Main Concepts in Biostatistics

Main Concepts in Biostatistics

• Biostatistics aims to equip students with the skills to interpret medical literature critically.
• The course provides a fundamental understanding of biostatistics.
• The primary goal of the biostatistics course is to teach basic skills, useful for medical consulting when designing, performing and reporting research.
• Medical researchers should learn biostatistics because medicine is becoming increasingly quantitative.
• Biostatistics is needed to improve population health, clarify disease factors, enumerate disease occurrences,disease etiologies, predict disease numbers and understand/critique medical literature.
• Medical students should learn biostatistics so that the planning, conduct, and interpretation of medical research can rely on statistical methods.

Planning and Conduct in Biostatistics

• Critical questions in planning include determining the number of patients to treat and how to allocate subjects to treatments.
• Identify other factors that might influence the response variable.
• Study conditions, matching requirements, and the necessity of blinding (single or double) need consideration.
• The importance of a control group and the potential placebo effect are factors.
• Determine which experimental design is more appropriate.

Reference Books:

• "Biostatistics: A Foundation for Analysis in the Health Sciences" by Wayne W. Daniel.
• "Basic & Clinical Biostatistics" by Beth Dawson, Robert G. Trapp (McGrow-Hill NewYork, 2004).
• "Primer of Biostatistics" by Stanton A. Glantz (McGrow-Hill NewYork, 2002).
• "Statistical Methods in Medical Research" by P. Armitage (Blackwell Science Oxford, 2002).

Interpretation Examples:

• In a study of coronary heart disease (CHD) with 609 males aged 40-76 between 1990-1999, 71 new CHD cases were identified.

• The study evaluated the link between obesity and CHD incidence.

• The CHD risk is 2.45 times higher among obese subjects (Risk Ratio given as R = (27/122) / (44/487)).

• In a study, the Distribution of women with thromboembolism and healthy women are split into blood groups.

• 58.2% of women with thromboembolism had blood group A as opposed to 51.7% of healthy women.

Statistics

• Statistics involves planning research, collecting and describing data, summarizing/presenting data, as well as analyzing and interpreting results.
• Statistics allows one to reach conclusions or discover new knowledge.
• Biostatistics applies statistical methods to health sciences.
• Basic statistical tasks include describing data and drawing inferences about the underlying population.
• Statistics is concerned with scientific methods for data collection, organization, summarization, presentation, and analysis.
• Used in context, statistics covers; employment, accidents, health, demographics, and research.
• Classifications include descriptive and inferential.

Descriptive Statistics

• The focus is on collecting, summarizing, and presenting data.
• Examples include the mean age of citizens in an area, book length, and cereal box weight variation.
• Organize data in tabular, graphical, or numerical formats.

Inferential Statistics

• This analyzes sample data to draw conclusions about a population.
• Statistical methods for making inferences about populations are based on probability theory.

Data and Observations

• Data is a set of values for one or more variables recorded on observational units.
• An observation or case is an individual data source.
• A variable is a measurable/non-measurable quantity that varies and takes a specified set of values.

Populations and Samples

• A population is a collection of individuals/objects/measurements whose properties are analyzed.
• A sample is a representative subset of the population.

Parameters and Statistics

• A parameter is a summary value describing a population's nature in a study variable.
• A statistic is a summary value calculated from a sample of observation.

Data Sources

• Common sources include routinely kept records, published data, electronic media, surveys, experimental research, census data and generated or artificial data.

Types of Data: Qualitative and Quantitative

• Qualitative data results from variables describing subject qualities.
• Quantitative data results from obtaining counts or measurements.

Collecting Data

• Collecting data concerning characteristics of a group of individuals or objects, such as heights and weights of students in a university can often be impractical to observe the entire group.
• One examines a smaller group called a sample, instead.

Variables and Constants

• A variable is a symbol that can assume any of a prescribed set of values, called the domain.
• A constant is a variable which can assume only one value.

Continuous and Discrete Variables

• A continuous variable can theoretically take any value between two given values, versus a discrete variable.
• The number of children in a family is a discrete variable.
• In contrast, age can be further divided so is a continuous variable.

Quantitative vs. Qualitative Variables

• A quantitative variable can be measured, such as height, weight.
• A qualitative variable cannot be numerically measured, such as eye color and hair color etc.
• Observations on quantitative variables may be continuous/discrete, the number of children (N) in a family are discrete
• Age (A) of an individual in years (or fractions thereof) is continuous

Population and Sample

• Population consists of all possible variable values.
• A sample is a part of a population, which might sometimes include the whole population.

Discrete and Continuous Data

• Discrete/continuous variables describe discrete or continuous data, respectively.
• The number of children in 1000 families is discrete, while the heights of 100 students is continuous.
• Measurements typically yield continuous data, while enumeration/counting yield discrete data.

Scales of Measurement

• Nominal scales are for simplest level of measurement where data fits into categories like "yes/no", nominal characteristics describe traits such as cardiac arrest (yes or no).

• Ordinal scales classify observations, and have have an inherent order as classifications, examples are tumors staged by development, severity of arthritis, etc.

  • Apgar scores assess newborn maturity (0-10), with lower scores indicating depression.

• Numerical Scales are quantitative because they measure something.

  • Continuous scales have values on a continuum (age, height, weight, lab values).
  • Discrete scales have integer values (number of fractures).

• Numerical scales are further divided into 4 different categories.

  • Nominal: Values are indicative of a category, but are not ranked, such as country of birth, sex etc.
  • Ordinal: A limited number of categories that are ranked, such as response to treatment.
  • Interval: Variables with ordering, and a measurable distance between categories, such as temperatures in Celcius and Farenheit.
  • Ratio: Interval scales with a true zero, such as temperatures in Kelvin, height and weight.

Discrete Data Examples

• Discrete data are organized into nominal and ordinal scales.
  • Nominal scale: One can own, or rent a home.
  • Ordinal: Level of customer satisfaction (very dissatisfied to very satisfied)

Continuous Data Examples

• Continuous Data are organized into interval and ratio scales.
  • Interval: Degrees in Fahrenheit.
  • Ratio Examples: Weight of packaged dog food.

Activity Level of Men Having Cardiac Arrest

• Shows 20 peoples activity level in minutes per week along with whether they were having a cardiac arrest at the time.
• Shows that of cardiac arrest patients, 3 were active, 17 inactive.
• Includes Habitual High-Intensity Activity (min/wk) shown in a contingency table for cardiac arrest data.

Rounding

• Basic rounding follows normal mathematical rules.

Scientific Notation

• Convenient for very large or small numbers.
• Involves using powers of 10.

Significant Figures

• They're the accurate digits, apart from zeros locating the decimal.

Calculations

• In multiplication, division, and roots, use the fewest significant figures from what you are using.
• In addition and subtraction, the final result will have no more figures after the decimal point than the numbers with the fewest significant figures using after the decimal.

Functions

• If each value a variable X can assume, there is one or more values of Y, then Y is a function of X, shown as Y = F(X), with X as an independent and Y as a dependent variable.
• If only one value of Y corresponds to each of X, we call Y a single-valued function of X, otherwise it is called a multiple-valued function of X.

Rectangular Coordinates

• Consider two mutually perpendicular lines X(OX) and Y(OY), called the x and y axes respectively, with appropriate scales.
• These lines divide the plane determined by them (called the xy plane) into four regions denoted by I, II, III and IV (called the first, second, third and fourth quadrants, respectively).
• Point O is called the origin or zero point. Given any point P, drop perpendiculars to the x and y axes from P.
• The values of x and y at the points where the perpendiculars meet these axes are called the rectangular coordinates or simply the coordinates of P, and are denoted by (x, y).
• The coordinate x is sometimes called the abscissa, and y is the ordinate of the point.
• In Figure, the abscissa of point P is 2, the ordinate is 3, and the coordinates of P are (2, 3).

Graphs

• A graph is a pictorial representation of the relationship between variables with bar graphs, pie graphs, and pictographs being the main types.

Equations

• Equations are statements of the form A = B, where A is called the left-hand member or side of the equation and B the right-hand member or side.
• Follows normal algebraic rules.

Inequalities

• The symbols < and > mean "less than" and "greater than", respectively. The symbols < and > mean "less than or equal to" and "greater than or equal to" respectively, they are known as inequality symbols.

Logarithms

• Every positive number N can be expressed as a power of 10, i.e. we can always find p such that N = 10^p, p is called the logarithm of N to the base 10 or the common logarithm of N, and write briefly = log N or or = log10 N.
• For example, Log10 1000 = 3 since 1000 = 103

Antilogarithms

• In the exponential form 2.36 = 10^0.3729, the number 2.36 is called the antilogarithm of 0.3729, or antilog 0.3729. It is the number whose logarithm is 0.3729.

Computations Using Logarithms

• log (M*N) = logM + logN
• log (M/N) = logM – logN
• log MP = p logM