🐛Biostatistics Unit 13 – Biostatistics: Software for Data Analysis

Key Concepts and Terminology

• Biostatistics combines statistical methods with biological and medical sciences to analyze and interpret data
• Variables can be categorical (qualitative) or numerical (quantitative) depending on the type of data they represent
• Descriptive statistics summarize and describe key features of a dataset such as measures of central tendency (mean, median, mode) and dispersion (range, variance, standard deviation)
• Inferential statistics draw conclusions about a population based on a sample using hypothesis testing and confidence intervals
• Probability distributions (normal, binomial, Poisson) model the likelihood of different outcomes in a given scenario
• Hypothesis testing assesses the strength of evidence against a null hypothesis using p-values and significance levels
  • Type I error (false positive) rejects a true null hypothesis
  • Type II error (false negative) fails to reject a false null hypothesis
• Correlation measures the strength and direction of the linear relationship between two variables
• Regression analysis models the relationship between a dependent variable and one or more independent variables

Statistical Software Overview

• Statistical software packages facilitate data analysis, visualization, and modeling in biostatistics
• R is a popular open-source programming language and environment for statistical computing and graphics
  • Provides a wide range of statistical and graphical techniques
  • Extensible through user-created packages for specialized analyses
• Python is a general-purpose programming language with powerful libraries for data analysis and scientific computing (NumPy, SciPy, Pandas)
• SAS (Statistical Analysis System) is a proprietary software suite for advanced analytics, multivariate analyses, and predictive modeling
• SPSS (Statistical Package for the Social Sciences) offers a user-friendly interface for statistical analysis and data visualization
• Stata is a general-purpose statistical software package with a command-line interface and a wide range of built-in methods
• JMP (pronounced "jump") is a data visualization and analysis tool emphasizing exploratory data analysis and interactive graphics

Data Import and Preprocessing

• Data import involves reading data from various file formats (CSV, Excel, SQL databases) into the statistical software environment
• Data preprocessing prepares raw data for analysis by cleaning, transforming, and formatting the dataset
• Data cleaning identifies and handles missing values, outliers, and inconsistencies in the data
  • Missing data can be removed (listwise deletion) or imputed using methods like mean imputation or multiple imputation
  • Outliers can be identified using visual inspection (box plots) or statistical methods (Z-scores) and handled by removal or transformation
• Data transformation modifies variables to meet assumptions of statistical tests or improve interpretability
  • Log transformation reduces skewness and compresses large values in a variable
  • Standardization (Z-scores) centers and scales variables to have a mean of 0 and a standard deviation of 1
• Data integration combines data from multiple sources or tables based on common variables or keys
• Data reshaping converts between wide (each subject on one row) and long (each observation on one row) formats depending on the analysis requirements

Descriptive Statistics and Visualization

• Descriptive statistics provide a summary of the main features of a dataset
• Measures of central tendency describe the typical or central value in a distribution
  • Mean is the arithmetic average of all values
  • Median is the middle value when the data is ordered
  • Mode is the most frequently occurring value
• Measures of dispersion quantify the spread or variability of a distribution
  • Range is the difference between the maximum and minimum values
  • Variance is the average squared deviation from the mean
  • Standard deviation is the square root of the variance
• Frequency tables and bar charts summarize the distribution of categorical variables
• Histograms and density plots visualize the distribution of continuous variables
  • Skewness indicates asymmetry in the distribution (positive skew: right tail, negative skew: left tail)
  • Kurtosis measures the heaviness of the tails relative to a normal distribution (leptokurtic: heavy tails, platykurtic: light tails)
• Box plots display the median, quartiles, and potential outliers of a continuous variable
• Scatter plots explore the relationship between two continuous variables

Hypothesis Testing and Inference

• Hypothesis testing is a statistical method to determine whether sample data support a particular hypothesis about the population
• Null hypothesis (H0) represents no effect or no difference between groups
• Alternative hypothesis (Ha) represents the presence of an effect or difference
• Test statistic quantifies the difference between the observed data and what is expected under the null hypothesis
  • Examples: t-statistic, z-statistic, chi-square statistic, F-statistic
• P-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true
  • Small p-values (typically < 0.05) suggest strong evidence against the null hypothesis
• Significance level (α) is the threshold for rejecting the null hypothesis, usually set at 0.05
• Confidence intervals provide a range of plausible values for a population parameter based on the sample data
  • 95% confidence interval means that if the sampling process were repeated many times, 95% of the intervals would contain the true population parameter
• One-sample tests compare a sample statistic to a known population value (one-sample t-test)
• Two-sample tests compare a statistic between two independent groups (independent t-test, Mann-Whitney U test)
• Paired tests compare a statistic between two related groups or repeated measures (paired t-test, Wilcoxon signed-rank test)

Regression Analysis Techniques

• Regression analysis models the relationship between a dependent variable and one or more independent variables
• Simple linear regression models the linear relationship between one independent variable (X) and one dependent variable (Y)
  • Equation: $Y = \beta_0 + \beta_1X + \epsilon$, where $\beta_0$ is the intercept, $\beta_1$ is the slope, and $\epsilon$ is the error term
  • Least squares method estimates the regression coefficients by minimizing the sum of squared residuals
• Multiple linear regression extends simple linear regression to include multiple independent variables
  • Equation: $Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + ... + \beta_pX_p + \epsilon$, where $p$ is the number of independent variables
• Assumptions of linear regression include linearity, independence, normality, and homoscedasticity of residuals
  • Residual plots can assess these assumptions graphically
• Coefficient of determination (R-squared) measures the proportion of variance in the dependent variable explained by the independent variable(s)
• Logistic regression models the relationship between independent variables and a binary dependent variable
  • Logit transformation: $\ln(\frac{p}{1-p}) = \beta_0 + \beta_1X_1 + \beta_2X_2 + ... + \beta_pX_p$, where $p$ is the probability of the event
• Odds ratios represent the change in odds of the event for a one-unit increase in the independent variable
• Receiver Operating Characteristic (ROC) curve evaluates the performance of a logistic regression model by plotting true positive rate against false positive rate

Advanced Statistical Methods

• Analysis of Variance (ANOVA) tests for differences in means between three or more groups
  • One-way ANOVA compares means across one categorical variable
  • Two-way ANOVA examines the effects of two categorical variables and their interaction on the dependent variable
• Post-hoc tests (Tukey's HSD, Bonferroni correction) conduct pairwise comparisons between groups while controlling for multiple testing
• Repeated measures ANOVA accounts for the correlation between repeated measurements on the same subjects over time or under different conditions
• Mixed-effects models include both fixed effects (independent variables) and random effects (subject-specific variability) to analyze clustered or longitudinal data
• Survival analysis examines the time until an event occurs and handles censored observations
  • Kaplan-Meier estimator calculates the survival function and median survival time
  • Cox proportional hazards model assesses the effect of covariates on the hazard rate
• Principal Component Analysis (PCA) reduces the dimensionality of a dataset by creating new uncorrelated variables (principal components) that capture the maximum variance
• Cluster analysis groups similar observations based on their characteristics using methods like hierarchical clustering or k-means clustering

Practical Applications and Case Studies

• Clinical trials use biostatistical methods to assess the safety and efficacy of new treatments or interventions
  • Randomized controlled trials randomly assign participants to treatment and control groups to minimize bias
  • Intention-to-treat analysis includes all randomized participants in the analysis, regardless of adherence to the assigned treatment
• Epidemiological studies investigate the distribution and determinants of health-related states or events in populations
  • Cohort studies follow a group of individuals over time to assess the incidence of an outcome and identify risk factors
  • Case-control studies compare the exposure history of cases (with the outcome) to controls (without the outcome) to identify potential risk factors
• Diagnostic test evaluation assesses the performance of a test in correctly identifying the presence or absence of a condition
  • Sensitivity is the proportion of true positives correctly identified by the test
  • Specificity is the proportion of true negatives correctly identified by the test
• Meta-analysis combines the results of multiple studies to provide a more precise estimate of the effect size and assess heterogeneity between studies
  • Forest plots display the effect sizes and confidence intervals of individual studies and the overall pooled estimate
• Biomarker discovery uses statistical methods to identify and validate biological markers associated with disease or treatment response
  • Receiver Operating Characteristic (ROC) curve evaluates the diagnostic accuracy of a biomarker by plotting sensitivity against 1-specificity
  • Logistic regression can assess the predictive value of multiple biomarkers while controlling for confounding factors