Transcript Surveys Sample Size R. Heberto Ghezzo Ph.D. Meakins-Christie laboratories

Surveys Sample Size
By
R. Heberto Ghezzo Ph.D.
Meakins-Christie laboratories
McGill University - Montreal - Canada
Objective of the Study
Estimation
Prevalence
Odds- Ratio [Relative Risk if Cohort]
Comparison
Prevalence
Odds-ratios [Relative Risk if Cohort]
Estimation
• Confidence level
- 90 %; 95 %; 99 %
• Acceptable width of interval
- 1 %, 5 %, 10 %, 20 %
Comparison
• Error type 1 - alpha
- 0.05 ; 0.01
• Smallest difference worth detecting
- delta
• Error type 2 - beta
- 0.10 ; 0.05 ; 0.01
Error type 1 - alpha
Error in claiming a difference when
there is none.
Alpha percent of normal people are
thus classified into “abnormal”
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 .
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 beta=0.01
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
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
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
Comparing 2 prevalence
n = {z1-a/2 2p(1-p) +
z1-b p1(1-p1)+p2(1-p2)}2/(p1-p2)2
If p < 0.05
N = (z1-a/2 + z1-b)2 /
[0.00061(arcsin p2 - arcsin p1)2]
p = (p1 + p2)/2
b = beta = 1-Power
Testing Odds Ratio > 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
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.
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.
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.
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
Imputation
To impute is to fake a value
that does not exist
Only to complete observations for
a multivariate technique