Biostatistics Lectures 1-4 Summary

Biostatistics Lectures 1-4 Summary

• Biostatistics involves collecting, classifying, analyzing, and interpreting data from biomedical research to generate medical knowledge.
• Science is empirical, based on observations and experiences, using inductive reasoning to generalize from observations.
• Basic and clinical research are interconnected. Clinical research must be randomized to ensure unbiased results.
• In biostatistics, samples are subsets of a population, but the sample itself is not the primary focus.
• Samples are studied to draw inferences about a population of interest.
• Larger samples increase the likelihood of accurate results. Small or biased samples may lead to random errors. Random error is the difference between sample and population means due to sampling.
• Sample quantities are known and measured, while population quantities are unknown and estimated.
• Clinical research involves a study design, data collection, data analysis, and data processing. Software like R facilitates reproducible research.
• Reproducible research involves using code throughout the entire research process and presents a direct link between analysis and final results.
• Rectangular data, typically in tabular format, includes a patient ID, age, sex, vaccination status, and COVID-19 status, among other variables.
• Units of observation are patients or other similar entities described by the data.
• Observations (records) are rows in the table, and variables (or fields) are columns in the table, representing characteristics of the observation unit or entity.
• Variables are classified as categorical or numeric. Numeric variables include continuous and discrete types. Categorical variables include nominal, ordinal, and dichotomous.
• Frequency tables present the number and percentage of participants in each category, useful for categorical and grouped numeric variables.
• Frequency tables may also be cumulative.
• Contingency tables (cross-tabulations) examine the relationship between two categorical variables, examining marginal totals and category-specific proportions.
• Plotting categorical variables involves pie charts and bar plots, illustrating relative frequencies (up to 100%) with appropriate colors/ordering choices.
• Histograms and box-and-whisker plots illustrate numerical (continuous or discrete) variables; for histograms, bins have the same width with no space between; for box-and-whisker plots, features include median, hinges, whiskers, and outliers.
• Measures of location include mean (average), median, quantiles, and mode.
• Measures of spread include variance, standard deviation, range, and interquartile range (IQR).
• Distributions describe the pattern of values in sample or population data and can be generalized to probability distributions for an individual.
• A normal distribution (Ν(μ,σ)) is described by its mean (μ) and standard deviation (σ), is bell-shaped, and is symmetric with mean =median =mode = 0.
• The characteristics of this distribution for a given range of values, and from −∞ to ∞: P(x) = 1. (with specific ranges representing specific probabilities).
• Determining (testing) if data follows a normal distribution involves contextual knowledge and statistical tests (e.g., Shapiro-Wilk test) or Q-Q plots.
• The central limit theorem shows that the means of repeated random samples from any distribution follow a normal distribution, even when the underlying variables aren't normally distributed.
• There are three distributions to consider (population, sample, sample mean of the variable) and their associated statistics (mean, standard deviation, standard error).
• Confidence intervals and the difference between two proportions give a range of values within which the mean and proportion are likely to lie.
• Confidence intervals are estimated and calculated using critical values.
• Statistical tests like the t-tests and non-parametric tests (Mann-Whitney) are useful for comparing sub-sample means, using probability values (p-values) for decision-making; the null hypothesis is that the means are the same, and the alternative hypothesis proposes otherwise. p-values represent probabilities of observing particular results (or more extreme values), thereby affecting decision-making on rejecting or not rejecting the null hypothesis.
• Proportions are calculated by comparing A/(A+B). The analysis of proportions does not use the normal/t-distributions but other special methods (exact method; Clopper-Pearson).
• The binomial distribution provides probabilities for discrete outcomes in binary trials.