Biostats pt 2

Cross-Sectional Study

Data are observed, measured, and collected at one point in time, not over a period of time.

Retrospective (case-control) study

Data are collected from a past time period by going back in time (through examination of records, interviews, and so on)

Prospective (Longitudinal/Cohort) study

data are collected in the future from groups that share common factors (such groups are called cohorts)

Bad Experimental Design

Treat all women subjects and give the men a placebo. (Problem: We don’t know if effects are due to sex or to treatment.)

Completely Randomized Experimental Design

Assign subjects to different treatment groups through a process of random selection. Use randomness to determine who gets the treatment and who gets the placebo

Randomized Block Design

A block is a group of subjects that are similar, but blocks differ in ways that might affect the outcome of the experiment. Use the following procedure:

1. Form blocks (or groups) of subjects with similar characteristics.

2. Randomly assign treatments to the subjects within each block.

Randomized Block Design

A design uses the same basic idea as stratified sampling, but this design are used when designing experiments, whereas stratified sampling is used for surveys

Matched Pairs Design

Compare two treatment groups (such as treatment and placebo) by using subjects matched in pairs that are somehow related or have similar characteristics, as in the following cases.

Get measurements from the same subjects before and after some treatment

Rigorously Controlled Design

Carefully assign subjects to different treatment groups, so that those given each treatment are similar in the ways that are important to the experiment.

This can be extremely difficult to implement, and often we can never be sure that we have accounted for all of the relevant factors

Random Sampling Error

occurs when the sample has been selected with a random method, but there is a discrepancy between a sample result and the true population result; such an error results from chance sample fluctuations

Non-sampling Error

is the result of human error, including such factors as wrong data entries, computing errors, questions with biased wording, false data provided by respondents, forming biased conclusions, or applying statistical methods that are not appropriate for the circumstances

Non-Random Sampling Error

is the result of using a sampling method that is not random, such as using a convenience sample or a voluntary response sample

Biostatistics

branch of statistics responsible for interpreting the scientific data that is generated in the health sciences, including the public health sphere.

Biostatisticians

Responsible to consider the variables in subjects (in public health, subjects are usually patients, communities, or populations), to understand them, and to make sense of different sources of variation

Objective of Biostatistics

to disentangle the data received and make valid inferences that can be used to solve problems in public health.

Application of Biostatistics

• chronic diseases managing & thriving

• Human growth development

• Genetics and environment

• Clinical medicine

• Health economics

Role of Biostatisticians

take complex, mathematical findings of clinical trials and research-related data and translate them into valuable information that is used to make public health decisions.

these professionals use mathematics to enhance science and bridge the gap between theory and practice

required to develop statistical methods for clinical trials, observational studies, longitudinal studies, and genomics

Informatics

known as bioinformatics, a science that relies on the basic disciplines of science, mathematics, probability and statistics, and computer science to build a solid statistical foundation for making advances, improvements, and even breakthroughs in public health and medicine.

Health Informatics

deals with the resources, devices, and methods required for the effective storage, use, and retrieval of information,

Public Health Informatics

public health informatics includes the application of informatics in public health areas, such as surveillance, prevention, preparedness, and health promotion.

System Analyst

write and troubleshoot the software used by biostatisticians and researchers. Their work may also include conducting their own research, designing databases, and developing algorithms for processing and analyzing information.

Responsibilities of System Analyst

• Incorporating bioinformatics/biostatistics into efficient and automated data analysis tools

• Developing and tracking quality workflow metrics for detecting variants and sequences

• Working with scientists and researchers to develop project plan

For Medical Professionals

• crucial for designing, analyzing, and interpreting medical research studies.

• Understanding biostatistics is essential for comprehending and applying research findings

• Statistical literacy helps identify errors in statistical methods and reporting in medical literature

Statistical Competence in Research

• Developing, teaching, and assessing statistical competencies is vital for medical researchers.

• Statistical competencies define the statistical knowledge and skills required for medical research.

• Research focuses on identifying and developing statistical competencies for medical research learners

A Cornerstone of Medical Research

• Biostatistics is the application of statistics to human health and disease.

• It covers a wide range of fields within medicine and health sciences.

• Biostatisticians collaborate with researchers in study design, data analysis, Interpretation, and reporting.

• Biostatistics plays a critical role in identifying causes of diseases and evaluating treatment effectivene

Cochran’s Formula

Developed by statistician William G. Cochran in 1963, this formula is designed to calculate a representative sample size for a large or unknown population based on a desired level of precision, confidence level, and estimated proportion of an attribute in the population

Confidence Level (Z)

The critical value corresponding to your desired Z = 1.96 confidence level (e.g., for a 95% confidence level)

Estimated Proportion

The expected proportion of the population that p has a particular attribute. If unknown, (50%) is used because it p = 0.5 provides the maximum possible sample size (most conservative estimate).

Complementary Proportion

q = 1− p

Margin of Error

The acceptable level of precision or error bound (e.g., e = 0.05 ±5 %for )

Uses of Cochran’s Formula

• conducting rigorous academic research, thesis work, or publication- grade studies.

• You know (or can estimate) the variance/proportion ( ) in the population. p

• You need to specify a precise confidence level (e.g., 99% or 90% rather than just a fixed default).

• The total population size is unknown, infinitely large, or very large.

Uses of Slovin’ Formula

• You are performing preliminary surveys, exploratory research, or rapid field studies.

• You have zero information about the population's variability or variance ( ). p N

• The population ( ) is finite and explicitly known.

• Strict mathematical precision is less critical than speed and ease of computation

Frequency Distribution

shows how data are partitioned among several categories (or classes) by listing the categories along with the number (frequency) of data values in each of them.

Lower Class Limits

are the smallest numbers that can belong to each of the different classes.

Upper Class Limits

are the largest numbers that can belong to each of the different classes

Class Boundaries

are the numbers used to separate the classes, but without the gaps created by class limits

Class Midpoints

are the values in the middle of the classes.

Class Width

is the difference between two consecutive lower class limits (or two consecutive lower class boundaries) in a frequency distribution.

Histograms

a graph consisting of bars of equal width drawn adjacent to each other (unless there are gaps in the data). The horizontal scale represents classes of quantitative data values, and the vertical scale represents frequencies. The heights of the bars correspond to frequency values.

Relative Frequency Histogram

A relative frequency histogram has the same shape and horizontal scale as a histogram, but the vertical scale uses relative frequencies (as percentages or proportions) instead of actual frequencies

Histogram Uses

• Visually displays the shape of the distribution of the data

• Shows the location of the center of the data

• Shows the spread of the data

• Identifies outliers

Normal Distribution

• Bell-shaped

• Many statistical methods require that sample data come from a population having a distribution approximately normal

• Aside from histograms, they are very helpful to assess normalit

Uniform Distribution

• The different possible values occur with approximately the same frequency, so the heights of the bars in the histogram are approximately uniform.

• The graph on the right depicts outcomes of last digits of weights from a large sample of randomly selected subjects, and such a graph is helpful in determining whether the subjects were actually weighed or whether they reported their weights

Normal Quantile Plot

Normal Distribution

Not a Normal Distribution

Normal Distribution

The population distribution is normal if the pattern of the points in the normal quantile plot is reasonably close to a straight line, and the points do not show some systematic pattern that is not a straight-line pattern.

Not a Normal Distribution

The population distribution is not normal if the normal quantile plot has either or both of these two conditions:

• The points do not lie reasonably close to a straight-line pattern.

• The points show some systematic pattern that is not a straight-line pattern

Dot Plot

consists of a graph of quantitative data in which each data value is plotted as a above a horizontal scale of values. Dots representing equal values are stacked.

• Displays the shape of the distribution of data.

• It is usually possible to recreate the original list of data values

Dot Plot

consists of a graph of quantitative data in which each data value is plotted as a above a horizontal scale of values. Dots representing equal values are stacked.

• Displays the shape of the distribution of data.

• It is usually possible to recreate the original list of data values

Time-Series Graph

which are quantitative data that have been collected at different points in time, such as monthly or yearly. An advantage of a time-series graph is that it reveals information about trends over time.

Reveals information about trends over tiMe

Bar Graph

uses bars of equal width to show frequencies of categories of categorical (or qualitative) data.

The bars may or may not be separated by small gaps.

Features:

■ Shows the relative distribution of categorical data so that it is easier to compare the different categories

Pareto Charts

is a bar graph for categorical data, with the added stipulation that the bars are arranged in descending order according to frequencies, so the bars decrease in height from left to right.

Features:

■ Shows the relative distribution of categorical data so that it is easier to compare the different categories

■ Draws attention to the more important categories

Pie Charts

a very common graph that depicts categorical data as slices of a circle, in which the size of each slice is proportional to the frequency count for the category. Although pie charts are very common, they are not as effective as Pareto charts.

Features:

■ Shows the distribution of categorical data in a commonly used forma

Frequency Polygon

uses line segments connected to points located directly above class midpoint values.

Relative Frequency Polygon

• uses relative frequencies (proportions or percentages) for the vertical scale.

• An advantage of relative frequency polygons is that two or more of them can be combined on a single graph for easy comparison

Boxplots

uses the relationships among the median, upper quartile, and lower quartile to describe the skewness of a distribution.

Graphs that Deceive

commonly used to mislead people, and we really don’t want statistics students to be among those susceptible to such deceptions. Graphs should be constructed in a way that is fair and objective. The readers should be allowed to make their own judgments, instead of being manipulated by misleading graphs

Nonzero Vertical Axis

involves using a vertical scale that starts at some value greater than zero to exaggerate differences between groups.

TIP: Always examine a graph carefully to see whether a vertical axis begins at some point other than zero so that differences are exaggerated

Pictographs

They are often misleading. Data that are one-dimensional in nature (such as budget amounts) are often depicted with two-dimensional objects (such as dollar bills) or three-dimensional objects (such as stacks of coins, homes, or barrels). Artists can create false impressions that grossly distort differences

Correlation

exists between two variables when the values of one variable are somehow associated with the values of the other variable.

Linear Correlation

exists between two variables when there is a correlation and the plotted points of paired data result in a pattern that can be approximated by a straight line

Scatterplot

a plot of paired (x, y) quantitative data with a horizontal x-axis and a vertical y-axis. The horizontal axis is used for the first variable (x), and the vertical axis is used for the second variable (y)

Linear Correlation Coefficient

denoted by r, and it measures the strength of the linear association between two variables

Regression Line

Given a collection of paired sample data, the regression line (or line of best fit or least-squares line) is the straight line that “best” fits the scatterplot of the data.