Surveys Sample Size

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Surveys Sample Size
By R. Heberto Ghezzo Ph.D. Meakins-Christie
laboratories McGill University - Montreal -
Canada
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Objective of the Study
Estimation
Prevalence
Odds- Ratio Relative Risk if Cohort
Comparison
Prevalence
Odds-ratios Relative Risk if Cohort
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Estimation

• Confidence level
  - 90 95 99
• Acceptable width of interval - 1 , 5
  , 10 , 20

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Comparison

• Error type 1 - alpha
  - 0.05 0.01
• Smallest difference worth detecting - delta
• Error type 2 - beta
  - 0.10 0.05 0.01

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Error type 1 - alpha
Error in claiming a difference when there is none.
Alpha percent of normal people are thus
classified into abnormal
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Error type 2 - beta
Error of not finding a difference when the
difference is greater than the threshold or value
of delta. Depends on the definition of the
threshold i.e. the difference worth detecting,
delta .
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Which size?
In surveys the errors are generally the
same i.e. alpha beta The level depends on the
importance of the issue. Critical studies use
beta0.01
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Estimation of a Prevalence
n z21-a/2 p(1 - p) / d2
n z21-a/2 (1 - p) / e2 p
a error type 1 - alpha
d absolute width of conf.interval
e relative width of conf.interval
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Estimation of an Odds-Ratio
n z21-a/2 1/p1(1-p1) 1/p2(1-p2) / ln2(1-e)
a error type 1 - alpha
e relative width of conf.interval
p1 proportion exposed in cases
p2 proportion exposed in controls.
OR p1(1-p2)/(1-p1)p2
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Estimation of a Relative Risk
n z21-a/2 (1-p1)/p1 (1-p2)/p2 / ln2(1-e)
a error type 1 - alpha
e relative width of conf.interval
p1 proportion exposed in cases
p2 proportion exposed in controls.
RR p1/p2
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Comparing 2 prevalence
n z1-a/2 2p(1-p) z1-b
p1(1-p1)p2(1-p2)2/(p1-p2)2
If p lt 0.05
N (z1-a/2 z1-b)2 / 0.00061(arcsin
p2 - arcsin p1)2
b beta 1-Power
p (p1 p2)/2
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Testing Odds Ratio gt 1.0
n z1-a/2 2p2(1-p2) z1-b
p1(1-p1)p2(1-p2)2/(p1-p2)2
p1 prevalence of exposure in cases
p2 prevalence of exposure in controls
b beta 1-Power
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Total Sample Size
If design is stratified and tests/estimations
will be done at each strata. The sample size
applies to each strata.
Otherwise all within strata comparisons or
estimations will have larger errors or confidence
intervals.
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True Size I
These formulae are theoretical. No real variable
is truly normal. The estimator of variability has
its own variability. There is no
guarantee that the precision postulated will
be achieved.
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True Size II
The estimator of variability comes from a
different study. If the variability of the
proposed study is larger the precision will
deteriorate. Always use a beta error smaller
than really needed and adjust the sample size
upwards to a round number.
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Non Response
The sample size refers to the number of complete
responses needed. Non response must be estimated
and taken into account to arrive to the final
size
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Imputation
To impute is to fake a value that does not
exist
Only to complete observations for a multivariate
technique