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![Page 1: Sampling and Sample Size Calculation Sources: -EPIET Introductory course, Thomas Grein, Denis Coulombier, Philippe Sudre, Mike Catchpole, Denise Antona.](https://reader034.fdocuments.in/reader034/viewer/2022051515/55152899550346a80c8b65c6/html5/thumbnails/1.jpg)
Sampling and Sample Size Calculation
Sources: -EPIET Introductory course, Thomas Grein, Denis Coulombier, Philippe Sudre, Mike Catchpole, Denise Antona-IDEA Brigitte Helynck, Philippe Malfait, Institut de veille sanitaire
Modified: Viviane Bremer, EPIET 2004, Suzanne Cotter 2005,Richard Pebody 2006
Lazereto de Mahón, Menorca, Spain
September 2006
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Objectives: sampling
• To understand:• Why we use sampling • Definitions in sampling • Sampling errors • Main methods of sampling• Sample size calculation
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Why do we use sampling?
Get information from large populations with:
– Reduced costs
– Reduced field time
– Increased accuracy
– Enhanced methods
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Definition of sampling
Procedure by which some members
of a given population are selected as representatives of the entire population
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Definition of sampling terms
Sampling unit (element)• Subject under observation on which
information is collected– Example: children <5 years, hospital discharges,
health events…
Sampling fraction• Ratio between sample size and population
size– Example: 100 out of 2000 (5%)
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Definition of sampling terms
Sampling frame • List of all the sampling units from which
sample is drawn– Lists: e.g. children < 5 years of age, households,
health care units…
Sampling scheme• Method of selecting sampling units from
sampling frame– Randomly, convenience sample…
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Survey errors
• Systematic error (or bias)
Sample not typical of population
– Inaccurate response (information bias)
– Selection bias
• Sampling error (random error)
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Representativeness (validity)
A sample should accurately reflect distribution ofrelevant variable in population
• Person e.g. age, sex• Place e.g. urban vs. rural• Time e.g. seasonality
Representativeness essential to generalise
Ensure representativeness before starting,
Confirm once completed
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Sampling and representativeness
Sample
Target Population
SamplingPopulation
Target Population Sampling Population Sample
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Sampling error
• Random difference between sample and population from which sample drawn
• Size of error can be measured in probability samples
• Expressed as “standard error”– of mean, proportion…
• Standard error (or precision) depends upon:– Size of the sample – Distribution of character of interest in population
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Sampling error
When simple random sample of size ‘n’ is selected from population of size N, standard error (s) for population mean or proportion is:
σ p(1-p)
n n
Used to calculate, 95% confidence intervals
xxsXsZX 2or 2
Estimated 95% confidence interval
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Quality of a sampling estimate
Precision & validity
No precision
Random error
Precision butno validity
Systematicerror (bias)
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Survey errors: example
Measuring height:• Measuring tape held differently by different
investigators
→ loss of precision – Large standard error
• Tape shrunk/wrong
→ systematic error– Bias (cannot be corrected afterwards)
179
177
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Types of sampling
• Non-probability samples
• Probability samples
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Non probability samples
• Convenience samples (ease of access)
• Snowball sampling (friend of friend….etc.)
• Purposive sampling (judgemental)• You chose who you think should be in the study
Probability of being chosen is unknownCheaper- but unable to generalise, potential for bias
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Probability samples
• Random sampling– Each subject has a known probability of being
selected
• Allows application of statistical sampling theory to results to: – Generalise – Test hypotheses
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Methods used in probability samples
• Simple random sampling• Systematic sampling• Stratified sampling• Multi-stage sampling • Cluster sampling
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Simple random sampling
• Principle– Equal chance/probability of drawing each unit
• Procedure– Take sampling population– Need listing of all sampling units (“sampling frame”)– Number all units– Randomly draw units
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Simple random sampling
• Advantages– Simple– Sampling error easily measured
• Disadvantages– Need complete list of units– Does not always achieve best representativeness– Units may be scattered and poorly accessible
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Example: evaluate the prevalence of tooth decay among 1200 children attending a school
• List of children attending the school• Children numerated from 1 to 1200• Sample size = 100 children• Random sampling of 100 numbers between 1
and 1200
How to randomly select?
Simple random sampling
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EPITABLE: random number listing
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EPITABLE: random number listing
Also possible in Excel
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Simple random sampling
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Systematic sampling
• Principle– Select sample at regular intervals based on sampling
fraction
• Advantages– Simple– Sampling error easily measured
• Disadvantages– Need complete list of units– Periodicity
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Systematic sampling
• N = 1200, and n = 60 sampling fraction = 1200/60 = 20
• List persons from 1 to 1200
• Randomly select a number between 1 and 20 (ex : 8)
1st person selected = the 8th on the list 2nd person = 8 + 20 = the 28th etc .....
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Systematic sampling
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Stratified sampling
• Principle :– Divide sampling frame into homogeneous
subgroups (strata) e.g. age-group, occupation;
– Draw random sample in each strata.
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Stratified sampling
• Advantages– Can acquire information about whole population and
individual strata– Precision increased if variability within strata is less
(homogenous) than between strata
• Disadvantages– Can be difficult to identify strata
– Loss of precision if small numbers in individual strata • resolve by sampling proportionate to stratum population
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Multiple stage sampling
Principle:
• consecutive sampling
• example : sampling unit = household– 1st stage: draw neighborhoods – 2nd stage: draw buildings– 3rd stage: draw households
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Cluster sampling
• Principle– Sample units not identified independently but in a
group (or “cluster”)
– Provides logistical advantage.
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Cluster sampling
• Principle– Whole population divided into groups e.g.
neighbourhoods
– Random sample taken of these groups (“clusters”)
– Within selected clusters, all units e.g. households included (or random sample of these units)
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Example: Cluster sampling
Section 4
Section 5
Section 3
Section 2Section 1
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Cluster sampling
• Advantages– Simple as complete list of sampling units within
population not required
– Less travel/resources required
• Disadvantages– Potential problem is that cluster members are more
likely to be alike, than those in another cluster
(homogenous)….
– This “dependence” needs to be taken into account in the
sample size….and the analysis (“design effect”)
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Selecting a sampling method
• Population to be studied– Size/geographical distribution– Heterogeneity with respect to variable
• Availability of list of sampling units• Level of precision required• Resources available
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Sample size estimation
• Estimate number needed to
• reliably measure factor of interest
• detect significant association
• Trade-off between study size and resources….
• Sample size determined by various factors:
• significance level (“alpha”)
• power (“1-beta”)
• expected prevalence of factor of interest
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Type 1 error
• The probability of finding a difference with our sample compared to population, and there really isn’t one….
• Known as the α (or “type 1 error”)
• Usually set at 5% (or 0.05)
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Type 2 error
• The probability of not finding a difference that actually exists between our sample compared to the population…
• Known as the β (or “type 2 error”)
• Power is (1- β) and is usually 80%
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A question?
Are the English more intelligent than the Dutch?
• H0 Null hypothesis: The English and Dutch have the same mean IQ
• Ha Alternative hypothesis: The mean IQ of the English is greater than the Dutch
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Type 1 and 2 errors
Truth
Decision H0 true H0 false
Reject H0 Type I error Correct decision
Accept H0 Correct Type II error
decision
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Power
• The easiest ways to increase power are to:– increase sample size
– increase desired difference (or effect size)
– decrease significance level desired e.g. 10%
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Steps in estimating sample size for descriptive survey
• Identify major study variable• Determine type of estimate (%, mean, ratio,...) • Indicate expected frequency of factor of interest• Decide on desired precision of the estimate • Decide on acceptable risk that estimate will fall outside
its real population value• Adjust for estimated design effect• Adjust for expected response rate
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Sample size fordescriptive survey
z: alpha risk expressed in z-score
p: expected prevalence
q: 1 - p
d: absolute precision
g: design effect
z² * p * q 1.96²*0.15*0.85n = -------------- ---------------------- = 544
d² 0.03²
Cluster sampling
z² * p * q 2*1.96²*0.15*0.85n = g* -------------- ------------------------ = 1088d² 0.03²
Simple random / systematic sampling
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Case-control sample size: issues to consider
• Number of cases• Number of controls per case • Odds ratio worth detecting• Proportion of exposed persons in source
population• Desired level of significance (α) • Power of the study (1-β)
– to detect at a statistically significant level a particular odds ratio
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Case-control:STATCALC Sample size
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Case-control: STATCALC Sample size
Risk of alpha error 5%
Power 80%
Proportion of controls exposed 20%
OR to detect > 2
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Case-control:STATCALC Sample size
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Statistical Power of aCase-Control Study
for different control-to-case ratios and odds ratios (with 50 cases)
0
0.2
0.4
0.6
0.8
1
1 2 3 4 5 6 7 8 9 10
Control-Case Ratio
Po
wer OR=2
OR=4
OR=3
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Conclusions
• Probability samples are the best
• Ensure – Representativeness– Precision
• …..within available constraints
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Conclusions
• If in doubt…
Call a statistician !!!!