2.4 Introduction to biostatistics

Biostatistics is crucial in public health, using statistical methods to analyze biological and medical data. It helps design studies, interpret results, and make evidence-based decisions about population health. From epidemiology to clinical trials, biostatistics guides research and policy.

Probability and distributions form the foundation of biostatistical analysis. Understanding concepts like probability distributions, parametric vs non-parametric methods, and sample size calculations is key. These tools help researchers draw meaningful conclusions from data and inform public health strategies.

Biostatistics in Public Health

Definition and Role

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• Biostatistics is the application of statistical methods to biological and medical data, particularly in the context of public health research and practice
• Biostatistics plays a crucial role in designing and analyzing studies to investigate the distribution and determinants of health and disease in populations
• Biostatistical methods are used to summarize and interpret data, test hypotheses, and make inferences about populations based on sample data
• Biostatisticians collaborate with public health researchers to develop study designs, determine appropriate sample sizes, and select suitable statistical methods for data analysis
• Biostatistics contributes to evidence-based decision-making in public health by providing quantitative tools to assess the effectiveness of interventions, identify risk factors, and evaluate health outcomes

Applications and Contributions

• Biostatistics is essential for conducting epidemiological studies, such as cohort studies and case-control studies, to investigate the causes and risk factors of diseases
• Biostatistical methods are used in clinical trials to evaluate the safety and efficacy of new treatments, vaccines, and preventive measures
• Biostatistics plays a key role in disease surveillance and monitoring, helping to detect outbreaks, track disease trends, and assess the impact of public health interventions
• Biostatistical analysis is crucial for health policy and resource allocation decisions, as it provides evidence on the burden of disease, health disparities, and the cost-effectiveness of interventions
• Biostatistics contributes to the development and validation of diagnostic tests, risk prediction models, and screening programs in public health

Probability and Distributions

Basic Concepts of Probability

• Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty
• The probability of an event A is denoted as P(A) and is calculated as the number of favorable outcomes divided by the total number of possible outcomes, assuming all outcomes are equally likely
• The complement of an event A, denoted as P(A'), is the probability that event A will not occur, calculated as 1 - P(A)
• Conditional probability is the probability of an event A occurring given that another event B has occurred, denoted as P(A|B) and calculated as the probability of the intersection of A and B divided by the probability of B

Probability Distributions

• Probability distributions describe the likelihood of different outcomes for a random variable, which can be discrete (taking on specific values) or continuous (taking on any value within a range)
• The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent trials, each with the same probability of success (coin flips)
• The normal distribution, also known as the Gaussian distribution, is a continuous probability distribution that is symmetric and bell-shaped, characterized by its mean and standard deviation (heights, weights, IQ scores)
• The standard normal distribution is a special case of the normal distribution with a mean of 0 and a standard deviation of 1, often used for standardizing variables and calculating probabilities
• Other important distributions in biostatistics include the Poisson distribution for modeling rare events (disease incidence), the exponential distribution for modeling waiting times (survival analysis), and the chi-square distribution for assessing goodness-of-fit and independence

Parametric vs Non-parametric Methods

Parametric Methods

• Parametric statistical methods assume that the data follow a specific probability distribution (usually normal) and that the parameters of the distribution (such as mean and variance) are known or can be estimated from the sample data
• Parametric methods, such as t-tests and ANOVA, are generally more powerful than non-parametric methods when the assumptions are met, meaning they are more likely to detect significant differences or associations when they exist
• Examples of parametric methods include:
  • Independent samples t-test for comparing means between two groups
  • Paired samples t-test for comparing means within the same group at different time points
  • One-way ANOVA for comparing means among three or more groups
  • Pearson correlation coefficient for assessing the linear relationship between two continuous variables

Non-parametric Methods

• Non-parametric statistical methods do not rely on assumptions about the underlying probability distribution of the data and are useful when the data do not meet the assumptions required for parametric methods
• Non-parametric methods, such as the Mann-Whitney U test and Kruskal-Wallis test, are more robust to outliers and can be used with ordinal or ranked data, as well as data that do not follow a normal distribution
• Examples of non-parametric methods include:
  • Mann-Whitney U test for comparing medians between two independent groups (blood pressure levels)
  • Wilcoxon signed-rank test for comparing medians within the same group at different time points (pain scores before and after treatment)
  • Kruskal-Wallis test for comparing medians among three or more independent groups (disease severity across different age groups)
  • Spearman rank correlation coefficient for assessing the monotonic relationship between two continuous or ordinal variables (education level and income)
• The choice between parametric and non-parametric methods depends on the nature of the data, the sample size, and the research question being addressed

Sample Size and Power in Analysis

Importance of Sample Size

• Sample size refers to the number of participants or observations included in a study, and it plays a critical role in determining the precision and reliability of the results
• Larger sample sizes generally increase statistical power, as they provide more precise estimates of population parameters and are more likely to detect significant differences or associations
• Insufficient sample size can lead to type II errors (failing to reject a false null hypothesis), while excessively large sample sizes can be inefficient and wasteful of resources
• Factors influencing the required sample size include the expected effect size, the desired level of statistical power, the chosen significance level (alpha), and the variability of the outcome measure

Statistical Power

• Statistical power is the probability of correctly rejecting a null hypothesis when it is false (i.e., detecting a significant effect when one exists) and is influenced by sample size, effect size, and the chosen significance level (alpha)
• A priori power analysis is used to determine the minimum sample size required to achieve a desired level of statistical power, given an expected effect size and significance level
  • For example, a researcher planning a study to compare the effectiveness of two treatments may conduct a power analysis to determine the number of participants needed to detect a clinically meaningful difference with 80% power at a 5% significance level
• Post hoc power analysis can be used to assess the achieved power of a completed study, based on the observed effect size and sample size
  • This can help interpret non-significant results and determine whether the study was underpowered to detect a meaningful effect
• Researchers should strive to balance the need for adequate statistical power with practical considerations such as time, cost, and participant burden when determining sample size
• Collaborative efforts between biostatisticians and subject matter experts are essential for ensuring that studies are designed with sufficient power to address the research question while minimizing resource waste and participant burden