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What is a sample?
Epidemiology matters: a new introduction to methodological foundationsChapter 4
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Epidemiology Matters – Chapter 1 2
Seven steps
1. Define the population of interest2. Conceptualize and create measures of exposures and health
indicators3. Take a sample of the population4. Estimate measures of association between exposures and health
indicators of interest5. Rigorously evaluate whether the association observed suggests a
causal association6. Assess the evidence for causes working together7. Assess the extent to which the result matters, is externally valid, to
other populations
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Epidemiology Matters – Chapter 4 3
1. Why take a sample?
2. How to take a representative sample
3. Quantifying sampling variability
4. How to take a purposive sample
5. Study design
6. Summary
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Epidemiology Matters – Chapter 4 4
1. Why take a sample?
2. How to take a representative sample
3. Quantifying sampling variability
4. How to take a purposive sample
5. Study design
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Epidemiology Matters – Chapter 4 5
Why take a sample?
Epidemiologists take samples to answer health-related research questions efficiently
A full census is the epidemiologic ideal Reasons not to take a census all the time include lack
of time, lack of money, and waste of resources
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Epidemiology Matters – Chapter 4 6
To take a sample
1. Specify population of interest2. Specify a research question of interest
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Epidemiology Matters – Chapter 4 7
Specify population of interest
What are the characteristics of the population in which we would like to understand health? Example: Do we want to know what the
prevalence of diabetes is within New York City? New York State? The United States? Do we want to know the causes of diabetes?
The population of interest has to be specified before the sampling strategy defined
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Epidemiology Matters – Chapter 4 8
Specifying a question
Question of interest can help clarify appropriate way to sample population of interest
Questions asked can include estimating population parameters, or estimating causal effects of exposures on outcomes
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Example, estimating population parametersQuestions concerned with population parameters include
What proportion of individuals in the population of interest has breast cancer?
What is the mean blood pressure in the population? How many new cases of HIV are diagnosed in the population
over three years?Population parameters include estimates of
Proportions Means Standard deviations
Sample required Representative sample
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Example, estimating causal effects of exposures on outcomes
Questions for which these measures are needed are Does exposure to pollution cause lung cancer? Does suffering abuse in childhood cause depression in
adulthood? Does a specific genetic marker cause Alzheimer’s disease?
Parameter of interest Causal effect of an exposure on a health outcome
Sampling concerns Not representativeness (as in population parameters) Whether individuals exposed to hypothesized cause of interest
are comparable to individuals not exposed Purposive sample sufficient
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Epidemiology Matters – Chapter 4 11
Representative and purposive A representative sample is one where the sample
that is taken has characteristics similar to the overall population
A purposive sample selects from the population base on some criterion
A representative sample may or may not include individuals who are comparable with respect to causal identification
A purposive sample may or may not be representative of a particular population of interest
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Epidemiology Matters – Chapter 4 12
1. Why take a sample?
2. How to take a representative sample
3. Quantifying sampling variability
4. How to take a purposive sample
5. Study design
6. Summary
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Epidemiology Matters – Chapter 4 13
How to take a representative sample
The simplest approach: a simple random sample
Each member of the population has an equal probability of being selected into the sample
A successful simple random sample should have the same basic characteristics as the original population
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Epidemiology Matters – Chapter 4 14
Taking a simple random sample
1. Enumerate all potential members of population of interest
2. Assign each member a probability of selection 3. Ensure selection of members are independent
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Epidemiology Matters – Chapter 4 15
Example: Sampling Farrlandia
30 residents in FarrlandiaOptions for random selection:
--Every 4th home, dice roll for selection within home
Challenges include (a) clustered exposures, (b) unequal ‘home’ sizeSelected for sample
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Epidemiology Matters – Chapter 4 16
Example: Sampling Farrlandia
30 residents in FarrlandiaSelect every Nth person in phone bookChallenges include that not everyone is in phone book
Selected for sample
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Epidemiology Matters – Chapter 4 17
There is no perfect sample The goal in epidemiology is to understand
limitations of sampling methods and account for them
The perfect sample?
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Epidemiology Matters – Chapter 4 18
Sampling Farrlandia
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Epidemiology Matters – Chapter 4 19
Sampling Farrlandia
We want to collect our sample in such a way that the sample also has 50% exposed and 30% dotted.
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Epidemiology Matters – Chapter 4 20
Sampling Farrlandia
We can use a simple random sample ½ the population (25) Probability of selection 1/50 or 2% Random number generator
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Epidemiology Matters – Chapter 4 21
Sampling Farrlandia
Original PopulationBlack solid 15 30%
Black dots 10 20%
Total black 25 50%
Gray solid 20 40%
Gray dots 5 10%
Total gray 25 50%
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Epidemiology Matters – Chapter 4 22
Sampling Farrlandia
Original Population Sample
Black solid 15 30%
Black dots 10 20%
Total black 25 50%
Gray solid 20 40%
Gray dots 5 10%
Total gray 25 50%
Black solid 8 32%
Black dots 5 20%
Total black 13 52%
Gray solid 10 40%
Gray dots 2 8%
Total gray 12 48%
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Epidemiology Matters – Chapter 4 23
1. Why take a sample?
2. How to take a representative sample
3. Quantifying sampling variability
4. How to take a purposive sample
5. Study design
6. Summary
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Epidemiology Matters – Chapter 4 24
Quantifying sampling variability
Sampled population will not have the exact same population parameters as complete population census
The ‘truth’, i.e., the population parameter of original population is called the true population parameter
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Epidemiology Matters – Chapter 4 25
Variations in possible samples
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Epidemiology Matters – Chapter 4 26
Variations in possible samples
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Epidemiology Matters – Chapter 4 27
Variations in possible samples
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Epidemiology Matters – Chapter 4 28
38,760 different possible samples of 5
Variations in possible samples
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Epidemiology Matters – Chapter 4 29
Quantifying uncertainty, Central Limit Theorem (CLT)
1. Average proportion across all possible samples = true population proportion Example:
50% of true population has diabetes Sample 1 has 100% diabetes Sample 2 has 0% diabetes Average of all samples will have 50% diabetes
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Epidemiology Matters – Chapter 4 30
Quantifying uncertainty, CLT
2. Variance around average sample proportions (standard error)
p = sample proportionn = sample size
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Epidemiology Matters – Chapter 4 31
Quantifying uncertainty, CLT
3. Large samples will have normally distributed samples > 30 people No group < 5 people
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Epidemiology Matters – Chapter 4 32
Quantifying uncertainty, CLT
Therefore the principal drivers of uncertainty are1. Prevalence in the sample2. Sample sizeThe larger the sample size, the smaller the amount of uncertainty in the sample estimate
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Epidemiology Matters – Chapter 4 33
1. Why take a sample?
2. How to take a representative sample
3. Quantifying sampling variability
4. How to take a purposive sample
5. Study design
6. Summary
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Epidemiology Matters – Chapter 4 34
Purposive sample
Eligibility criteria for study is the central design element; entry is based on exposure status, or sometimes on health outcome status
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Epidemiology Matters – Chapter 4 35
1. Why take a sample?
2. How to take a representative sample
3. Quantifying sampling variability
4. How to take a purposive sample
5. Study design
6. Summary
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Epidemiology Matters – Chapter 4 36
Study design
Study design considerations are similar for representative or purposive sample
Study design reflects decisions made at one time point or over time
Timing of disease process can inform the study design
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Epidemiology Matters – Chapter 4 37
Study design options
1. Sample one moment in time, irrespective of disease status, measure disease and potential cause simultaneously
2. Sample over time, start with disease free individuals only, measure disease over time
3. Sample one moment in time, based on disease status
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Epidemiology Matters – Chapter 4 38
Farrlandia population
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Epidemiology Matters – Chapter 4 39
Farrlandia population
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Epidemiology Matters – Chapter 4 40
Farrlandia population
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Epidemiology Matters – Chapter 4 41
Farrlandia population
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Epidemiology Matters – Chapter 4 42
Farrlandia population
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Epidemiology Matters – Chapter 4 43
Farrlandia population
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Epidemiology Matters – Chapter 4 44
Farrlandia population
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Epidemiology Matters – Chapter 4 45
Farrlandia population
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Epidemiology Matters – Chapter 4 46
Farrlandia population
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Epidemiology Matters – Chapter 4 47
Option 1, Cross-sectional
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Epidemiology Matters – Chapter 4 48
Option 2, Cohort
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Epidemiology Matters – Chapter 4 49
Option 3, Case-control
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Epidemiology Matters – Chapter 4 50
1. Why take a sample?
2. How to take a representative sample
3. Quantifying sampling variability
4. How to take a purposive sample
5. Study design
6. Summary
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Epidemiology Matters – Chapter 4 51
Summary
1. Samples are efficient, representative or purposive
2. Representative sample; e.g., simple random sample
3. Sampling variability, standard error
4. Purposive sample, selection on exposure or disease status
5. Study designs can be cross-sectional, cohort, case-control
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Epidemiology Matters – Chapter 1 52
Seven steps
1. Define the population of interest2. Conceptualize and create measures of exposures and health
indicators3. Take a sample of the population4. Estimate measures of association between exposures and health
indicators of interest5. Rigorously evaluate whether the association observed suggests a
causal association6. Assess the evidence for causes working together7. Assess the extent to which the result matters, is externally valid, to
other populations
![Page 53: What is a sample?](https://reader035.vdocument.in/reader035/viewer/2022062811/568161e3550346895dd1fcda/html5/thumbnails/53.jpg)
Epidemiology Matters – Chapter 1 53
epidemiologymatters.org