2.4 Introduction to biostatistics
6 min read•august 14, 2024
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.
and distributions form the foundation of biostatistical analysis. Understanding concepts like , parametric vs , and 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 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 , also known as the Gaussian distribution, is a continuous probability distribution that is symmetric and bell-shaped, characterized by its and (heights, weights, IQ scores)
- The 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 for modeling rare events (disease incidence), the for modeling waiting times (survival analysis), and the 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
- , such as and , 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
- 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 and , 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)
- 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)
- 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 , 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 ), 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
Key Terms to Review (32)
Alternative hypothesis: An alternative hypothesis is a statement that proposes a potential outcome or effect that contrasts with the null hypothesis, suggesting that there is a significant relationship or difference between variables in a study. This concept is central to testing theories and making conclusions based on statistical evidence, as it represents the researcher’s prediction of what they expect to find in their research. Understanding the alternative hypothesis is essential for distinguishing between different statistical outcomes and determining the implications of research findings.
ANOVA: ANOVA, which stands for Analysis of Variance, is a statistical method used to determine if there are significant differences between the means of three or more independent groups. This technique helps in assessing whether the variations among group means are greater than the variations within the groups, thus allowing researchers to understand if any treatment or condition has an effect.
Binomial Distribution: Binomial distribution is a probability distribution that summarizes the likelihood of a given number of successes out of a fixed number of independent trials, where each trial has two possible outcomes: success or failure. It is a crucial concept in statistics and biostatistics, allowing researchers to model and analyze scenarios where the outcomes can be simplified into binary choices, such as infected vs. not infected or successful vs. unsuccessful treatments.
Biostatistics: Biostatistics is a branch of statistics that applies statistical methods to analyze data related to living organisms, particularly in the fields of public health, medicine, and biology. It plays a crucial role in interpreting data from health studies and clinical trials, helping to establish links between health outcomes and various factors. The insights gained through biostatistics support evidence-based decision-making in public health initiatives and health informatics.
Case-control study: A case-control study is an observational research design used in epidemiology to identify and compare individuals with a specific condition (cases) to those without the condition (controls). This method helps determine potential risk factors or associations by analyzing past exposure to certain variables between the two groups. It is particularly useful for studying rare diseases and understanding how specific factors might influence health outcomes.
Chi-square distribution: The chi-square distribution is a statistical distribution that is commonly used in hypothesis testing, particularly for categorical data. It helps in determining how the observed frequencies in a dataset compare to the expected frequencies, providing insight into whether any discrepancies are due to chance or indicate a significant difference. The distribution is characterized by its degrees of freedom, which depend on the number of categories involved.
Cohort Study: A cohort study is an observational study design that follows a group of individuals over time to assess the development of specific health outcomes related to exposures or risk factors. This design allows researchers to observe the incidence of disease in a population that is defined by shared characteristics, enabling the evaluation of associations between exposures and outcomes while accounting for temporal relationships.
Confidence Interval: A confidence interval is a range of values that is used to estimate the true value of a population parameter with a specified level of confidence, typically expressed as a percentage such as 95% or 99%. It provides an interval within which we expect the true value lies, reflecting both the variability in the data and the size of the sample. Understanding confidence intervals is essential for interpreting study results, assessing measures of disease frequency and association, and making informed decisions based on statistical data.
Exponential Distribution: Exponential distribution is a probability distribution that describes the time between events in a Poisson process, where events occur continuously and independently at a constant average rate. This distribution is often used in various fields, including public health, to model the time until an event occurs, like the time until failure of medical devices or the time between arrivals of patients at a clinic. Understanding exponential distribution helps in analyzing survival data and waiting times in different scenarios.
John Snow: John Snow was a pioneering English physician and a key figure in the history of public health, best known for his work in epidemiology and for being one of the first to use statistical analysis to investigate disease outbreaks. His groundbreaking investigation of the 1854 cholera outbreak in London not only showcased the importance of mapping disease distribution but also laid the foundation for modern epidemiological methods and public health practices.
Kruskal-Wallis Test: The Kruskal-Wallis test is a non-parametric statistical method used to determine if there are significant differences between three or more independent groups based on ranked data. This test is particularly useful when the assumptions of ANOVA, such as normality and homogeneity of variances, cannot be met. By analyzing the ranks rather than the raw data, it provides a way to assess differences without requiring the data to follow a normal distribution.
Mann-Whitney U Test: The Mann-Whitney U Test is a non-parametric statistical test used to determine whether there is a significant difference between the distributions of two independent groups. It is particularly useful when the assumptions of normality for parametric tests are not met, making it a valuable tool in biostatistics for analyzing ordinal data or continuous data that do not adhere to normal distribution.
Mean: The mean is a statistical measure that represents the average value of a set of numbers, calculated by summing all the values and dividing by the count of those values. It is a fundamental concept in statistics, often used to summarize data and provide insights into its central tendency. Understanding the mean is essential for analyzing data distributions and making comparisons across different datasets.
Non-parametric methods: Non-parametric methods are statistical techniques that do not assume a specific distribution for the data, allowing for analysis without the constraints of normality. These methods are particularly useful when dealing with ordinal data, small sample sizes, or when the data violates assumptions required for parametric tests, making them a versatile choice in various biostatistical applications.
Normal distribution: Normal distribution is a statistical concept that describes how values of a variable are distributed, characterized by a symmetric, bell-shaped curve where most observations cluster around the mean. This concept is fundamental in statistics because it applies to many natural phenomena and allows for the use of various statistical techniques that assume a normal distribution of data.
Null Hypothesis: The null hypothesis is a statement in statistics that assumes there is no effect or no difference between groups or conditions. It serves as a starting point for statistical testing, where researchers aim to gather evidence to either reject or fail to reject this hypothesis. The null hypothesis is crucial in both biostatistics and statistical analysis, as it helps to frame research questions and guide the interpretation of data.
P-value: A p-value is a statistical measure that helps determine the significance of results from a hypothesis test. It indicates the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true. A smaller p-value suggests stronger evidence against the null hypothesis, while a larger p-value suggests weaker evidence. Understanding p-values is essential for interpreting data analysis, applying biostatistics principles, and differentiating between descriptive and inferential statistics.
Parametric methods: Parametric methods are statistical techniques that make assumptions about the parameters of the population distribution from which samples are drawn. These methods rely on specific distributions, such as the normal distribution, to perform statistical analyses and infer population characteristics based on sample data. They are powerful tools in biostatistics because they can provide precise estimates and confidence intervals, assuming the underlying distribution assumptions are met.
Pearson correlation coefficient: The Pearson correlation coefficient is a statistical measure that quantifies the strength and direction of a linear relationship between two continuous variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 signifies no correlation, and 1 denotes a perfect positive correlation. This measure is essential in biostatistics for understanding how variables are related, helping researchers determine associations in data analysis.
Poisson Distribution: The Poisson distribution is a statistical probability distribution that expresses the likelihood of a given number of events occurring in a fixed interval of time or space, given that these events happen with a known constant mean rate and independently of the time since the last event. This distribution is particularly useful in fields such as public health and biostatistics for modeling rare events, like disease occurrences or the number of patient arrivals at a hospital.
Probability: Probability is a branch of mathematics that deals with the likelihood of different outcomes occurring within a certain context. It provides a framework for quantifying uncertainty and is foundational for statistical analysis, enabling researchers to make informed predictions and decisions based on data. Understanding probability is essential for interpreting results in biostatistics, as it helps assess risks and make sense of variability in health-related data.
Probability Distributions: A probability distribution is a mathematical function that describes the likelihood of different outcomes in a random experiment. It provides a comprehensive overview of the probabilities associated with all possible values of a random variable, making it essential for analyzing data and understanding variability in public health contexts. By categorizing the probability of various outcomes, probability distributions help researchers make predictions and draw conclusions based on statistical data.
Random sampling: Random sampling is a method used to select a subset of individuals from a larger population, ensuring that each individual has an equal chance of being chosen. This technique helps eliminate bias in the selection process, which is crucial for obtaining reliable and valid results in research. By using random sampling, researchers can make inferences about the entire population based on the characteristics of the sample, which ties into statistical analysis and interpretation.
Sample size: Sample size refers to the number of individual observations or data points collected in a study, which is crucial for obtaining valid and reliable results. A well-chosen sample size can enhance the accuracy of the findings, allowing researchers to make generalizations about a larger population. Determining the appropriate sample size is essential to balancing statistical power and practical constraints, ensuring that the study can detect meaningful differences or associations without being unnecessarily large or costly.
Spearman Rank Correlation Coefficient: The Spearman Rank Correlation Coefficient is a non-parametric measure that assesses the strength and direction of the association between two ranked variables. It evaluates how well the relationship between the two variables can be described using a monotonic function, which means it looks at whether increases in one variable tend to be associated with increases (or decreases) in another variable, regardless of the actual values or distributions of the data.
Standard Deviation: Standard deviation is a statistical measure that quantifies the amount of variation or dispersion of a set of values. It tells us how much individual data points differ from the mean of the dataset. In public health and biostatistics, understanding standard deviation helps in interpreting the reliability of disease frequency measures and associations, providing insights into variability within populations.
Standard Normal Distribution: The standard normal distribution is a special type of normal distribution with a mean of 0 and a standard deviation of 1. This distribution is fundamental in statistics, as it allows for the comparison of different data sets by converting them into a common scale through the process of standardization, also known as z-scores. It serves as a reference point for understanding probabilities and percentiles in various statistical applications.
Statistical Power: Statistical power is the probability that a statistical test will correctly reject a false null hypothesis. It reflects the test's ability to detect an effect or difference when one truly exists, which is essential in research and data analysis. High statistical power reduces the risk of Type II errors, which occur when a test fails to detect an effect that is present.
Stratified Sampling: Stratified sampling is a method of sampling that involves dividing a population into distinct subgroups, known as strata, which share similar characteristics. This technique ensures that each subgroup is adequately represented in the sample, leading to more accurate and reliable results. By reflecting the diversity of the population, stratified sampling enhances data analysis, improves inferential statistics, and aids in effective interpretation of findings.
T-tests: A t-test is a statistical method used to determine if there is a significant difference between the means of two groups. It helps researchers understand whether any observed differences in data are likely due to chance or reflect a true effect, making it essential for hypothesis testing in various fields, including public health. By comparing sample data to population parameters, t-tests play a crucial role in making data-driven decisions based on evidence.
Wilcoxon Signed-Rank Test: The Wilcoxon signed-rank test is a non-parametric statistical method used to compare two related samples or matched observations to assess whether their population mean ranks differ. This test is particularly useful when the data does not meet the assumptions of normality required for parametric tests like the paired t-test, making it ideal for analyzing ordinal data or continuous data that may not follow a normal distribution.
William Farr: William Farr was a pioneering British epidemiologist and statistician, known for his work in developing vital statistics and public health measures in the 19th century. His innovative methods of data collection and analysis laid the groundwork for modern biostatistics and played a critical role in outbreak investigations, enabling better understanding of disease patterns and health trends.