introduction to biostatistics

INTRODUCTION TO BIOSTATISTICS

Oleg Devinyak, UzhNU

Common statistical terms

Data Measurements or observations of a variable

Variable A characteristic that is observed or manipulated Can take on different values


Statistical terms (cont.)

Independent variables Precede dependent variables in time Are often manipulated by the researcher The treatment or intervention that is used in a

study Dependent variables

What is measured as an outcome in a study Values depend on the independent variable


Population and parameters

Population (statistical aggregate, statistical totality) A group of individuals that we would like to know something

about Parameter

A characteristic of the population in which we have a particular interest Often denoted with Greek letters (μ, σ, ρ) Examples:

The proportion of the population that would respond to a certain drug

The association between a risk factor and a disease in a population


Samples and Statistics

Sample A subset of a population (hopefully representative)

Statistic A characteristic of the sample

Examples: The observed proportion of the sample that responds to

treatment The observed association between a risk factor and a

disease in this sample


Populations and Samples

Studying populations is too expensive and time-consuming, and thus impractical

If a sample is representative of the population, then by observing the sample we can learn something about the population And thus by looking at the characteristics of the

sample (statistics), we may learn something about the characteristics of the population (parameters)


Random samples

Subjects are selected from a population so that each individual has an equal chance of being selected

Random samples are representative of the source population

Non-random samples are not representative May be biased regarding age, severity of the

condition, socioeconomic status etc.


Sample vs. Population

Population Sample


Statistical Analyses

Two steps Descriptive Statistics

Describe the sample Inference

Make inferences about the population using what is observed in the sample

Primarily performed in two ways: Hypothesis testing Estimation


Issues

Samples are random If we had chosen a different sample, then we

would obtain different statistics (sampling variation or random variation) However, note that we are trying to estimate the same

(constant) population parameters


Descriptive Statistics

Describe the Sample Begin one variable at a time Describe important variables in your analyses

(e.g., endpoints, demographics, confounders, etc.)


Types of Data

Several types of data Nominal Ordinal Discrete Continuous Time-to-event with censoring

The type of data influences the analysis methods to be employed


Nominal Data

Mutually exclusive unordered categories

Examples Sex (male, female) Race/ethnicity (white, black, latino, asian, native american,

etc.) Site

Can summarize in: Tables – using counts and percentages Bar chart/graph


Ordinal Data

Ordered Categories

Examples Adverse events

Mild, moderate, severe, life-threatening, death Income

Low, medium, high


Discrete Data

Often only integer numbers are possible

If there are many different discrete values, then discrete data is often treated as continuous Examples: CD4 count, HIV viral load

If there are very few discrete values, then discrete data is often treated as ordinal


Continuous Data

Any value on the continuum is possible (even fractions or decimals)

Examples: Height Weight Many “discrete” variables are often treated as

continuous Examples: CD4 count, viral load


Survival Data

Time to an event (continuous variable) The event does not have to be survival

Concept of “Censoring” If we follow a person until the event, then the survival time

is clear If we follow someone for a length of time but the event

does not occur, the the time is censored (but we still have partial information; namely that the event did not occur during the follow up period)

Examples: time to progression (cancer), time to response, time to relapse, time to death


Types of variables


Dataset Structure

Think of data as a rectangular matrix of rows and columns

Simplest structure Rows represent the “experimental unit” (e.g., person)

Each row is an independent observation Columns represent “variables” measured on the

experimental unit

More complex structures Multiple rows per person (e.g., multiple timepoints)


Visual Data Summaries

Some visual ways to summarize data (one variable at a time): Tables Graphs

Bar charts Histograms Box plots


Frequency Tables

Summarizes a variable with counts and percentages

The variable is categorical (e.g., nominal or ordinal)


Example: Serum Cholesterol Levels

Frequencies of serum cholesterol levels Cumulative Cholesterol level Cumulative Relative Relative (mg/100 ml) Frequency Frequency Frequency (%) Frequency (%) _______________________________________________________________ 80-119 13 13 1.2 1.2 120-159 150 163 14.1 15.3 160-199 442 605 41.4 56.7 200-239 299 904 28.0 84.7 240-279 115 1019 10.8 95.5 280-319 34 1053 3.2 98.7 320-360 9 1062 0.8 99.5 360-399 5 1067 0.5 100.0 _______________________________________________________________ Total 1067 100.0 Note. The choice of intervals (and “cut-off” values) in a frequency table is very important. However, there are no established rules for determining them.


Graphical Summaries

Bar Graphs Nominal data

No order to horizontal axis

Histograms Continuous or ordinal data on horizontal axis

Box Plots Continuous data


Bar Chart – Cause of Death

Cause of Death

Motor Vehicle Drowning House Fire Homicide Other

0

20

40

60


Histogram – Cigarette Consumption (1900-1990)

Cigarette consum ption between 1900 and 1990

0

1000

2000

3000

4000

C igare tte consum ption

19001910

19201930

19401950

19601970

19801990


Medical indeces

— Extensive; The extensive parameter or a parameter of distribution characterizes

a parts of the phenomena (structure), that is it shows, what part from the general number of all diseases (died) is made with this or that disease which enters into total.

— Intensive; The intensive parameter characterizes frequency. It shows how

frequently the given phenomenon occurs in the given environment.— Relative intensity;

Parameters of relative intensity represent a numerical ratio of two or several structures of the same elements of a set, which is studied

— Visualization; The parameter of visualization characterizes the relation of any of

comparable values to the initial level accepted for 100— Correlation.

The parameter of correlation characterizes the relation between diverse values. For example, the parameter of average bed occupancy per nurse, etc.


HOMEWORK

Count all your grades (marks get at exams) and create the corresponding frequency table. Write the table to your copybooks.

introduction to biostatistics

Education

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