Faculty of Medicine Epidemiology and Biostatistics

واإلحصاء الحيوي الوبائيات (31505204)

Lecture 2 Definition of Biostatistics , Purposes of

Biostatistics Population and Sample Types

By

Hatim Jaber MD MPH JBCM PhD

5-6-2017

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Presentation outline 5-6-2017

Time

Research , epidemiology and biostatistics. 10:25 to 10:30

Basic statistical concepts and their application to healthcare research

10:30 to 10:40

Population and samples 10: 40 to 10:59

Types of samples and when to use it. 11:00 to 11:10

Data sources and data quality 11:10 to 11:20

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Definition of Statistics • Different authors have defined statistics differently. The best

definition of statistics is given by Croxton and Cowden according

to whom statistics may be defined as the science, which deals with collection, presentation, analysis and interpretation of numerical data.

• The science and art of dealing with variation in data through collection, classification, and analysis in such a way as to obtain reliable results. —(John M. Last, A Dictionary of Epidemiology )

• Branch of mathematics that deals with the collection, organization, and analysis of numerical data and with such problems as experiment design and decision making. —(Microsoft Encarta Premium 2009)

Definition of Biostatistics = Medical statistics

• Biostatistics may be defined as application

of statistical methods to medical, biological and public health related problems.

• It is the scientific treatment given to the

medical data derived from group of individuals or patients

Role of Statistics in Clinical Medicine

The main theory of statistics lies in the term variability. There is No two individuals are same. For example, blood pressure of person may vary from time to time as well as from person to person. We can also have instrumental variability as well as observers variability. Methods of statistical inference provide largely objective means for drawing conclusions from the data about the issue under study. Medical science is full of uncertainties and statistics deals with uncertainties. Statistical methods try to quantify the uncertainties present in medical science. It helps the researcher to arrive at a scientific judgment about a hypothesis. It has been argued that decision making is an integral part of a physician’s work. Frequently, decision making is probability based.

Role of Statistics in Public Health and Community Medicine

Statistics finds an extensive use in Public Health and Community Medicine. Statistical methods are foundations for public health administrators to understand what is happening to the population under their care at community level as well as individual level. If reliable information regarding the disease is available, the public health administrator is in a position to:

●● Assess community needs ●● Understand socio-economic determinants of health ●● Plan experiment in health research ●● Analyze their results ●● Study diagnosis and prognosis of the disease for taking effective action ●● Scientifically test the efficacy of new medicines and methods of treatment.

Why we need to study Medical

Statistics?

Three reasons:

(1) Basic requirement of medical research.

(2) Update your medical knowledge.

(3) Data management and treatment.

Biostatistics

It is the science which deals with development and application of the most appropriate methods for the: Collection of data. Presentation of the collected data. Analysis and interpretation of the results. Making decisions on the basis of such analysis

Other definitions for “Statistics”

Frequently used in referral to recorded data

Denotes characteristics calculated for a set of data : sample mean

Role of statisticians To guide the design of an experiment or survey

prior to data collection

To analyze data using proper statistical procedures and techniques

To present and interpret the results to researchers and other decision makers

Statistics is a widely-used tool in virtually all fields of science and technology

It’s the corner stone of any research

Uses and Application of Statistics

It presents facts in a definite form It facilitates comparisons It simplifies the masses of figures It helps in formulating and testing hypothesis It helps in prediction

Application of Biostatistics in Health Sciences

-- Defining normal and not normal in context of various aspects related to health and illness

-- Establishing the accuracy of the diagnostic procedures

-- Planning of experiments and analysis of results -- Assessment of treatment protocol and

different interventions used for care and treatment of the patients

-- Collections, analysis, and dissemination of various population health statistics

Basic concepts

• Homogeneity: All individuals have similar values or belong to same category.

Example: all individuals are Chinese, women, middle age (30~40

years old), work in a computer factory ---- homogeneity in nationality, gender, age and occupation.

• Variation: the differences in feature, voice… • Throw a coin: The mark face may be up or down ---- variation!

• Treat the patients suffering from pneumonia with same antibiotics: A part of them recovered and others didn’t ---- variation!

• If there is no variation, there is no need for statistics.

• Many examples of variation in medical field: height, weight, pulse, blood pressure, … …

Population and Sample

• Population: The whole collection of individuals that one intends to study.

• Sample: A representative part of the population.

• Randomization: An important way to make the sample representative.

limited population and limitless population

• All the cases with hepatitis B collected in a hospital in Changchun. (limited)

• All the deaths found from the permanent residents in a city. (limited)

• All the rats for testing the toxicity of a medicine.

(limitless)

• All the patients for testing the effect of a medicine. (limitless) hypertensive, diabetic, …

Random

By chance!

• Random event: the event may occur or may not occur in one experiment.

Before one experiment, nobody is sure whether the event occurs or not.

Example: weather, traffic accident, …

There must be some regulation in a large number of experiments.

Probability

• Measure the possibility of occurrence of a random event.

• A : random event

• P(A) : Probability of the random event A

P(A)=1, if an event always occurs.

P(A)=0, if an event never occurs.

Estimation of Probability----Frequency

• Number of observations: n (large enough)

Number of occurrences of random event A: m

f(A) m/n

(Frequency or Relative frequency)

Example: Throw a coin event:

n=100, m (Times of the mark face occurred)=46

m/n=46%, this is the frequency; P(A)=1/2=50%,

this is the Probability.

Parameter and Statistic • Parameter : A measure of population or A measure of the distribution of population. Parameter is usually presented by Greek letter.

such as μ,π,σ.

-- Parameters are unknown usually

To know the parameter of a population, we need a sample • Statistic: A measure of sample or A measure of the distribution of sample. Statistic is usually presented by Latin letter such as s , p, t.

Sampling Error

error :The difference between observed

value and true value.

Three kinds of error:

(1) Systematic error (fixed)

(2) Measurement error (random) (Observational error)

(3) Sampling error (random)

Sampling error • The statistics of different samples from

same population: different each other!

• The statistics: different from the parameter!

The sampling error exists in any sampling research.

It can not be avoided but may be estimated.

Stages of any Scientific Research

--- Stating problems

--- Postulation of research question (s)

--- Setting research tools

--- Choosing sampling frame and type

--- Data collection (a number of related (variables

--- Data systematization, summarization, and tabulation

--- Data analysis

--- Interpretation of results

--- Drawing conclusions

--- Presentation

Statistical designs Descriptive Statistics describing and

summarizing data bases. e.g.

--- census

--- characteristics of mentally retarded

Analytical Statistics enabling researchers to take decisions and make judgment regarding the population being studied. e.g. --- evaluation of a new method of teaching

--- comparison between groups

--- evaluation of a new drug

Concept of SETTING

• Location of the study - can affect results

• Natural Setting: Uncontrolled, real life situation

• Partially Controlled: Manipulated or modified in some way

• Highly Controlled: Artificial environment for sole purpose of doing research. Decreases effects of outside influences.

• Populations and Samples

• A sample consists

only of observations drawn from the population

• A measurable characteristic of a sample is called a statistic

• The mean of a sample is denoted by the symbol ¯X

• A population includes

each element from the set of observations that can be made

• A measurable characteristic of a population, such as a mean or standard deviation, is called a parameter

• The mean of a population is denoted by the symbol μ

Statistics refer to samples

S S

Parameters refer to populations

P P

Populations

--- A statistical population need not be made up of people

Population of birth-weights

Population of haemoglobin levels

Population of mentally retarded

Population of red cell counts

--- Characteristic of the population studied is

being fully defined

--- A Parameter is a constant figure used to describe the population

Samples

--- A sampling method is a procedure for selecting sample elements from a fully defined population

--- A syringe-full of your blood taken now is a sample of your blood circulation at the moment

--- Inferences from a sample refer only to the particular population defined at that moment

--- Statistic is a figure used to describe samples taken from the defined population

--- From any particular sample one can estimate the parameters in the relevant fully defined population only

SAMPLING

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• A sample is “a smaller (but hopefully representative) collection of units from a population used to determine truths about that population” (Field, 2005)

• Why sample?

– Resources (time, money) and workload

– Gives results with known accuracy that can be calculated mathematically

• The sampling frame is the list from which the potential respondents are drawn

– Registrar’s office

– Class rosters

– Must assess sampling frame errors

SAMPLING…….

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TARGET POPULATION

STUDY POPULATION

SAMPLE

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Process

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• The sampling process comprises several stages:

–Defining the population of concern

–Specifying a sampling frame, a set of items or events possible to measure

–Specifying a sampling method for selecting items or events from the frame

–Determining the sample size

–Implementing the sampling plan

–Sampling and data collecting

–Reviewing the sampling process

SAMPLING……

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• What is your population of interest?

• To whom do you want to generalize your

results?

–All doctors

–School children

– Indians

–Women aged 15-45 years

–Other

• Can you sample the entire population?....

SAMPLING…….

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• 3 factors that influence sample representative- ness

• Sampling procedure

• Sample size

• Participation (response)

• When might you sample the entire population? • When your population is very small

• When you have extensive resources

• When you don’t expect a very high response

Sample Size Issues

Sample size must be big enough for the study to have appropriate statistical power – the ability to demonstrate an association if one exists

Sample size calculations are based

on a number of study design factors:

• prevalence

• acceptable error

• the detectable difference

Types of Sampling 1 . Probability sampling: it is the one in which each

sample has the same probability of being chosen Purposive sampling: it is the one in which the

person who is selecting the sample is who tries to make the sample representative,

depending on his opinion or purpose, thus being the representation subjective

No-rule sampling: we take a sample without any

rule, being the sample representative if the population is homogeneous and we have no

selection bias

Types of Samples

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• Probability (Random) Samples

• Simple random sample

–Systematic random sample

–Stratified random sample

–Multistage sample

–Multiphase sample

–Cluster sample

• Non-Probability Samples

–Convenience sample

–Purposive sample

–Quota

Probability Sampling

• Random sampling with and without replacement

• Stratified sampling

• Cluster sampling

• Systematic sampling

• Other types of sampling techniques

Simple Random Sampling

Simple random sampling refers to a sampling method that has the following properties:

-- The population consists of N objects

-- The sample consists of n objects

-- All possible samples of n objects are equally likely to occur

SIMPLE RANDOM SAMPLING

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• Applicable when population is small, homogeneous & readily available

• All subsets of the frame are given an equal probability. Each element of the frame thus has an equal probability of selection.

• It provides for greatest number of possible samples. This is done by assigning a number to each unit in the sampling frame.

• A table of random number or lottery system is used to determine which units are to be selected.

Simple Random Sampling

One way would be the lottery method

Each of the N population members is assigned a unique number. The numbers are placed in a bowl and thoroughly mixed. Then, a blind-folded researcher selects n numbers. Population members having the selected numbers are included in the sample

Second method, Random Number Generator

Stratified Sampling

We divide our sample in such a way that we have elements of all the strata

Advantages:

-- We can have more precise information inside the subpopulations about the variables we are studying

-- We can raise precision of the estimators of the variables of the whole population

Stratified Random Sample

• The population is divided into two or more groups called strata, according to some criterion, such as geographic location, grade level, age, or income, and subsamples are randomly selected from each strata.

Cluster Sampling

Advantages:

The reason to make this sampling is that sometimes it is too expensive to make a complete list of all the elements of the population that we want to study

Disadvantages:

The main disadvantage that we may have is that if the clusters are not homogeneous among them, the final sample may not be representative of the population

Cluster Sample

• The population is divided into subgroups (clusters) like families. A simple random sample is taken of the subgroups and then all members of the cluster selected are surveyed.

Disadvantages:

• The choice of the size of the samples inside each stratus to let the sample size be n

• It may be difficult in some populations to divide into strata

Two-stage sampling

Two-stage sampling is a particular case of cluster sampling in which in the second stage we do not select all the elements of the cluster, but some elements chosen in a random way

Clusters in the first stage are called primary units and the ones in the second stage are secondary units

Multistage Sampling

We would choose our sample in the following way:

-- We select a stratified sample. We would take at least one stratus (one quarter)

-- We choose randomly some buildings of each of the selected quarters

-- We take randomly one or several houses of each of the buildings selected

Systematic Sample

• Every kth member ( for example: every 10th person) is selected from a list of all population members.

Systematic Sampling

Advantages:

-- Extends the sample to all the population

-- It is very easy to apply it

Disadvantages:

-- If there is periodicity in the numbering of the elements, selection bias can occur

Samples

Population

All units that satisfy the study criteria

Units

Sampling frame

All units in the population

Definitions

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Stratified Sampling There may often be factors which divide up the population into sub-populations (groups / strata) and we may expect the measurement of interest to vary among the different sub-populations. This has to be accounted for when we select a sample from the population in order that we obtain a sample that is representative of the population. This is achieved by stratified sampling. Example Suppose a farmer wishes to work out the average milk yield of each cow type in his herd which consists of Ayrshire, Friesian, Galloway and Jersey cows. He could divide up his herd into the four sub-groups and take samples from these.

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A stratified sampling approach is most effective when three conditions are met •Variability within strata are minimized

•Variability between strata are maximized

•The variables upon which the population is stratified are strongly correlated with the desired dependent variable. Advantages over other sampling methods

•Focuses on important subpopulations and ignores irrelevant ones. •Allows use of different sampling techniques for different subpopulations. •Improves the accuracy/efficiency of estimation. •Permits greater balancing of statistical power of tests of differences between strata by sampling equal numbers from strata varying widely in size. Disadvantages •Requires selection of relevant stratification variables which can be difficult. •Is not useful when there are no homogeneous subgroups. •Can be expensive to implement

Multistage random

The sample is drawn in steps

Example: sample of Jordan children

1-Take a cluster sample of children (using governorates as clusters)

2- Take a cluster sample from the sampled governorates (using the villages and cities as clusters)

3- Take a third cluster sample from the sampled villages or cities (using houses as clusters)

OR

3- take a simple random sample of children in each selected village

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Cluster sampling is commonly implemented as multistage sampling. This is a complex form of cluster sampling in which two or more levels of units are embedded one in the other. The first stage consists of constructing the clusters that will be used to sample from. In the second stage, a sample of primary units is randomly selected from each cluster (rather than using all units contained in all selected clusters). In following stages, in each of those selected clusters, additional samples of units are selected, and so on. All ultimate units (individuals, for instance) selected at the last step of this procedure are then surveyed. This technique, thus, is essentially the process of taking random subsamples of preceding random samples. Multistage sampling can substantially reduce sampling costs, where the complete population list would need to be constructed (before other sampling methods could be applied). By eliminating the work involved in describing clusters that are not selected, multistage sampling can reduce the large costs associated with traditional cluster sampling. However, each sample may not be a full representative of the whole population.

Non-Probability

• Purposive

• Convenient

Disease representative samples

+ Inclusion criteria

Could be representative samples

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• Quota

• Snow ball

• RDS (Respondent Driven Sample)

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Purposive sample:

Usually this specifies place where the specified

patients are present.

E.g. Cancer institute to study malignant diseases.

Cardiac institute to study heart conditions.

Justify the place selection.

Convenient sample:

The criteria concerns patients and not place.

E.g. Males between 20 and 30 years old, with

moderate hypertension, diagnosed for the first time.

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Quota sample: Why and How

Quota Sampling

Quota sampling is a method of sampling widely used in

opinion polling and market research.

Interviewers are each given a quota of subjects of

specified type to attempt to recruit for example, an

interviewer might be told to go out and select 20 adult

men and 20 adult women, 10 teenage girls and 10

teenage boys so that they could interview them about

their television viewing.

It suffers from a number of methodological flaws, the

most basic of which is that the sample is not a random

sample and therefore the sampling distributions of

any statistics are unknown.

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Accidental sampling Accidental sampling (sometimes known as grab, convenience or opportunity sampling) is a type of

nonprobability sampling which involves the sample being drawn from that part of the population which is close to hand.

That is, a population is selected because it is readily available and convenient. It

may be through meeting the person or including a person in the sample when one meets them or chosen by finding them through technological means such as the internet or through phone. The researcher using such a sample cannot scientifically make generalizations about the total population from this sample because it would not be representative enough. For example, if the interviewer were to conduct such a survey at a shopping center early in the morning on a given day, the people that he/she could interview would be limited to those given there at that given time, which would not represent the views of other members of society in such an area, if the survey were to be conducted at different times of day and several times per week. This type of sampling is most useful for pilot testing. Several important considerations for researchers using convenience samples include: •Are there controls within the research design or experiment which can serve to lessen the impact of a non-random convenience sample, thereby ensuring the results will be more representative of the population?

•Is there good reason to believe that a particular convenience sample would or should respond or behave differently than a random sample from the same population?

•Is the question being asked by the research one that can adequately be answered using a convenience sample?

Snowball sampling

The sampling procedure in which the initial respondents are chosen by probability or non-probability methods, and then additional respondents are obtained by information provided by the initial respondents

Randomization

Clinical trials (Testing treatment modalities)

1. Inclusion criteria

2. Number of cases

3. Assign patient order to treatment

4. Card for each patient

5. Shuffle

6. Number cards

7. Put a card in closed envelop

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Sample size determinants

• Importance of study

• Number of variables

• Magnitude of problem

• More important

Larger size when

• Many variables,

with multiple levels

• Lower prevalence

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Sample size determinants

• Facilities available Time Money Personnel

• Expected implementation problems Refusal Availability

• Statistical analysis proposed Test Power Significance

Primary variable Type of analysis

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Simple formula for sample size calculation

2

ce)significan of (level2

estimate sample of difference

without) pwith n(proportioZ Number

Assume that you want to see if the disease is present among 2.5% of the

population or more.

You expect the prevalence of disease in sample lies between 1.5% to 3.5%

975 1

97.5%) (2.5% 2

2

2

Number

Professional Master's Degree in Health Economics 68

More Important Study

More power of the sample is needed.

2

2 ce)significan of (level

2

estimate sample of difference

without) pwith n(proportio Power Z Number

3900 1

97.5%) (2.5% 2 2

22

2

Number

Professional Master's Degree in Health Economics 69

Lower prevalence

400 3

90%) (10% 2

2

2

Number

144 5

90%) (10% 2

2

2

Number

Professional Master's Degree in Health Economics 70