Post on 15-Oct-2015
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An imal disease
surveys
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Veterinary surveys
Information may be obtained from:
Censuses
Sample surveys
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To gain information on:
Counts (e.g. prevalence)
Measurements (e.g. milk yield)
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Surveys of widespread relevance:
National picture of disease(e.g. lameness, mastitis)
National and regional control and
eradication campaigns(e.g. rinderpest)
Local (farm) eradication and controlcampaigns (e.g. enzootic abortion)
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Bias
Systematic(as opposed torandom)
departures from true values
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Veterinary surveys:
Definitions
Target population
Study population
Elementary units
Stratum
Sampling frame
Sampling unit(may, or may not, be elementary units)
Sampling fraction
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Types of sampling
1.Non-probability sampling:
2. Probability sampling:
- choice of investigator
- a deliberate unbiasedprocess
- each sampling unit has an equalprobability of selection
- basis of random sampling
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Non-probability sampling methods
Convenience sampling
Purposive selection
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Probability sampling methods
Simple random sampling
Systematic sampling
Stratified sampling
Cluster sampling
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Random sampling
Methods:1. Tables
2. Pocket calculators
3. Software
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Region Number of
cows
Number sampled
Devon and Cornwall 302 647 302 647 x 0.05 = 15 132SW England other than
Devon and Cornwall
469 486 469 486 x 0.05 = 23 474
S England 271 225 271 225 x 0.05 = 13 561
E England 119 835 119 835 x 0.05 = 5 992
East Midlands 189 817 189 817 x 0.05 = 9 491
West Midlands 462 826 462 826 x 0.05 = 23 141
Wales 342 346 342 346 x 0.05 = 17 117
Yorkshire/Lancashire 255 626 255 626 x 0.05 = 12 781
N England 273 838 273 838 x 0.05 = 13 692
Scotland 260 366 260 366 x 0.05 = 13 018
Totals 2 948 012 147 399
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50300 1020 40 km
A
B
C
PUNAKHA
WANGDI
BUMTHANG
LHUNTSHI
THIMPHU
PARDHA
PHODRANG TONSA
SAMCHI
CHHUKHA
DAGA
CHIRANGLEYLEGPRUG
SHEMGANG
MONGAR
TASHIGANG
SAMDRUP
JONGKHAR
PEMA-
GATSEL
Thimphu
A
B
C
PUNAKHA
WANGDI
BUMTHANG
LHUNTSHI
THIMPHU
PARDHA
PHODRANG TONSA
SAMCHI
CHHUKHA
DAGA
CHIRANGLEYLEGPRUG
SHEMGANG
MONGAR
TASHIGANG
SAMDRUP
JONGKHAR
PEMA-
GATSEL
Thimphu
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Cluster sampling
Used when:
1. Sampling frame is incomplete
2. Random sampling from all clusters is
impracticable
May be:
1. One-stage: sampleallanimals in
selected clusters2. Two-stage: sample someanimals in
selected clusters
{3. Multistage}
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Sample size determination
Estimation of disease prevalence
Detecting the presence of disease
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Sample size determination
Not a matter of guess-workor convenience
For proportions, depends on:
Expected proportion (P)
Precision of sample estimate (d)
Degree of confidence in estimate
(usually 95%)
Population size
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How many animals?
Simple random sampling
n=1.962 Pexp(1-Pexp)
d2
Where:
n = required sample size
Pexp = expected prevalence
d = desired absolute precision
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n = 1.962 0.30 (1-0.30)
0.052
Pexp = 0.30
d = 0.05
Example:
= 3.84 x 0.21
0.0025
= 323
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nadj = (Nx n) / (N+ n)
where N= population size
Finite correction
N = 900Example
nadj = (900 x 323) / (900 + 323)
= 238
S l i i d t tt i d i d fid
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Sample size required to attain desired confidenceinterval around expected percentage of 5%
Percenta e
6000
4000
2000
1000800
600
400
200
10080
60
40
20
0 5 10 15 20 25 30 35 40 45
95%
95%
99%
6000
4000
2000
1000800
600
400
200
10080
60
40
20
99%
Re
quiredsamplesize
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If an idea of estimated prevalence
is not available ( a common event!)
What do we do??
Assume 0.5 (50%)
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Detecting the presence of disease
(Certifying absence )
n= {1(1-p1)1/d} {N-d/2} + 1,
Where:
N = population size
d = number of affected animalsin the population
n = required sample size
p1 = probability of finding atleast one case in the sample
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Example: (Pan-African Rinderpest Campaign)
N = 200d = 10 (5% of 200)
N = {1- (1-0.95)1/10} {20010/2} + 1
p1 = 0.95
Assume at least 5% seroconvert in infected herds Set p1at 0.95
Apply to herd size 200
= {1- 0.051/10} x 195 + 1= {1- 0.74113} x 195 + 1
= 0.2589 x 195 + 1
= 50 + 1
= 51
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FMD serosurveillance
EU council directive 85/511/EC Probability 0.95
Flock prevalence: 2%
Within-flock prevalence: 5%
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Sampling frames
Dumfries & Galloway (+ Wigton):752 premises
Duns: 176 premises
Jedburgh: 129 premises
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Samples: premises (animals)
Dumfries & Galloway (+ Wigton):138 (18,040)
Duns: 102 (11,187)
Jedburgh: 91 (10,614)
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Calculation of confidence intervals:
Simple proportion
(e.g., simple random sampling)
1. Exact method (binomial)
2. Approximate methods:
Normal approximation
Poisson approximation(for rare diseases)
C fid i t l f l
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P* = Sample estimate
n = Number in sample
Thus:P* = 0.40
E.g., in a sample 100 animals, taken from a population of
10,000, 40 are diseased.
Normal approximation:for a 95% interval
Where:
95% c.i. = 0.401.96 (0.40 x 0.60 / 100)
Confidence intervals for prevalence:simple random samples
P*- 1.96P* (1-P*)
n, P*+ 1.96
P* (1-P*)n
to 0.40 + 1.96 (0.40 x 0.60 / 100)= (0.400.096), (0.40 + 0.096)= 0.304, 0.496
30.4% - 49.6%
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Finite correction:
If the sampling fraction, f, is large (say,
>10%):
The numerator, P* (1-P*), should be
multiplied by (1-f)
E.g., if a sample of 100 animals is drawn
from a population of total size 500, thenf= 0.20, and (1-f ) = 0.80
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Multipliers used in construction of
common confidence intervals, based
on the Normal distribution
Confidence
interval
80% 90% 95% 99% 99.9%
Multiplier 1.282 1.645 1.960 2.576 3.291
Confidence intervals for
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If P* = estimated prevalence
andn = sample size
1. P 0.05
Formula should only be used when:
Restriction on asymptotic method:
and
Confidence intervals forsimple random samples:
2. nPand n(1-P) 5
If these conditions do not apply, use the exactbinomial method:
1. from tables
2. with appropriate software, e.g., WINPEPI
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Calculation of confidence intervals
Systematic sampling
If no periodicity:use simple proportion formula
Stratified samplingFor proportional allocation:
use simple proportion formula
Cluster sampling complex!!Formula for simple proportion will produce
too narrowa confidence interval
(i t i )