviation of 15.8 kg."

Inferential Statistics

• Sample mean = 70 kg
• National average (H₀) = 65 kg
• Run a one-sample t-test
• Result: p = 0.03 (less than 0.05)
• 95% CI: (66 to 74 kg)

"The mean weight of patients in this hospital (70 kg) is significantly higher than the national average of 65 kg (p = 0.03). The 95% CI of 66-74 kg does not include 65 kg, confirming the finding."

Key Difference in One Line

• Descriptive = Describe what's in front of you (like describing a photo)
• Inferential = Infer what's true for everyone (like predicting the weather from a sample reading)

Descriptive Statistics — Medical Example

"The 8 diabetic patients had a mean fasting blood sugar of 125 ± 18.6 mg/dL, with values ranging from 98 to 160 mg/dL."

Inferential Statistics — Medical Example

• Group 1 (Drug A) — 30 patients → Mean SBP = 128 mmHg
• Group 2 (Drug B) — 30 patients → Mean SBP = 140 mmHg

• H₀: No difference between Drug A and Drug B
• H₁: Drug A lowers BP more than Drug B

• Difference = 12 mmHg
• p = 0.001 (less than 0.05 → statistically significant)
• 95% CI: 6 to 18 mmHg (does not cross zero → confirms significance)

"Drug A significantly reduced systolic blood pressure compared to Drug B by 12 mmHg (p = 0.001, 95% CI: 6–18 mmHg). H₀ is rejected. This result applies to the broader hypertensive population, not just these 60 patients."

Another Quick Medical Example — Chi-square (Inferential)

• Test used: Chi-square test (categorical data)
• Result: p < 0.001

"There is a statistically significant association between smoking and lung cancer (p < 0.001). Smokers are significantly more likely to develop lung cancer."

Side-by-Side Comparison

• Descriptive → "Here is what I found in MY patients."
• Inferential → "Here is what this means for ALL patients like them."

Measures of Central Tendency

1. Introduction

1. Mean (Arithmetic Average)
2. Median (Middle Value)
3. Mode (Most Frequent Value)

"Central tendency in a normal (Gaussian) distribution is characterized by: (1) Mean - the sum of values divided by the number of observations; (2) Median - the value point where the number of observations above equals those below; (3) Mode - the most frequently occurring value."

2. The Arithmetic Mean (x̄)

Definition

Formula

• Σx = sum of all values
• n = total number of observations

Medical Example

Properties of the Mean

Merits

• Simple to calculate and easy to understand
• Based on all observations
• Suitable for further statistical analysis (SD, t-test, ANOVA)
• Stable - does not fluctuate much from sample to sample

Demerits

• Distorted by outliers (extreme values)
• Not suitable for skewed data
• Cannot be calculated for open-ended frequency distributions
• Cannot be used for qualitative (categorical) data

Medical Application

• Mean blood pressure in a hypertension study
• Mean birth weight of neonates
• Mean fasting blood sugar in a diabetic clinic

3. The Median

Definition

"An alternative measure of central tendency is the median, which divides all data points exactly in half, with one half being higher and one half lower. The median is also called the 50th percentile. It is not calculated from a formula because it is taken from a straight count of the data points; thus, it is termed a nonparametric method."

How to Calculate

• If n is odd: Median = the [(n+1)/2]th value
• If n is even: Median = average of (n/2)th and (n/2 + 1)th values

Medical Example (Odd n)

Medical Example (Even n)

Properties of the Median

Merits

• Not distorted by outliers or extreme values
• Can be used for ordinal data (e.g., pain scores, Likert scales)
• Easy to locate graphically
• Best representative for skewed distributions

Demerits

• Does not use all data values
• Cannot be used for further algebraic calculations
• Less stable than mean in repeated sampling

Medical Application

• Median income in health economics (income data is usually skewed)
• Median survival time in cancer studies
• Median pain scores in post-operative research

4. The Mode

Definition

"The mode is the most common value (i.e., the value of the variable that has the greatest number of data points). It does have a role in understanding when a data set consists of two or more different populations that result in more than one mode. If two separate subpopulations are present, it is called a bimodal population."

Medical Example

Another Example (Bimodal)

Properties of the Mode

Merits

• Easy to identify
• Only average applicable to nominal/categorical data (blood group, gender, religion)
• Not affected by extreme values
• Useful for bimodal distributions to identify two subgroups

Demerits

• May not be unique (can be bimodal/multimodal)
• May not exist in some datasets
• Not suitable for further calculations
• Ignores most of the data

Medical Application

• Most common blood group in a population
• Most frequently prescribed drug in a hospital
• Most common diagnosis in an outpatient department

5. Relationship Between Mean, Median, and Mode

In a Normal (Gaussian) Distribution

"In a perfect Gaussian distribution, mean, median, and mode are identical."

In a Positively Skewed Distribution (Skewed Right)

In a Negatively Skewed Distribution (Skewed Left)

Summary Table

"Some datasets are non-Gaussian - skewed positively or negatively. Skews alter the mean and median but do not affect the mode. In a positively skewed set of data, mean > median > mode."

6. The Geometric Mean

Definition

"The geometric mean is calculated as the nth root of the product of a distribution of n numbers; its use for estimating central tendency minimizes the effects from extreme values such as are found in a log-normal distribution."

Formula

Medical Application

• Antibody titres (e.g., HBsAb levels after vaccination)
• Bacterial colony counts
• Drug concentration data (pharmacokinetics)

• Arithmetic mean = 7.2
• Geometric mean = 6.09 (better reflects the preponderance of lower values)

7. Which Measure to Use? (Decision Guide)

"When SD is very large (larger than the mean value), the data often have an asymmetric distribution and should be described by the median and interquartile range. When in doubt, the median should always be used over the mean."

8. Worked Comprehensive Medical Example

• Mean (138) < Median (140) < Mode (145)
• This suggests a slightly negatively skewed distribution
• The median (140 mmHg) is the best representative value for this skewed data
• The mode (145 mmHg) is the most common blood pressure recorded

9. Clinical Significance of Choosing the Right Measure

10. Summary Table

Conclusion

References:

• Quick Compendium of Clinical Pathology, 5th ed. - Section 8.3.1.1
• Henry's Clinical Diagnosis and Management by Laboratory Methods - Central Tendency & Statistics
• Swanson's Family Medicine Review - Biostatistics chapter
• Rockwood and Green's Fractures in Adults, 10th ed. - Descriptive Statistics