Class Notes: Principles of Biostatistics
Subject: Public Health / Medicine / Life Sciences
Topic: Foundations of Biostatistics
I. What is Biostatistics?
Definition: Biostatistics is the application of statistical principles to questions
and problems in medicine, public health, and biology. It is the science of
collecting, summarizing, analyzing, and interpreting data to make decisions and
draw conclusions about biological phenomena.
Bio: Pertains to life, health, and biological processes.
Statistics: The science of learning from data.
Core Idea: Variability is inherent in all biological data (e.g., not all patients
respond the same way to a drug). Biostatistics provides the tools to understand,
measure, and account for this variability to find meaningful patterns and signals
amidst the "noise."
II. Why is it Important? (Key Roles)
Evidence-Based Medicine: Forms the backbone of clinical research. Determines if a
new treatment is truly effective.
Public Health Policy: Identifies risk factors for diseases (e.g., smoking and lung
cancer), tracks epidemics, and evaluates health programs.
Design and Analysis of Studies: Provides the framework for designing robust
clinical trials, cohort studies, and case-control studies.
Diagnosis and Prognosis: Develops and validates diagnostic tests and models to
predict patient outcomes.
Informing Decision-Making: Helps clinicians, researchers, and policymakers make
decisions under uncertainty.
III. Core Principles of Biostatistics
Biostatistics can be broadly divided into two main branches:
A. Descriptive Statistics
Purpose: To summarize and describe the main features of a collected dataset.
Tools:
Measures of Central Tendency: Mean (average), Median (middle value), Mode (most
frequent value).
Measures of Spread (Dispersion): Range, Variance, Standard Deviation (SD),
Interquartile Range (IQR).
Example: "The average (mean) age of participants in the study was 45 years, with a
standard deviation of 5 years."
B. Inferential Statistics
Purpose: To make predictions or inferences about a larger population based on data
from a sample.
This is where the core scientific reasoning happens.
Key Concepts:
Population vs. Sample:
Population: The entire group you are interested in (e.g., all diabetic patients in
the country).
Sample: A manageable subset selected from the population. It must be representative
to allow generalization (often achieved through random sampling).
Probability: The foundation of inference. It quantifies uncertainty and the
likelihood of an event occurring.
Hypothesis Testing:
A formal procedure to test an idea or claim about a population.
Null Hypothesis (H₀): The default assumption of "no effect" or "no difference"
(e.g., "The new drug has the same effect as the placebo").
Alternative Hypothesis (H₁ or Ha): The research hypothesis (e.g., "The new drug has
a different effect than the placebo").
p-value: The probability of observing the collected data (or something more
extreme) if the null hypothesis is true. A small p-value (conventionally < 0.05)
provides evidence against the null hypothesis.
Type I Error (α): False Positive. Rejecting the null hypothesis when it is actually
true.
Type II Error (β): False Negative. Failing to reject the null hypothesis when it is
actually false.
Confidence Intervals (CI):
A range of values that is likely to contain the true population parameter (e.g.,
the true mean difference).
A 95% CI means we are 95% confident the interval contains the true value. It
provides more information than a simple p-value.
IV. Common Applications in Health Sciences
Clinical Trials: Phase I-IV trials to test safety and efficacy of interventions.
(Uses Randomized Controlled Trial (RCT) design, the gold standard).
Epidemiology: Studying the distribution and determinants of diseases in populations
(e.g., cohort studies, case-control studies).
Epidemic Investigation: Modeling the spread of infectious diseases (e.g., R0 value
for COVID-19).
Health Services Research: Analyzing the efficiency and quality of healthcare
delivery.
Genetics and Genomics: Identifying genes associated with diseases (e.g., genome-
wide association studies - GWAS).
V. Steps in a Biostatistical Investigation
Design the Study: The most critical step. Define the research question, choose the
right study design, determine sample size, and plan how to collect data. A poorly
designed study cannot be saved by advanced statistics.
Collect the Data: Accurately and ethically gather data according to the study
protocol.
Describe the Data: Use descriptive statistics and graphs (e.g., histograms, box
plots) to explore and summarize the data.
Analyze the Data: Apply appropriate inferential statistical methods (e.g., t-tests,
chi-square tests, regression analysis) to answer the research question.
Interpret the Results: Translate the statistical findings (p-values, confidence
intervals) into a biological or clinical conclusion. Association does not imply
causation.
Communicate the Findings: Present the results clearly in reports, publications, or
presentations, stating both the strengths and limitations of the study.
VI. Important Considerations & Pitfalls
Causality vs. Correlation: Just because two variables are associated does not mean
one causes the other (e.g., ice cream sales and drowning rates are correlated
because both are related to hot weather, not to each other).
Bias: Systematic errors in the design, conduct, or analysis of a study that lead to
incorrect results. (e.g., selection bias, measurement bias).
Confounding: When a third variable influences both the independent and dependent
variables, creating a spurious association. (e.g., a study might find that coffee
drinking is associated with lung cancer, but this is confounded by smoking—smokers
drink more coffee and get more lung cancer).
Statistical Significance vs. Clinical Significance: A result can be statistically
significant (very unlikely due to chance) but be so small that it is irrelevant in
a real-world clinical setting.
VII. Summary Table: Key Terms
Term Definition Example
Population The entire group of interest All men over 50 in the US
Sample A subset of the population 1,000 men randomly selected
Parameter A numerical characteristic of a population True average blood
pressure of all US men over 50
Statistic A numerical characteristic of a sample Average blood pressure of the
1,000 men in the sample
p-value Probability of the data if H₀ is true p = 0.03 means there's a 3%
chance of seeing this result if the drug had no effect
Confidence Interval A range of plausible values for a parameter We are 95%
confident the true reduction in BP is between 5 and 10 mmHg
Remember: Biostatistics is a tool for thinking clearly about uncertainty and
evidence in health and science. It helps us move from anecdote to evidence.
